Mini GMAT Quant. Test - 10 Questions
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A student’s average (arithmetic mean) test score on 4 tests is 78. What must be the student’s score on a 5th test for the student’s average score on the 5 tests to be 80?
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80
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82
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84
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86
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88
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This Mini GMAT Quant. Test comprises 10 questions focusing on probability, algebra, and arithmetic. It assesses critical thinking and problem-solving skills, essential for business school aspirants preparing for the GMAT.
Quiz Preview
- 2.
Lines m and n intersect, as shown in the figure above. What is the value of u - w? (1) u = 90 (2) Lines m and n are perpendicular.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. EACH statement ALONE is sufficient.Explanation
From statement (1), we know that u = 90. Since u is one of the angles formed by the intersection of lines m and n, we can conclude that u is a right angle. Therefore, w must be the complementary angle to u, which means w = 90. Therefore, u - w = 90 - 90 = 0.
From statement (2), we know that lines m and n are perpendicular. This means that the angles formed by their intersection must be right angles. Therefore, u is a right angle and w is a right angle. Again, u - w = 90 - 90 = 0.
In both cases, we can determine that u - w = 0, so each statement alone is sufficient to answer the question.Rate this question:
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- 3.
What is the total value of Company H&rsquos stock? (1) Investor P owns of the shares of Company H&rsquos total stock. (2) The total value of Investor Q&rsquos shares of Company H&rsquos stock is $16000.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
The total value of Company H's stock cannot be determined based on the given statements alone. Statement (1) only provides information about the ownership of the shares by Investor P, but it does not give any information about the total value of the stock. Statement (2) only provides information about the total value of Investor Q's shares, but it does not give any information about the total value of the stock or the ownership of other investors. Therefore, both statements together are not sufficient to determine the total value of Company H's stock.Rate this question:
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- 4.
If the length of a certain rectangle is 2 greater than the width of the rectangle, what is the perimeter of the rectangle? (1) The length of each diagonal of the rectangle is 10. (2) The area of the rectangular region is 48.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. EACH statement ALONE is sufficient.Explanation
Statement (1) alone is sufficient to find the perimeter of the rectangle. If the length of each diagonal is 10, we can use the Pythagorean theorem to find the relationship between the length and width of the rectangle. Since the length is 2 greater than the width, we can set up the equation x^2 + (x+2)^2 = 10^2, where x is the width. Solving this equation will give us the width, and we can then calculate the perimeter using the formula P = 2(length + width). Therefore, statement (1) alone is sufficient to find the perimeter.Rate this question:
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- 5.
If x and y are integers, is x + y greater than 0? (1) x is greater than 0. (2) y is less than 1.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
-
Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
From statement (1), we know that x is greater than 0. However, this does not provide any information about the value of y. Therefore, statement (1) alone is not sufficient to determine whether x + y is greater than 0.
From statement (2), we know that y is less than 1. However, this does not provide any information about the value of x. Therefore, statement (2) alone is not sufficient to determine whether x + y is greater than 0.
Combining both statements, we still do not have enough information to determine whether x + y is greater than 0. Therefore, both statements together are not sufficient.Rate this question:
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- 6.
On a map Town G is 10 centimeters due east of Town H and 8 centimeters due south of Town J. Which of the following is closest to the straight-line distance, in centimeters, between Town H and Town J on the map?
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6
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13
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18
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20
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24
Correct Answer
A. 13Explanation
Town G is located 10 centimeters due east of Town H and 8 centimeters due south of Town J. To find the straight-line distance between Town H and Town J, we can draw a right-angled triangle with Town G as the right angle. The distance between Town H and Town J can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the straight-line distance) is equal to the sum of the squares of the other two sides. In this case, the distance between Town H and Town J is the hypotenuse, and the distances due east and due south from Town G are the other two sides. Using the Pythagorean theorem, we can calculate that the straight-line distance between Town H and Town J is closest to 13 centimeters.Rate this question:
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- 7.
A glass was filled with 10 ounces of water, and 0.01 ounce of the water evaporated each day during a twenty-day period. What percent of the original amount of water evaporated during this period?
