1.
Which of the following numbers is between 3 and 4?
Correct Answer
B. B. 15/4
Explanation
Option A is not correct as 12/5 = 2.4
Option B is correct as 15/4 = 3.75 and 3.75 lies between 3 and 4.
Option C is not correct as 17/4 = 4.25
Option D is not correct as 13/6 = 2.1666...
Option E is not correct as 11/6 = 1.83...
2.
A team of 24 men can complete a job in 18 days working 9 hours per day. How many hours a day would 27 men have to work in order to finish it in 12 days?
Correct Answer
A. A. 12
Explanation
As other options are not equal to the calculated answers, only option A is correct.
Men Days Hours
24 18 9
27 12 ?
The number of men and the number of days vary inversely with the number of hours.
No. of hours = 24*18*9 / 27*12 = 12 hours
3.
4 pens cost as much as 6 pencils; 2 pencils cost as much as 4 erasers; If the cost of 1 eraser is $1, what is the cost of four pens?
Correct Answer
D. D. $12
Explanation
As other options are not equal to the calculated answer, only option D is correct.
Cost of 4 pens = cost of 6 pencils or
Cost of 1 pen = 6/4 cost of 1 pencil = 3/2 cost of 1 pencil
Cost of 2 pencils = cost of 4 erasers or
Cost of 1 pencil = 4/2 cost of 1 eraser = 2 cost of 1 eraser
Cost of 1 eraser = $1
Cost of 1 pencil = 2 * cost of 1 eraser = 2 * 1 = $2
Cost of 1 pen = 3/2 cost of 1 pencil
= 3/2 * 2 = $3
Cost of 4 pens = 4 * 3 = $12
4.
The table given below shows the number of credit points scored by five students in a five week course. Which student has earned total maximum credit points in the course?
Correct Answer
A. A. Jane
Explanation
Option A is correct. Jane´s total credit points = 9 + 7 + 20 + 21 + 7 = 64
Option B is not correct. Mike´s total credit points = 10 + 6 + 16 + 22 + 8 = 62
Option C is not correct. Mathew's total credit points = 15+ 8 +22 + 5 + 11 = 61
Option D is not correct. Peter´s total credit points = 20 + 6 + 14 + 5 + 12 = 57
Option E is not correct. Stephen´s total credit points = 8 + 20 + 16 + 7 + 5 = 56
5.
If y = 3/4 xz, what is the value of z when x = 2 and y = 27
Correct Answer
C. C. 18
Explanation
Option A is not correct. If z =2, 3/4 xz = 3/4 * 2 * 2 = 3 ≠ 27
Option B is not correct. If z = 6, 3/4 xz = 3/4 * 2 * 6 = 9 ≠ 27
Option C is correct. If z = 18, 3/4 xz = 3/4 * 2 * 18 = 27 = y
Option E is not correct. If z = 27, 3/4 xz = 3/4 *2 * 27 = 81/2 ≠ 27
Option E is not correct. If z = 9, 3/4 xz = 3/4 * 2 * 9 = 27/2 ≠ 27
6.
If x is a positive integer, which of the following is(are) true.

If x is odd, then (x+1)^{2}is even.

If x is even, then (x1)^{2}is odd.

If x is even, then is irrational.
Correct Answer
A. A. I and II
Explanation
Option A is correct.
Let us take x as 5 which is odd, then (x + 1)^2 is (5 + 1)^2 which is equal to 36, which is even. Hence I is true. Let us take x as 8 which is even, then (x  1)^2 is (8  1)^2 which is equal to 49, which is odd. Hence II is also true. As I and II are true option A is correct.
Option B is not correct.
I is true as seen above. If x is 8 which is even, then √(81) = √7
is irrational, but If x is 10 which is even, then √(101) = √9 = 3 is rational, hence III is not true.
Option C is not correct.
II is true as seen above but III is not true as seen above.
Option D is not correct.
Only I is false, as both I and II are true.
Option E is not correct.
Only II is false, as both I and II are true.
7.
If a and b are the lengths of the legs of a right triangle whose hypotenuse is 10 units and whose area is 20 square units, what is the value of (a + b)^{2}?
Correct Answer
E. E. 180
Explanation
As other options are not equal to the calculated answer, only option E is correct. Let the sides of the right triangle be a, b and c in increasing order. Hence, c is its hypotenuse. According to Pythagora's theorem,
a^2 + b^2 = c^2, or a^2 + b^2 = 102 or a^2 + b^2 = 100
Area of a right triangle = 1/2 ab or 1/2 ab = 20 or ab = 40
(a+b)^2 = a^2 + b^2 + 2ab = 100 + 2 * 40 = 180
8.
