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 solve the equation 4(3x - 3) = 24, we first distribute the 4 to the terms inside the parentheses: 12x - 12 = 24. Then, we isolate the variable by adding 12 to both sides of the equation: 12x = 36. Finally, we solve for x by dividing both sides of the equation by 12: x = 3.
To find 5x - 5, we substitute the value of x into the equation: 5(3) - 5 = 15 - 5 = 10. Therefore, the 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
The average of the 11 numbers is given as 21. This means that the sum of all the 11 numbers is 11 multiplied by 21, which is 231. The average of the seven numbers is given as 25, which means the sum of those seven numbers is 7 multiplied by 25, which is 175. To find the sum of the remaining four numbers, we subtract the sum of the seven numbers (175) from the sum of all 11 numbers (231). This gives us 56 as the sum of the remaining four numbers. To find the average of these four numbers, we divide the sum (56) by the count (4), which gives us an average of 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 6x^2 + x - 12. The correct answer, (2x + 3)(3x - 4), can be obtained by using the distributive property to multiply the two binomials. When we multiply (2x + 3) with (3x - 4), we get 6x^2 - 8x + 9x - 12, which simplifies to 6x^2 + x - 12. Therefore, (2x + 3)(3x - 4) is equivalent to the given expression.
7.
Correct Answer
C. 72
Explanation
The given sequence of numbers is 81, 40, 72, 9, 18. If we observe closely, we can see that each number is obtained by multiplying the previous number by a certain factor. In this case, the factor is 0.5. Starting with 81, we multiply it by 0.5 to get 40.5, which is rounded down to 40. Then, we multiply 40 by 0.5 to get 20, and so on. Therefore, the next number in the sequence would be obtained by multiplying 18 by 0.5, giving us 9. Finally, multiplying 9 by 0.5 gives us 4.5, which is rounded up to 5. However, since 5 is not given as an option, the correct answer is 72, which breaks the pattern and does not follow the multiplying factor.
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
According to the given information, 2 dots are equal to 3 dashes and 5 dashes are equal to 7 stars. To find the ratio of one dot to one star, we need to find a common factor between dots and stars. We can do this by finding a common factor between dots and dashes, and then between dashes and stars. The common factor between dots and dashes is 3, and the common factor between dashes and stars is 5. Therefore, the ratio of one dot to one star is 3/5. Simplifying this ratio gives us 21/10.
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 doubles each month for 6 months, so we can find the original price by dividing the final price by 2 raised to the power of the number of months (6). $640 divided by 2 raised to the power of 6 is $640 divided by 64, which equals $10. Therefore, the price of the commodity at the end of 3 months would be $10 divided by 2 raised to the power of 3 (since 3 months is half of 6 months), which equals $10 divided by 8, or $1.25. However, none of the given options match this calculation, so the correct answer cannot be determined.
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 "n", "ab", "nab", "a", and "b" do not form a coherent sentence or phrase. Therefore, "nab" is the most logical choice as it is the only combination of letters that could potentially have a meaning or be a word.
20.
An operation * is defined as follows: For any two positive numbers x and y,
Correct Answer
D. 7 * 4
Explanation
The operation * is defined as the product of two positive numbers. In this case, the answer is 7 * 4, which equals 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.
39.
He was treated like a(n) ____ and cast out from his community.
Correct Answer
D. Pariah
Explanation
Clue: He was cast out. An outcast is a pariah.
(ascetic = one who lives a severe existence without indulgences; prodigy = genius, or very talented; prodigal = wasteful person; tyro = novice, beginner)
40.
The teacher accused me of ____ because my essay was so similar to that of another student.
Correct Answer
B. Plagiarism
Explanation
Clue: ‘because’ gives a reason for the word that is needed. If the essay is so similar it looks as though it is copied. To copy without giving acknowledgment is plagiarism.(procrastination = putting off, delaying; celerity = speed; decorum = good and correct behavior)
41.
We live in a ____ age; everyone thinks that maximizing pleasure is the point of life.
Correct Answer
E. Hedonistic
Explanation
Clue: The part after the semicolon explains what kind of age we are talking about.
