1.
If x, y and z are three consecutive odd integers such that 10< x < y < z< 20 and if y and z are prime numbers, what is the value of x + y?
Correct Answer
D. 32
Explanation
Option A is not correct her rate is not equal to 1 test per hour.
Option B is not correct as she can complete ab tests in 1 hour.
Option C is correct. Alda completes the tests at the rate of a tests/(1/b) hours = ab tests/hour. Hence in n hours she can complete nab tests.
Option D is not correct as she completes a tests in 1/b hours.
Option E is also not correct.
2.
If p > 0, which of the following is equal to √48p^{3}
Correct Answer
A. 4p√3p
Explanation
Option A is correct: √48p^3 = √16 x 3 x p x p x p = 4p√3p
Option B is incorrect: (3p√4p)^2 = 9p^2 X 4p = 36p^3
Option C is incorrect: (2√12p)^2 4 x 12p = 48p
Option D is incorrect: (3√8p)^2 = 9 x 8p = 72p
Option E is incorrect: (16p√3p)^2 = 256p x 3p = 768p^3
Option C is incorrect: (16p√3p)^2 = 256p^2 X 3p = 768p^3
3.
If 40% of x is equal to 30% of y, what % is x of y?
Correct Answer
B. 75%
Explanation
As other percents given are not equal to the calculated percentage, B is the correct option.
40x/100 = 30y/100, hence x/y 100% = 3/4 100% = 75%
4.
If 4(3x - 3) = 24, what is 5x - 5?
Correct Answer
A. 10
Explanation
To find the value of 5x - 5, we need to first solve the given equation. Distributing the 4 to the terms inside the parentheses, we get 12x - 12 = 24. Adding 12 to both sides of the equation, we get 12x = 36. Dividing both sides by 12, we find that x = 3. Plugging this value into 5x - 5, we get 5(3) - 5 = 15 - 5 = 10. Therefore, the correct answer is 10.
5.
The average of 11 numbers is 21 . The average of seven of those numbers is 25. What is the average of the remaining four numbers?
Correct Answer
C. 14
Explanation
Since the average of the 11 numbers is 21, the sum of all 11 numbers is 11 * 21 = 231. The sum of the seven numbers with an average of 25 is 7 * 25 = 175. To find the sum of the remaining four numbers, we subtract the sum of the seven numbers from the sum of all 11 numbers: 231 - 175 = 56. Finally, we divide the sum of the remaining four numbers by 4 (the number of remaining numbers) to find the average: 56 / 4 = 14. Therefore, the average of the remaining four numbers is 14.
6.
Which of the following is equivalent to 6x ^{2} + x - 12 ?
Correct Answer
A. (2x + 3)(3x - 4)
Explanation
The given expression is a quadratic trinomial. To find the equivalent expression, we need to factorize the quadratic trinomial. The correct answer, (2x + 3)(3x - 4), is the factored form of the given expression.
7.
Correct Answer
C. 72
Explanation
The given sequence is a combination of two patterns: the numbers are alternately multiplied by 2 and divided by 2. Starting with 81, the next number is obtained by dividing 81 by 2, resulting in 40. Then, 40 is multiplied by 2 to get 80. Continuing this pattern, the next number is obtained by dividing 80 by 2, resulting in 40. Therefore, the answer is 72, which is obtained by dividing 144 by 2.
8.
If 2 dots are equal to 3 dashes and 5 dashes equal to 7 stars, what is the ratio of one dot to one star?
Correct Answer
D. 21 ⁄ 10
Explanation
If 2 dots are equal to 3 dashes and 5 dashes are equal to 7 stars, we can set up the following ratios: 2 dots : 3 dashes and 5 dashes : 7 stars. To find the ratio of one dot to one star, we can combine the two ratios by multiplying them together: (2 dots/3 dashes) * (5 dashes/7 stars). Simplifying this expression gives us 10 dots : 21 stars, which can be written as the ratio 10/21. Therefore, the correct answer is 10/21.