The average sale of soaps of 24 salesmen excluding Michael´s is 46 pieces per day, whereas Michael alone sells 96 pieces per day. What will be the average sale of soaps if Michael´s sale is also included in it?
Correct Answer
C. C. 48
Explanation
Option A is not correct as average sale of 24 salesmen itself is greater than 36.
Option B is not correct as average sale of 24 salesmen itself is greater than 38.
Option C is correct.
Average sale = total sale / number of salesmen or
Total sale = Average sale * number of salesmen
= 46 * 24 = 1104
Michael´s sale per day = 96
Total sale including Michael´s sale = 1104 + 96 = 1200
Total number of salesmen including Michael =24 + 1 = 25
Average sale of soaps including Michael´s sale = 1200/25 = 48
Option D is not correct as average sale of 24 salesmen itself is greater than 46.
Option E is not correct as average sale figure of 140 is too high, compared to the average sale of 24 salesmen.
9.
If x > 2y and , then which of the following is true?
Correct Answer
A. A. x > 6z
Explanation
Only option A is correct as other options do not satisfy the given inequalities.
x > 2y and z < y/3 or x > 2y and 3z < y or y > 3z or x > 2* 3z or x > 6z
10.
Which of the following has the greatest perimeter?
Correct Answer
C. C. A rectangle with 10 units length and 40 square units area.
Explanation
Option A is not correct.
Area of the square = 36 square units = s2 or s = 6 units.
Perimeter of the square= 4s = 4 * 6 units = 24 units.
Option B is not correct.
Side of the equilateral triangle = a = 9 units.
Perimeter of an equilateral triangle = 3a = 3 * 9 units = 27 units.
Option C is correct.
Length of the rectangle = 10 units.
Area of the rectangle = 40 square units.
Width of the rectangle = 40/10 units = 4 units.
Perimeter of the rectangle = 2(l + w)
= 2(10 + 4) units
= 2 * 14 = 28 units.
Option D is not correct.
In a right triangle c2= a2 + b2 or 52 = 42 + b2 or b2 = 25  16 or b2 = 9
Or b = 3. Perimeter of the triangle = (3 + 4 + 5) units = 12 units.
Option E is not correct as is observed no two of the given figures have the same perimeter.
11.
Which of the following is the correct factorization of the quadratic expression 6z^{2}  11z + 4?
Correct Answer
A. A. (3z  4)(2z  1)
Explanation
Option A is correct: 6z^2  11z + 4 = 6z^2  8z  3z + 4
= 2z(3z  4)  1(3z 4)
= (3z4) (2z  1)
Option B is not correct as 6z^2  11z + 4 ≠ (3z + 4) ( 2z 1)
Option C is not correct as 6z^2  11z + 4 ≠ (3z 4) (2z +1)
Option D is not correct as 6z^2  11z + 4 ≠ (3z + 4) (2z +1)
Option E is not correct as 6z^2  11z + 4 ≠ (2z 4) (3z 1)
12.
If a  5/6 = 1/243, then what does a equal?
Correct Answer
D. D. 729
Explanation
Option A is not correct. 1/243 = 3^5, If a = 3, then 3^5/6 6z^2  11z + 4 ≠ 3^5
Option B is not correct. 1/243 = 3^5. If a = 81, then (81)^5/6 = (3^4)^5/6 ≠ 3^5
Option C is not correct. 1/243 = 3^5. If a = 243, then (243)^5/6 = (3^5)^5/6 ≠ 3^5
Option D is not correct 1/243 = 3^5. If a = 729, then (729)^5/6 = (^6)^5/6 ≠ 3^5
Option E is not correct 1/243 = 3^5. If a = 3, then (27)^5/6 = (^3)^5/6 ≠ 3^5
13.
If x and y are multiples of 3, which of the following cannot also be a multiple of 3?
Correct Answer
E. E. x + y + 1
Explanation
Option A is not correct. x + y is a multiple of 3. For example 6 and 15 are multiples of 3, 6 + 15 = 21 is also a multiple of 3.
Option B is not correct. xy is a multiple of 3. For example 6 and 9 are multiples of 3 their product 6 * 9 = 54 is also a multiple of 3.
Option C is not correct. xy + 3 is a multiple of 3. For example 3 and 6 are multiples of 3. 3 * 6 + 3 = 21 is also a multiple of 3.
Option D is not correct. For example 12 and 9 are multiples of 3, 12  9 = 3 is also a multiple of 3.
Option E is correct. For example 6 and 21 are multiples of 3, 6 + 21 + 1 = 28 is not a multiple of 3.
14.
In a group of 15 persons 10 are mathematicians and 8 are statisticians. How many people are both mathematicians and statisticians?