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0.002%
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0.02%
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0.2%
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2%
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20%
Correct Answer
A. 2%Explanation
During the twenty-day period, 0.01 ounce of water evaporated each day. To find the total amount of water evaporated, we multiply 0.01 ounce by 20 days, which equals 0.2 ounces. To find the percentage, we divide the amount evaporated (0.2 ounces) by the original amount of water (10 ounces) and multiply by 100. This gives us a percentage of 2%.Rate this question:
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- 8.
At a garage sale, all of the prices of the items sold were different. If the price of a radio sold at the garage sale was both the 15th highest price and the 20th lowest price among the prices of the items sold, how many items were sold at the garage sale?
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33
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34
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35
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36
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37
Correct Answer
A. 34 -
- 9.
If and which of the following is NOT a possible value of ?
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-2
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-1
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0
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1
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2
Correct Answer
A. 1Explanation
The possible values of x are -2, -1, 0, and 2. Therefore, the value 1 is not a possible value for x.Rate this question:
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- 10.
If S is a set of ten consecutive integers, is the integer 5 in S? (1) The integer –3 is in S. (2) The integer 4 is in S.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
From statement (1), we know that the integer -3 is in S. Since S is a set of ten consecutive integers, we can determine that the lowest integer in S is -3 and the highest integer in S is 6. However, we still don't have enough information to determine if the integer 5 is in S.
From statement (2), we know that the integer 4 is in S. This gives us some information about the range of S, but it still doesn't tell us if the integer 5 is in S.
By combining both statements, we know that the lowest integer in S is -3 and the highest integer in S is 6, and that the integer 4 is in S. However, we still don't have enough information to determine if the integer 5 is in S. Therefore, both statements together are not sufficient to answer the question.Rate this question:
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- 11.
A farm used two harvesting machines, H and K, to harvest 100 acres of wheat. Harvesting machine H, working alone at its constant rate, harvested 40 acres of wheat in 8 hours. Then harvesting machine K was brought in, and harvesting machines H and K, working together at their respective contant rates, harvested the remaining acres of wheat in 5 hours. Harvesting machine K harvested how many acres of wheat per hour? (1) Working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water. (2) Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank with water.
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7
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8
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12
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13
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15
Correct Answer
A. 7 -
- 12.
In how many different ways can a chairperson and a secretary be selected from a committee of 9 people?
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24
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36
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72
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80
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120
Correct Answer
A. 72Explanation
In order to select a chairperson and a secretary from a committee of 9 people, we need to consider the order in which they are selected. The chairperson can be selected in 9 different ways (as there are 9 people to choose from), and once the chairperson is selected, the secretary can be selected in 8 different ways (as there are now only 8 people left to choose from). Therefore, the total number of ways to select a chairperson and a secretary is 9 * 8 = 72.Rate this question:
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- 13.
If x is equal to the sum of the even integers from 40 to 60, inclusive, and y is the number of even integers from 40 to 60, inclusive, what is the value of x+y ?
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550
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551
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560
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561
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572
Correct Answer
A. 561Explanation
The value of x is equal to the sum of the even integers from 40 to 60, inclusive. The even integers in this range are 40, 42, 44, 46, 48, 50, 52, 54, 56, and 60. Adding these numbers together gives us a total of 502.
The value of y is the number of even integers from 40 to 60, inclusive. Counting these numbers gives us a total of 11 even integers.
To find the value of x+y, we simply add 502 and 11 together, which equals 513. Therefore, the correct answer is 513.Rate this question:
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- 14.
Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?
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8
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10
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12
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15
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20
Correct Answer
A. 20Explanation
If R, S, and T can complete the job together in 4 hours, it means that their combined rate is 1/4 of the job per hour. If S and T can complete the job together in 5 hours, their combined rate is 1/5 of the job per hour. Subtracting the combined rate of S and T from the combined rate of R, S, and T gives the rate of R alone, which is 1/4 - 1/5 = 1/20 of the job per hour. Therefore, it would take R 20 hours to complete the job alone.Rate this question:
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- 15.
Lines k and m are parallel to each other. Is the slope of line k positive? (1) Line k passes through the point (3, 2). (2) Line m passes through the point (-3, 2).