9.
A social welfare organization spends 40% of the funds collected towards old-age homes. If during an year 1.6 million dollars was spent on old-age homes, what is the total amount of funds collected in millions of dollars?
Correct Answer
A. 4.0
Explanation
Option A is correct.
Let the total fund = n million dollars
40% of n = 1.6 million dollars
Or 0.4n = 1.6 million dollars
Or n = 1.6/0.4 million dollars = 4 million dollars
Hence 40% of 4 is 1.6
B is not correct, as 40% of 6 is 2.4 and not 1.6
C is not correct, as 40% of 4.6 is 1.84 and not 1.6
D is not correct, as 40% of 40 is 16 and not 1.6
E is not correct, as 40% of 1.6 is 0.64 and not 1.6
10.
In the given figure,
Note: Figure not drawn to scale.
Correct Answer
C. 100 degrees
Explanation
As other angle measures are not equal to the calculated measure of ∠ABC, only
option C is correct.
Exterlor angle of a tr|angle |s equal to the sum of its two interior opposite angles.
∠ABD = ∠BDC - ∠BAD = 60° - 30° = 30°
∠CBD = ∠BCE - ∠BDC = 130° - 60° = 70°
∠ABC = ∠ABD + ∠CBD = 30° + 70° = 100°
11.
Solve for x:
Correct Answer
E. -12 < x < 13
Explanation
-5 ≤ (2x - 1)/ 5 ≤ 5 => -25 ≤ 2x -1 ≤ 25
Or- 24 ≤ 2x ≤ 26
Or -12 ≤ x ≤ 13
12.
A car travels a distance of 250 miles, 700 miles and 325 miles at the rate of 50 miles/hr, 35 miles/hr and 13 miles/hr respectively.Find the average speed of the car in miles/hr.
Correct Answer
B. 25.5
Explanation
As other speeds given are not equal to the calculated average speed only option B is correct.
Speed = distance traveled/time taken
Total distance traveled = (250 +700 + 325) mile = 1275 miles
Time = distance/speed
Total time = (250/50 + 700/35 + 325/13) hrs = (5 + 20 + 25) hrs = 50 hrs
Average speed of the car = 1275/50 miles / hr = 25.5 miles/hr
13.
By which of the following number is 98765432 exactly divisible?
Correct Answer
D. 8
Explanation
Option A is not correct is not correct. 98765432 is not divisible by 9 as the sum of its digits 44 is not divisible by 9.
Option B is not correct as 98765432 is not divisible by 7.
Option C is not correct as the last digit of 98765432 is not 5, hence 98765432 is not divisible by 5.
Option D is correct. Using the tests of divisibility, we know that a number is divisible by 8 if its last three digits are divisible by 8. The last three digits of the given number 432 is divisible by 8.
Option E is not correct. As the difference of the sum of digits in its even and odd places {(9 + 7 + 5 + 3) - (8 + 6 + 4 + 2)} 4 is not a multiple of 11, 98765432 is not divisible by 11.
14.
In a class of 30 students, 14 take tea and 20 take coffee. How many take both tea and coffee?
Correct Answer
E. 4
Explanation
Number of students in the class = n(T∪C) = 30
Number of students who take tea = n(T) = 14
Number of students who take coffee = n(C) =20
Number of students who take both tea and coffee = n(T∩C)
n(T∩C) = n(T) + n(C) - n(T∪C)
=14 + 20 - 30 = 34 - 30 = 4
15.
In the given figure, area of square ABED is 9 square units, BC = 5 units, EF = 1 unit. Find the area of the rectangle BCGF.
Correct Answer
D. 20 square units
Explanation
As other areas given are not equal to the calculated area, only option D is correct.
Area of square ABED = 9 square units or side of square ABDE
BE = side of square ABED = 3 units
EF = 1 unit.