Correct Answer
C. C. 3
Explanation
As the calculated answer is not equal to the other options given, only option C is correct.
Total number of persons in the group = n(M∪S) = 15
Number of mathematicians = n(M) = 10
Number of statisticians = n(S) = 8
Number of persons who know both subjects = n(M∩S)
n(M∪S) =n(M) + n(S)  n(M∩S) or n(M∩S) = 10 + 8 + 15 + 18  15 = 3
15.
A club has 108 members. Twothirds of them are men and the rest are women. All members are married except for 9 women members. How many married women are there in the club?
Correct Answer
C. C. 27
Explanation
As the calculated answer is not equal to the other options, only option C is correct.
Total number of members in the club = 108
Number of male members = 2/3 * 108 = 72
Number of women members = 108  72 = 36
Number of women who are not married = 9
Number of married women in the club = 36  9 = 27
16.
If p#q@r = (p + q + r)(p^{2} + q^{2} + r^{2}), then find the value of 8#5@2.
Correct Answer
E. E. 1395
Explanation
Option A is not correct. 8#5@2 ≠ 15
Option B is not correct. 8#5@2 ≠ 80
Option C is not correct. 8#5@2 ≠ 120
Option D is not correct. 8#5@2 ≠ 135
Option E is correct. According to the give rule,
Here p = 8, q = 5, and r = 2,
hence, 8#5@2 = (8 + 5 + 2 )(8^2 + 5^2 + 2^2)
= 15 * (64 + 25 + 4)
= 15 * 93
= 1395
17.
In the given figure, O is the centre of the circle.
Note: Figure not drawn to scale.
Correct Answer
D. D. 100 degrees
Explanation
As the calculated answer is not equal to the other options, only option D is correct.
Join PO. ∠OQP = ∠OPQ = 30 degrees (Isosceles triangle property)
∠ORP = ∠OPR = 20 degrees (Isosceles triangle property)
∠QPR = ∠OPQ + ∠OPR = 30 degrees + 20 degrees = 50 degrees
∠QOR = 2 * ∠QPR = 2 * 50 degrees = 100 degrees (angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at any other point on the remaining circle)
18.
The percent increase from 8 to 14 is equal to the percent increase from 12 to what number.
Correct Answer
A. A. 21
Explanation
As the calculated answer is not equal to the other options only option A is correct.This problem can be solved either using percentages or ratios.
Using ratios makes it simpler.
(14  8)/8 = (x  12)/1 2
Or 6/8 = (x  12)/12
Or (x  12) * 8 = 6 * 12
Or x  12 = 72/8 or x  12 = 9 or x = 9 + 12 or x = 21
Therefore, the required number is 21.
19.
Johnson has to cover a distance of 240 miles, of which
Correct Answer
C. C. 40
Explanation
As the calculated answer is not equal to the other options, only option C is correct.
Total distance traveled = 240 miles.
Distance traveled at a speed of 30 miles/hr =1/4 * 240 miles = 60 miles.
Time taken to travel 60 miles = 60/30 hrs = 2 hrs (Time = distance/speed)
Distance traveled at a speed of 40 miles/hr = 1/3 * 240 miles = 80 miles.
Time taken to travel 80 miles = 80/40 hrs = 2 hrs.
Distance traveled at a speed of 50 miles/hr = {240  (60 + 80)}miles
= 100 miles.
Time taken to travel 100 miles = 100/50 hrs = 2 hrs.
Total time taken to travel 240 miles = 2hrs + 2hrs + 2hrs = 6hrs
Average speed of Johnson = total distance traveled/total time taken
= 240 miles/6hrs
= 40 miles/hr.
20.
Mrs. Alice is four times as old as her son. After 4 years the sum of their ages would be 63 years. Find her son´s present age.
Correct Answer
B. B. 11
Explanation
Option A is not correct. If son is 12 years, then mother would be 48 years old, after 4 years sum of their ages = 12 + 4 + 48 + 4 = 68 63.
Option B is correct.
Let´s son´s present age be x years.
Mrs. Alice´s age = 4x years
Son's age's age after 4 years = (x + 4) years
Mrs. Alice's age after 4 years = (4x + 4) years
Given, x + 4 + 4x + 4 = 63
Or 5x + 8 = 63 or 5x = 63  8 = 55 or 5x = 55 or x = 11
Hence son's present age = 11 years.
Option C is not correct. If son is 4 years, then mother would be 16 years old,after 4 years sum of their ages = 4 + 4 +16 + 4 = 28 63
Option D is not correct. If son is 2 years, then mother would be 8 years old, which is absurd.
Option E is not correct. If son is 15 years, then mother would be 60 years old,after 4 years sum of their ages = 15 + 4 + 60 + 4 = 83 63