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
The slope of a line can be determined by comparing the y-coordinates of two points on the line and the x-coordinates of the same two points. In this case, neither statement alone provides enough information to determine the slope of line k. Statement (1) only provides the coordinates of one point on line k, while statement (2) only provides the coordinates of one point on line m. Therefore, both statements together are still not sufficient to determine the slope of line k.Rate this question:
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- 16.
In a poll involving two yes- or no-questions, all the people who were asked the two questions answered “yes” or “no”. If 75 percent of these people answered “yes” to the first question, 55 percent of the people answered “yes” to the second question, and 20 percent of the people answered “no” to both questions, what percentage of the people answered “yes” to both questions?
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70%
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50%
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25%
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20%
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10%
Correct Answer
A. 50% -
- 17.
Two different pipes fill the same pool. Pipe A fills of the capacity of the pool in 3 hours while pipe B fills of it in 6 hours. If the two pipes fill the pool simultaneously with their respective rates how long will it take for the pool to be filled to capacity?
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3 hours
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3 hours 20 minutes
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3 hours 36 minutes
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4 hours 20 minutes
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4 hours 30 minutes
Correct Answer
A. 3 hours 36 minutesExplanation
Pipe A fills the pool in 3 hours, which means it fills 1/3 of the pool's capacity per hour. Pipe B fills the pool in 6 hours, which means it fills 1/6 of the pool's capacity per hour. When both pipes are filling the pool simultaneously, their combined rate is 1/3 + 1/6 = 1/2 of the pool's capacity per hour. Therefore, it will take 2 hours for the pool to be filled to half of its capacity. Since the question asks for the pool to be filled to full capacity, it will take twice as long, which is 2 x 2 = 4 hours. Additionally, 1/2 hour is equal to 30 minutes, so the total time is 4 hours + 30 minutes = 4 hours 30 minutes.Rate this question:
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- 18.
If the symbol ▼ represents either addition, subtraction, multiplication, or division, what is the value of 6 ▼ 2? (1) 10 ▼ 5 = 2 (2) 4 ▼ 2 = 2
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Explanation
From statement (1), we know that 10 ▼ 5 = 2. However, we don't know the specific operation represented by ▼. Therefore, we cannot determine the value of 6 ▼ 2 based on statement (1) alone.
From statement (2), we know that 4 ▼ 2 = 2. Again, we don't know the specific operation represented by ▼. Therefore, we cannot determine the value of 6 ▼ 2 based on statement (2) alone.
When we consider both statements together, we still don't have enough information to determine the specific operation represented by ▼. Therefore, the value of 6 ▼ 2 cannot be determined.
Hence, statement (1) alone is sufficient, but statement (2) alone is not sufficient.Rate this question:
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- 19.
Three thousand families live in a certain town. How many families who live in the town own neither a car nor a television set? (1) Of the families who live in the town, 2,980 own a car. (2) Of the families who live in the town, 2,970 own both a car and a television set.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient. -
- 20.
Working independently at their respective constant rates, pumps X and Y took 48 minutes to fill an empty tank with water. What fraction of the water in the full tank came from pump X? (1) Working alone at its constant rate, pump X would have taken 80 minutes to fill the tank with water. (2) Working alone at its constant rate, pump Y would have taken 120 minutes to fill the tank with water.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. EACH statement ALONE is sufficient.Explanation
Statement (1) alone is sufficient to answer the question. Since pump X would have taken 80 minutes to fill the tank alone, and it took 48 minutes for both pumps to fill the tank, it means that pump Y took 48 - 80 = -32 minutes to fill the tank alone. This is not possible, so pump Y did not contribute any water to the tank. Therefore, all the water in the tank came from pump X.Rate this question:
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- 21.
A certain candy manufacturer reduced the weight of candy bar M by 20 percent but left the price unchanged. What was the resulting percent increase in the price per ounce of the candy bar M?