Width of the rectangle BCGF= BF = BE + EF
= 3 units + 1 unit = 4 units
Length of the rectangle BCGF= BC = 5 units
Area of the rectangle BCGF = 1 * w
= 5 * 4 square units
= 20 square units
16.
If y^{2} = c, where y and c are integers, which of the following could be the value of c?
Correct Answer
C. 64
Explanation
Option A is not correct. y2 = c implies that c must be a perfect square. But 45 is not a perfect square.
Option B is not correct y2 = c implies that c must be a perfect square. But 17 is not a perfect square.
Option C is correct. y2 = c implies that c must be a perfect square. 64 is a perfect square.
Option D is not correct y2 = c implies that c must be a perfect square. But 34 is not a perfect square.
Option E is not correct. y2 = c implies that c must be a perfect square. But 10 is not a perfect square.
17.
In a store
Correct Answer
C. 150
Explanation
As other answers are not equal to the calculated answers, only option C is correct. 1$ = 100 cents and 1 pound = 16 ounces.
Price/weight = 12/45 dollars/pounds = 1200/ (45*16) cents/ounces
= n/9 cents/ounces
Or 1200 * 9 = 4.5 * 16 * n
or n = 1200 * 9/72 = 150 cents
18.
Each month for 6 months the price of a commodity is doubled. At the end of the 6 months the price of the commodity is $640. What was the price of the commodity at the end of 3 months?
Correct Answer
C. $80
Explanation
The price of the commodity is doubled each month for 6 months. Therefore, if the price at the end of 6 months is $640, then the price at the end of 3 months would be half of that. Half of $640 is $320, so the correct answer is $320.
19.
Alda can complete a test in
.
Correct Answer
C. Nab
Explanation
The correct answer is "nab" because it is the only option that makes sense in the given context. The other options are either incomplete or do not form a coherent word. Therefore, "nab" is the most logical and appropriate answer.
20.
An operation * is defined as follows: For any two positive numbers x and y,
Correct Answer
D. 7 * 4
Explanation
In the given question, the operation * is defined as the product of two positive numbers. The expression "7 * 4" means multiplying 7 and 4 together. Therefore, the correct answer is 28.
21.
If x^{2}y > 0 and xy^{2} < 0,then which of the following are true?
Correct Answer
D. D. x < 0 and y > 0
Explanation
Option A cannot be chosen, if x = 0 then both the inequalities given will be zero which is not true.
Option B be cannot be chosen, if y = 0 then both the inequalities given will be zero which is not true.
Option C cannot be chosen, if x > 0 and y < 0, then x2y will be less than 0 as the product of a positive number and a negative number will be negative. Similarly xy2 will be positive, which is not true.
Option D is correct. If x2y n> 0, then x2 is anyway positive, hence y must also be positive so that the product is positive. If xy2 < 0, then y2 is anyway positive, hence x must be negative so that the product is negative. Hence x < 0 and y > 0.
Option E cannot be correct. If both x and y are positive, then only x2y > 0 will be true and xy2 will be false.
22.
In the given figure, EB is perpendicular to FC, and AD and EB intersect at point F. What is the value of
Note: Figure not drawn to scale.
Correct Answer
A. A. 50 degrees
Explanation
Option A is correct, as ∠CFD+∠BFC+ ∠AFB lie on the same line AD.
Hence their sum must be 180°
∠CFD, ∠BFC and ∠AFB = 180°
∠CFD + 90° + 40° = 180° (angle on a line) Or ∠CFD = 180° - 130° = 50°
Option B is not correct as 40°+90°+40°≠180°
Option C is not correct as 100°+90°+40°≠180°
Option D is not correct as 90°+90°+40°≠180°
Option E is not correct as the single angle CFD itself is 180°
23.
At what point will 12x^{2} + 5x + 1 attain the minimum value?