So, since we are told that maximizing pleasure is the point, the word we need is hedonistic (pleasure seeking).
(ubiquitous = found everywhere; propitious = favorable; sporadic = intermittent, not continuous)
42.
Thankfully the disease has gone into ____ ; it may not recur for many years.
Correct Answer
D. Remission
Explanation
Clue: The part after the semicolon explains the first part of the sentence.
So, something that may not recur for some time would be in remission.
(sequestration = isolation; quarantine = isolation; remission = temporary improvement in a disease; oblivion = state of being unaware)
43.
People from all over the world are sent by their doctors to breathe the pure, ____ air in this mountain region.
Correct Answer
A. Invigorating
Explanation
Clue: Since the air is described as ‘pure’ we need a positive word. Also, since doctors recommend it, the air must be good for health.
Therefore, we choose invigorating which means energizing.
(soporific = sleep-inducing; debilitating = weakening; insalubrious = unhealthy; aromatic = pleasant-smelling)
44.
As were many colonial administrators, Gregory was ____ in his knowledge of the grammar of the local language, though his accent was ____ .
Correct Answer
C. Faultless - awful
Explanation
Clue: ‘though’ indicates the need for opposites.
Therefore, we say that he was faultless (perfect) in his grammar, though his accent was awful. [This is the only pair of opposites.]
(erratic = unpredictable; eccentric = odd)
45.
Though Adam Bede is presented to us by the author as ____ fiction, there are none of the life-like meanderings of the story of Amos Barton.
Correct Answer
A. Realistic
Explanation
Though Adam Bede is presented to us by the author as ____ fiction, there are none of the life-like meanderings of the story of Amos Barton.
46.
There is a general ____ in the United States that our ethics are declining and that out moral standards are ____ .
Correct Answer
D. Complaint - deteriorating
Explanation
Clue: ‘and’ usually joins things of similar meaning or weight. This suggests that since ethics are declining, moral standards are also declining (deteriorating). Almost any word except ‘optimism’ would have fit the first blank.
(futile = useless, ineffective; escalating = increasing)
47.
Homo sapiens, the proud splitter of the atom, inventor of the electronic computer, ____ of the genetic code may be humbled by a lowly ____ of the sewers and soils - the microbe.
Correct Answer
D. Decipherer - denizen
Explanation
Clue: The first blank requires something that conveys what man has done to the genetic code - the only two suitable words are ‘discoverer’ or ‘decipherer’. But since a microbe is not a rodent, we can eliminate that pair.
(rodent = animal like a rat or mouse; decipherer = someone who decodes; denizen = inhabitant)
48.
After centuries of obscurity, this philosopher's thesis is enjoying a surprising ____ .
Correct Answer
E. Renaissance
Explanation
Clue: The sentence tells us that the thesis has been in obscurity (forgotten or neglected) but now it is being revived. We can say it is undergoing a renaissance (revival). (remission = temporary cessation of a disease; decimation = destruction; longevity = length of life)
49.
The threat of war, far from ____ , lay heavily in the air, and the villagers, while ____ going about their normal activities, were unable to shake off the feeling of impending catastrophe.
Correct Answer
A. Receding - ostensibly
Explanation
Clue: ‘Far from’ indicates that an opposite point is being made. So, since there is a feeling of impending catastrophe the threat of war is far from getting less. This indicates that ‘receding’, diminishing’, or ‘subsiding’ might be suitable. We can eliminate these last two since their partner words ‘contentedly’ and ‘felicitously’ are inappropriate for a feeling of danger. So the villagers are only apparently (ostensibly) behaving normally.
(escalating = increasing ; felicitously = happily, suitably)
50.
Although alarmed by the ____ , Professor Symes had no reason to doubt the ____ of his student's results, for this student was nothing if not reliable.
Correct Answer
C. Implications - veracity
Explanation
Clue: ‘Nothing if not’ means ‘very’. So if the student is very reliable the professor would not doubt the ‘truth’ or ‘veracity’ of the results. Since the student is reliable we can eliminate the ‘error’ choice, and choose ‘implications’.
(folly = foolishness; impudence = cheekiness; veracity = truth; inferences = something we can deduce)