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5%
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10%
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15%
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20%
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25%
Correct Answer
A. 25%Explanation
When the weight of candy bar M is reduced by 20 percent but the price remains unchanged, the price per ounce of the candy bar increases. To find the resulting percent increase in price per ounce, we can use the formula: (New price per ounce - Original price per ounce) / Original price per ounce * 100. Since the price remains unchanged, the new price per ounce is the same as the original price per ounce. Therefore, the resulting percent increase in the price per ounce is 25%.Rate this question:
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- 22.
In the figure above, O is the center of the circle. If the area of the shaded region is 2π, what is the value of x?
Correct Answer
A.Explanation
To find the value of x, we need to determine the length of the arc of the shaded region. Since the area of the shaded region is given as 2π, we can use the formula for the area of a sector of a circle (A = (θ/360) * π * r^2) to find the angle of the sector. The area of the sector is equal to the area of the shaded region plus the area of the triangle formed by the radii of the sector. By subtracting the area of the triangle from the total area of the sector, we can find the area of the shaded region. Setting this equal to 2π, we can solve for the angle of the sector, which is equal to x.Rate this question:
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- 23.
If 5x – 5x - 3 = (124)(5y), what is y in terms of x?
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X
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X - 6
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- 3/620 of x
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2x + 3
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2x + 6
Correct Answer
A. - 3/620 of x -
- 24.
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?
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0.008
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0.128
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0.488
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0.512
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0.640
Correct Answer
A. 0.128Explanation
The probability of Malachi returning home at the end of the first day it rains is 0.2. Since it is given that Malachi will return home at the end of the first day it rains, the probability of it raining on the first day is 0.2. Therefore, the probability of it not raining on the first day is 1 - 0.2 = 0.8. Since it is not specified when the camping vacation starts, we assume it starts on Saturday. Therefore, the probability of it not raining on Saturday, Sunday, and Monday is (0.8)^3 = 0.512. Therefore, the probability of Malachi returning home at the end of the day on Monday is 0.512 * 0.2 = 0.1024, which is approximately 0.128.Rate this question:
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- 25.
Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. What percent of the families in City X owned a personal computer in 1998?
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50%
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52%
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56%
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70%
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74%
Correct Answer
A. 50%Explanation
In 1994, 40% of the families in City X owned a personal computer. In 1998, the number of families owning a computer increased by 30% compared to 1994. Additionally, the total number of families in City X increased by 4% in 1998 compared to 1994. Therefore, the percentage of families owning a personal computer in 1998 can be calculated by adding the 30% increase to the initial 40% ownership rate. This gives us a total of 70% ownership. However, since the total number of families also increased by 4%, the percentage of families owning a personal computer in 1998 will be slightly less than 70%. The closest option is 50%, which is the correct answer.Rate this question:
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- 26.
Each of the numbers w x y and z is equal to either 0 or 1. What is the value of (1) (2)
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. EACH statement ALONE is sufficient.Explanation
Since each of the numbers w, x, y, and z can only be either 0 or 1, the value of w & x & y & z will be 0 if any of the variables is 0, and it will be 1 only if all the variables are 1. Therefore, knowing the value of any one variable (either from statement 1 or statement 2) is sufficient to determine the value of w & x & y & z. Hence, each statement alone is sufficient.Rate this question:
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- 27.
70, 75, 80, 85, 90, 105, 105, 130,130,130 The list shown consists of the times, in seconds, that it took each of 10 students to run a distance of 400 meters. If the standard deviation of the 10 running times is 22.4 sec, rounded to nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
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One
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Two
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Three
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Four
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Five
Correct Answer
A. TwoExplanation
The mean of the 10 running times can be calculated by summing all the times and dividing by 10. The standard deviation is a measure of how spread out the data is from the mean. If a value is more than 1 standard deviation below the mean, it means that it is significantly lower than the average. In this case, since the standard deviation is 22.4 sec, any running time that is more than 22.4 sec below the mean would be considered more than 1 standard deviation below. Looking at the list, there are two running times that meet this criteria, which are 70 sec and 75 sec. Therefore, the answer is Two.Rate this question:
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- 28.
The operation ○ is defined by the equation = where y &ne -x. If then =
Correct Answer
A. -
- 29.