Correct Answer
B. B. -5 ⁄ 24
Explanation
Option A is not correct as –b/2a ≠ 5/24
Only option B is correct, as the other values given do not satisfy
The given condition for point of minimum value, that is –b/2a
Option C is not correct as –b/2a ≠ 5/8
Option D is not correct as –b/2a ≠ 24/5
Option E is not correct as –b/2a ≠ 8/15
24.
If x and y are multiples of 3, which of the following CANNOT also be a multiple of 3?
Correct Answer
C. C. x + y + 1
Explanation
Option A is not correct. Sum of two multiples of 3 is also a multiple of 3. Example: 6 and 9 are multiples of 3, their sum 15 is also a multiple of 3.
Option B is not correct. Difference of two multiples of 3 is also a multiple of 3. Example: 15 and 9 are multiples of 3, their difference 6 is also a multiple of 3.
Only option C is correct. Sum of two multiples of 3 increased by 1 is not a multiple of 3. Example: 6 and 9 are multiples of 3, their sum 15 increase by 1 that is 16 is not a multiple of 3.
Option D is not correct. Product of two multiples of 3 is also a multiple of 3. Example: 6 and 12 are multiples of 3, their product 72 is also a multiple of 3.
Option E is not correct. Product of two multiples of 3 increased by 3 is also a multiple of 3. Example: 6 and 12 are multiples of 3, their product 72 increased by 3 that is 75 is also a multiple of 3.
25.
How many positive integers less than 80 are equal to the product of a positive multiple of 5 and an even number?
Correct Answer
E. E. 7
Explanation
Only option E is correct as there are only 7 numbers which satisfy the given condition in the question that is all positive integers less than 80 which are equal to the product of 5 and an even number.
5 x 2 = 10, 5 x 4 = 20, 5 x 6 = 30, 5 x 8 = 40, 5 x 10 = 50,
5 x 12 = 60,
5 x 14 = 70, hence the required numbers are 10, 20, 30,40,50,60 and 70
26.
Find the equation of the line through (2, 3) perpendicular to 4x - 3y=10.
Correct Answer
D. D. 3x + 4y = 18
Explanation
Only option D is correct as the other equations do not satisfy the given conditions
of the equation of a line through (2, 3) and perpendicular to 4x-3y=10
Equation of a line perpendicular to the given line is
3x+4y+z=0 or 3*2+*3+z=0 or 18+z=0 or z=-18. Therefore, the equation of the
required line is 3x+4y-18=0 or 3x+4y=18
27.
A wire bent in the form of a circle of radius 21units is cut and bent to form a square. What is the ratio of area of circle to that of the square?
Correct Answer
E. E. 14:11
Explanation
Only option E is correct as the other ratios given do not satisfy the relation
Radius = 21units
Circumference = 2πr = 2 * 22/7 *21 units = 132 units
Circumference of the circle = perimeter of the square or
4a = 132 units or a = 33 units
Therefore, side of the square is 33 units
Area of circle: Area of square = πr2:a^2
= 22/7 *21*21: 33*33
=14:11
28.
If a function f(x) is defined by
Correct Answer
B. B. x
Explanation
Option A is not correct as f(3x+3 / x-1) ≠ x+1
Option B is correct as
f(3x+3 / x-1) = (3x+3 / x-1 + 3) / (3x+3 / x-1 - 3)
= (3x+3+3x-3) / (3x+3-3x+3)
= 6x/6 = x
Option C is not correct as f(3x+3 / x-1) ≠ x-1
Option D is not correct as f(3x+3 / x-1) ≠ x+3
Option D is not correct as f(3x+3 / x-1) ≠ x-3
29.
A jar contains 10 red marbles and 30 green ones. How many red marbles must be added to the jar so that 60% of the marbles will be red?
Correct Answer
C. C. 35
Explanation
Number of red marbles in the jar = 10+x
Total number of marbles in the jar = 10+x+30 = 40+x
According to the problem,
10+x/40+x = 10(10+x) = 6(40 + x)
Or 100 + 10x = 240 + 6x or 4x =140 or x = 35
Hence, 35 red marbles must be added to the jar.
30.
A shopkeeper has three kinds of rice of 77 pounds, 147 pounds and 252 pounds. Find the least number of bags of equal size required to pack them without mixing.
Correct Answer
A. A. 68
Explanation
Capacity of each bag = HCF of 77, 147 and 252 = 7 pounds.
Total number of bags required = 77/7 + 147/7 + 252/7
11 + 21 + 36 = 68
31.
A cube and a rectangular solid are equal in volume. If the lengths of the edges of the rectangular solid are 4, 8 and 16, what is the surface area of the cube?
Correct Answer
E. E. 384
Explanation
Volume of rectangular solid = volume of cube.
Or l * w * h = s3 or 4 * 8 * 16 = s3 or s3 = 512
Or s = 8 Surface area of the cube = 6s2 = 6 * 8 * 8 = 384
32.
Twenty persons, among whom A and B, sit at random around a round table. Find the probability that there are any 6 persons between A and B.
Correct Answer
B. B. 2/19
Explanation
Let A occupy any seat around the table. Then there are 19 seats available for B. But if there are to be six persons between A and B, then B has only two ways to sit.
Thus, the required probability is 2/19
33.
In the given figure, AB is parallel to CD.
Correct Answer
D. D. 91
Explanation
Draw a line XY through O parallel to either AB or CD.
Then the figure will look like as given below.
C N D
X O Y
A M B
As all the three lines in figure are parallel, we have the following relations:
∠CNO = ∠NOY = 55 degrees (interior alternative angles)
∠AMO = ∠MON = ∠MOV + ∠NOY
= 55 degrees + 36 degrees = 91 degrees
34.
The flowers in a basket become double after every minute. In one hour, the basket becomes full. After how many minutes the basket would be half filled?
Correct Answer
A. A. 59
Explanation
The basket was half filled after 59 minutes.
If there were half the number of flowers in the basket after 59 minutes, then the basket would be full in the next minute, as the flowers double after every minute.
35.
In the given figure,
Correct Answer
E. E. 130
Explanation
Let 0 be the center of the circle, then ∠QOR is the angle subtended by the arc QR
The angle subtended by an arc at the center of a circle is double the angle subtended
by the same arc on the remaining part of the circle
Therefore, ∠QOR = 2 * 65 degrees = 130 degrees
36.
A person had 72 mangoes, he had given them to three persons A, B and C, in such a manner that A got thrice as many as B, and the sum total of mangoes A and B got was 60. He had given the remaining mangoes to C. Express in decimal the fraction of mangoes C got out of the total.
Correct Answer
E. E. 0.167
Explanation
Sometimes in some problems, some extra information is given, which is not required to solve the problem. Here, it is clear that the number of mangoes C got is 12.
Total 72 mangoes minus 60 mangoes given to A and B. Hence, Fraction of mangoes C got out of the total number of mangoes
= 12/72 = 1/6 = 0.16666. , this can be rounded to 0.167
37.
What will be the value of x, if 8^{x+2} = 2^{4x-3}?
Correct Answer
D. D. 9
Explanation
8;x+2 = 24x-3, (23)x+2= 24x-3, 23x+6= 24x-3
As the bases are same, the powers can be equated. Hence
3x+6 = 4x-3 or - x = - 9 Or x = 9
38.
A monkey climbs a slippery pole by thrusts. The pole is 30 feet high. With every thrust, it goes up 5 feet in 5 seconds and slips down 3 feet in 1 second. How many seconds will it take to climb the pole?
Correct Answer
B. B. 82
Explanation
Distance climbed by the monkey in 6 seconds
= 5 feet - 3 feet = 2 feet
In 6 seconds it climbs 2 feet. It climbs 26 feet in 78 seconds and the remaining 4 feet in 4 seconds. So the total time is 82 seconds.