In the xy-plane line l and line k intersect at the point . What is the slope of line l? (1) The product of the slopes of line l and line k is &ndash1. (2) Line k passes through the origin.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Explanation
The slope of line l can be determined by using both statements together. Statement (1) tells us that the product of the slopes of line l and line k is -1. This means that the slopes of the two lines are negative reciprocals of each other. Statement (2) tells us that line k passes through the origin. Since line k passes through the origin, its y-intercept is 0, which means its slope is also 0. Therefore, the slope of line l can be determined by finding the negative reciprocal of 0, which is undefined. Thus, both statements together are sufficient to determine the slope of line l.Rate this question:
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- 30.
Joshua and Jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers will be randomly chosen to be interviewd. What is the probability that Joshua and Jose both will be chosen?
Correct Answer
A.Explanation
The probability that Joshua will be chosen is 1/6, since there are 2 workers out of 6 who will be chosen. The probability that Jose will be chosen is 1/5, since there will be 1 worker out of 5 left to be chosen after Joshua is chosen. Therefore, the probability that both Joshua and Jose will be chosen is (1/6) * (1/5) = 1/30.Rate this question:
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- 31.
Which of the following is equal to ?
Correct Answer
A. -
- 32.
The figure above shows two entries, indicated by m and n, in an addition table. What is the value of n + m? (1) d + y = -3 (2) e + z = 12
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Explanation
From statement (1), we know that d + y = -3. However, this does not provide any information about the values of m and n.
From statement (2), we know that e + z = 12. Similarly, this does not provide any information about the values of m and n.
However, when we combine both statements, we can solve for the values of m and n. Since both equations involve different variables, we cannot directly solve for m and n. Therefore, BOTH statements TOGETHER are sufficient to determine the value of n + m.Rate this question:
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- 33.
In the figure shown what is the area of the circular region with center O and diameter BC? (1) (2)
-
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
-
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
-
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
-
Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. -
- 34.
If and are integers is ? (1) (2)
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
-
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
-
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
-
EACH statement ALONE is sufficient.
-
Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Explanation
The answer is both statements together are sufficient but neither statement alone is sufficient. This means that both statements provide enough information to answer the question, but each statement on its own does not provide enough information.Rate this question:
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- 35.
If r, s, and t are positive integers, is r + s + t even? (1) r + s is even. (2) s + t is even.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
-
Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
The given question asks whether the sum of three positive integers, r + s + t, is even.
Statement (1) tells us that r + s is even. However, this does not provide any information about the parity of t. It is possible that t is odd, which would make the sum r + s + t odd. Therefore, statement (1) alone is not sufficient to determine whether r + s + t is even.
Statement (2) tells us that s + t is even. However, this does not provide any information about the parity of r. It is possible that r is odd, which would make the sum r + s + t odd. Therefore, statement (2) alone is not sufficient to determine whether r + s + t is even.
When we consider both statements together, we still do not have enough information to determine the parity of r + s + t. It is possible that r is odd and t is even, or vice versa, which would make the sum r + s + t odd. Therefore, statements (1) and (2) together are not sufficient to determine whether r + s + t is even.
Hence, the correct answer is that statements (1) and (2) together are not sufficient.Rate this question:
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- 36.
In the parallelogram shown, what is the value of x? (1) y = 2x (2) x + z = 120
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. EACH statement ALONE is sufficient.Explanation
From statement (1), we know that y = 2x. Since opposite angles in a parallelogram are equal, we can conclude that y = x. Therefore, statement (1) alone is sufficient to determine the value of x. We do not need statement (2) to find the value of x. Hence, the correct answer is that EACH statement ALONE is sufficient.Rate this question:
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- 37.
In the xy-plane, line k passes through the point (1,1) and line m passes through the point (1,-1).Are the lines k and m perpendicular to each other? (1) Lines k and m intersect at the point (1,-1). (2) Line k intersects the x axis at the point (1,0).
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
The given statements are not sufficient to determine whether lines k and m are perpendicular to each other. Statement (1) tells us that the lines intersect at a certain point, but it does not provide any information about their slopes or angles. Statement (2) tells us that line k intersects the x-axis at a certain point, but it does not provide any information about the slope or angle of line m. Therefore, without additional information, we cannot determine whether the lines are perpendicular.Rate this question:
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- 38.
In the figure shown the length of line segment QS is . What is the perimeter of equilateral triangle PQR ?
Correct Answer
A. -
- 39.
One day Hotel Merinda rented 75 percent of its rooms, including of its luxury rooms. If 60 percent of Hotel Merinda’s rooms are luxury rooms, what percent of the rooms that were NOT rented are luxury rooms?
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80%
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40%
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30%
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33.33%
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10%
Correct Answer
A. 80%Explanation
Since 60% of the hotel's rooms are luxury rooms, it means that 40% of the rooms are not luxury rooms.
If 75% of the hotel's rooms were rented, it means that 25% of the rooms were not rented.
Out of those 25% of rooms that were not rented, 40% of them are luxury rooms.
Therefore, the percentage of the rooms that were not rented and are luxury rooms is 40% of 25%, which is equal to 10%.
However, the question is asking for the percentage of the rooms that were not rented and are luxury rooms, so we need to find the complement of 10%, which is 100% - 10% = 90%.
Therefore, the correct answer is 90%.Rate this question:
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- 40.
If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2i3k5m7p, then i + k + m + p =
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4
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7
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8
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11
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12
Correct Answer
A. 7Explanation
To find i, k, m, and p in the equation x = 2^i * 3^k * 5^m * 7^p, we can break down the prime factorization of x, which is the product of the positive integers from 1 to 8, inclusive.
x = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8
Now, let's find the prime factorization of x:
x = 2^3 * 3^2 * 5^1 * 7^1
So, we can see that i = 3, k = 2, m = 1, and p = 1.
To find i + k + m + p:
i + k + m + p = 3 + 2 + 1 + 1 = 7
So, i + k + m + p is equal to 7.Rate this question:
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- 41.
What is the remainder when the positive integer n is divided by 3? (1) The remainder when n is divided by 2 is 1. (2) The remainder when n + 1 is divided by 3 is 2.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.Explanation
From statement (1), we know that the remainder when n is divided by 2 is 1. This means that n is an odd number. However, we don't have any information about the remainder when n is divided by 3 from this statement.
From statement (2), we know that the remainder when n + 1 is divided by 3 is 2. This means that (n + 1) is 2 more than a multiple of 3. Simplifying this, we get n is 1 less than a multiple of 3. In other words, n is 2 more than a multiple of 3. This means that the remainder when n is divided by 3 is 2.
Therefore, statement (2) alone is sufficient to determine the remainder when n is divided by 3, but statement (1) alone is not sufficient.Rate this question:
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- 42.
The mass of 1 cubic meter of a substance is 800 kilograms under certain conditions. What is the volume, in cubic centimeters of 1 gram of this substance under these condition (1 kilogram= 1000 grams and 1 cubic meter = 1,000,000 cubic centimeters.
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0.80
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1.25
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8.00
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12.50
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80.00
Correct Answer
A. 1.25Explanation
The mass of 1 cubic meter of the substance is 800 kilograms. To find the volume of 1 gram of the substance, we need to convert the mass from kilograms to grams and the volume from cubic meters to cubic centimeters. Since 1 kilogram is equal to 1000 grams and 1 cubic meter is equal to 1,000,000 cubic centimeters, we can calculate the volume as follows:
Volume = (1 gram / 800 kilograms) * (1,000,000 cubic centimeters / 1 cubic meter) = 1,250 cubic centimeters. Therefore, the volume of 1 gram of the substance under these conditions is 1.25 cubic centimeters.Rate this question:
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- 43.
In a survey of 200 college graduates, 30 percent said they had received student loans during their college careers, and 40 percent said they had received scholarships. What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers? (1) 25 percent of those surveyed said that they had received scholarships but no loans. (2) 50 percent of those surveyed who said that they had received loans also said that they had received scholarships.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. EACH statement ALONE is sufficient.Explanation
Statement (1) alone is sufficient to determine the percent of those surveyed who said they had received neither student loans nor scholarships. It states that 25 percent of those surveyed said they had received scholarships but no loans. Since 30 percent said they had received student loans and 40 percent said they had received scholarships, we can subtract these percentages from 100 to find the percentage of those who received neither. Therefore, the percent of those surveyed who said they received neither student loans nor scholarships is 100 - 30 - 40 - 25 = 5 percent.
Similarly, statement (2) alone is also sufficient to determine the percent of those surveyed who said they had received neither student loans nor scholarships. It states that 50 percent of those surveyed who said they had received loans also said they had received scholarships. Since 30 percent said they had received student loans, we can subtract this percentage from 100 to find the percentage of those who received neither. Therefore, the percent of those surveyed who said they received neither student loans nor scholarships is 100 - 30 = 70 percent.
Hence, each statement alone is sufficient to determine the percent of those surveyed who said they had received neither student loans nor scholarships.Rate this question:
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- 44.
The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?
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72
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74
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75
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78
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80
Correct Answer
A. 74Explanation
The given sequence follows a pattern where each term is equal to the term four places before it. By examining the first few terms of the sequence, we can see that it repeats every four terms: 2, -3, 5, -1, 2, -3, 5, -1, ... Therefore, we can group the terms into sets of four: (2, -3, 5, -1), (2, -3, 5, -1), ... The sum of each set of four terms is 3, so we can calculate the number of sets in 97 terms by dividing 97 by 4, which gives us 24 with a remainder of 1. Therefore, the sum of the first 97 terms is 24 * 3 + 2 = 74.Rate this question:
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- 45.
In parallelogram PQRS shown, if PQ = 4 and QR = 6, what is the area of PQRS?
Correct Answer
A.Explanation
To find the area of a parallelogram, we need to multiply the base by the height. In this case, the base is PQ and the height is QR. Therefore, the area of PQRS is 4 * 6 = 24.Rate this question:
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- 46.
What is the value of │x + 7│? (1) │x + 3│= 14 (2) (x + 2)2 = 169
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Explanation
Statement (1) gives the absolute value of (x + 3) as 14. This means that (x + 3) can either be 14 or -14. Therefore, x can be either 11 or -17. However, this does not give us the value of │x + 7│ directly.
Statement (2) gives us (x + 2)² = 169. Taking the square root of both sides, we get x + 2 = ±13. This means that x can be either 11 or -15. However, this also does not give us the value of │x + 7│ directly.
By combining both statements, we can narrow down the possible values of x to 11. Therefore, we can determine that the value of │x + 7│ is 18.Rate this question:
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- 47.
What is the sum of a certain pair of consecutive odd integers? (1) At least one of the integers is negative. (2) At least one of the integers is positive.
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Explanation
Statement (1) tells us that at least one of the integers is negative. This means that the sum of the consecutive odd integers could be negative, depending on the specific values of the integers. Therefore, statement (1) alone is not sufficient to determine the sum of the integers.
Statement (2) tells us that at least one of the integers is positive. This means that the sum of the consecutive odd integers could be positive, depending on the specific values of the integers. Therefore, statement (2) alone is not sufficient to determine the sum of the integers.
However, when we consider both statements together, we know that one integer is negative and one integer is positive, which means their sum will always be an odd number. Therefore, both statements together are sufficient to determine the sum of the integers.Rate this question:
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- 48.
If x and y are integers and x > 0, is y > 0? (1) 7x – 2y > 0 (2) -y < x
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statements (1) and (2) TOGETHER are NOT sufficient.Explanation
To determine if y is greater than 0, we need to analyze both statements together.
From statement (1), we have 7x - 2y > 0. This means that 7x > 2y. However, we do not have any information about the relation between x and y, so we cannot determine if y is greater than 0 based on this statement alone.
From statement (2), we have -y < x. This means that y > -x. Again, we do not have enough information to determine if y is greater than 0 based on this statement alone.
Since neither statement alone provides enough information, and we need both statements together to determine if y is greater than 0, the correct answer is that statements (1) and (2) together are not sufficient.Rate this question:
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- 49.
If what is the value of ? (1) (2)
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Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
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BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
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EACH statement ALONE is sufficient.
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Statements (1) and (2) TOGETHER are NOT sufficient.
Correct Answer
A. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. -
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