1.
P is a prime number.
Quantity A Quantity B
A prime number whose square Prime number whose Cube is
is a 2-digit number with the sum of a 3-digit number with the sum of its
its digits as a prime number digits divisible by 10
Correct Answer
D. The relationship can not be determined from the information given.
Explanation
ANS. (D) (Only 5 & 7 prime nos. have their squares of 2-digits and sum of the digits of their squares is prime for both. So Quantity A can be both 5 & 7. Similarly, only 5 & 7 have their cubes of 3-digits but the sum of the digits of the cube of 7 i.e. 343 is 10. So Quantity B is 7. So Quantity B can be more or equal to Quantity A. So the relationship can not be determined from the information given. Hence (D) is correct.)
2.
Car A leaves at a speed of M miles per hour (mph) from New York City for Chicago at 13:00 hours. Another car B also leaves from New York City for Chicago at a speed of N mph at 15:00 hours. Both the cars take the same route and 1.4 M > N.
Quantity A Quantity B
At 21:00 hours, distance covered At 21:00 hours, distance covered
by car A by car B
Correct Answer
D. The relationship can not be determined from the information given.
Explanation
ANS: (D) (2nd car started 2 hours late, so 1st car would be 2M miles ahead at 15:00 hours. The gap between 2 cars would vary depending upon the difference in speeds of the cars. As per the question, N < 1.4M, let N = 1.35 M Distance covered by car A at 21:00 hours = 8 M And distance covered by car B = 6 x 1.35 = 8.1 M So distance covered by car B will be more. Let N = 1.3 M Distance covered by car B at 21:00 hours = 6 x 1.3 = 7.8 M So distance covered by car A will be more. So for some values, 2nd car would be ahead (1.35M) & for some values (1.3M), 1st car would be ahead. Hence the relationship can not be determined from the information given.)
3.
25 liter of a solution has 55% sodium and rest water. 30 liter of another solution has 45% sodium and rest water. Both these solutions are mixed up.
Quantity A Quantity B
% Sodium in the mixture % Water in the mixture
Correct Answer
B. Quantity B is greater.
Explanation
ANS. B (55% of 25 liter = 13.75 liter. 45% of 30 liter = 13.5 liter. Total sodium in mixed solution= 13.75 + 13.5 = 27.25 liter So Quantity A is 27.25 liter Total water in mixed solution = 55 – 27.25 = 27.75 liter So Quantity B is 27.75 liter Obviously Quantity B is greater.)
4.
N = 3 X (Y^{2}) + 4 (X^{2}) Y, where X and Y are integers and Y is even.
Quantity A Quantity B
49^{N} – 31^{(N+2)} 49(^{N-1)} – 31^{(N+2)}
Correct Answer
B. Quantity B is greater.
Explanation
ANS: (B) (The last digit of 49x will be 9, when x is odd (9, 9x9x9 = 729 etc.) and will be 1, when x is even (9x9 = 81, 9x9x9x9 = 6561 etc.). Similarly last digit of 31(x+2) will always be 1 for all values of x (31X31 = 961 etc.). So for even values of x, the last digit of expression would be 0 (1 – 1) and 8 (9 – 1) for odd values of N. For N = 3 X (Y2) + 4 (X2) Y, since Y is even, so 3 X (Y2) and 4 (X2) Y both are even, hence N is also even. Quantity A is 0 since N is even. Since (N – 1) is odd, so Quantity B is 8. Hence Quantity B is greater.)
5.
In the figure, two identical squares are inscribed in the rectangle. The perimeter of one square is 6.
Quantity A Quantity B
The perimeter of the rectangle Perimeter of both the squares
Correct Answer
A. Quantity A is greater.
Explanation
ANS. A (Length of rectangle = 2x diagonal of square and width = diagonal of square. Side of square= 6/4 = 3/2, Diagonal of square= (3/2) SQRT(2). So the perimeter of rectangle = 2 (3 times the diagonal of square) Or = 9 SQRT (2) = 9 x 1.414 = 12.7 (Quantity A) Perimeter of both the squares = 12 (Quantity B) So Quantity A is greater.)
6.
X.Y = Z, where Z = 0. Quantity A Quantity B X Y
Correct Answer
D. The relationship can not be determined from the information given.
Explanation
ANS. D (If either of X or Y or both X & Y are 0, then Z will also be 0. But from the question nothing can be said about values of X & Y, whether any one of these if 0 and which one or both are 0. So the relationship can not be determined from the information given.)
7.
Susan and Lucy have invested in a venture. Susan invested an amount in the initial months and then reduced that amount by 1/4^{th} after 4 months and then again reduced the amount by 1/2 of the currently being invested after 8 months. Lucy joined after 2 months from Susan’s initial month and invested 90 % of Susan’s last month's contribution every month.
Quantity A Quantity B
Susan’s share in profit after Lucy’s share in profit after one
one year year
Correct Answer
A. Quantity A is greater.
Explanation
ANS: A (The share in profit will in proportion to the total investment by each. Let Susan invested $A initially every month. She would invest $A every month for 4 months. After 4 months, she would invest (A – (¼)A) = 3/4 A every month for 4 months. Finally, she would invest 3/4 A – 1/2 of 3/4 A = 3/8 A. So Susan’s total investment in one year = 4xA + 4x3/4 A + 4x3/8 A = 17/2 A. Now Lucy’s contribution = 10 x 0.9 (3/8 A) = 27/8 A. (90% of Susan’s last month contribution (3/8 A)). The share in profit of Susan & Lucy = (17/2) A : (27/8) A = 68 : 27 ((17/2) A / (27/8) A). Hence Quantity A is greater.)
8.
The slope of line m is 1. Quantity A Quantity B x1 y2
Correct Answer
C. The two quantities are equal.
Explanation
Ans: C (For C, y1 will be 0 (on x –axis, y = 0)
Similarly for D, x2 = 0
Slope = (Difference in the y-coordinates)/(Difference in the x-coordinates)
Or slope = y2/x1 = 1
So y2 = x1)
9.
An auditorium has 3 entrances. 3 men have to get into the auditorium. What is the probability that all 3 men will enter from different entrances?
Correct Answer
E. 2/9
Explanation
ANS: (E) (Total no. of ways in which 3 men can enter 3 gates = 3x3x3 = 27. (1st can enter in any of the 3 gates, 2nd can do same & 3rd can also do same.) No. of possible combinations in which 3 men can enter 3 different gates = 3P3 (ABC, ACB, BCA, BAC, CAB, CBA) Or = 3!/1! = 6 So the probability that all 3 men will enter from different entrances = 6/27 = 2/9.)
10.
Incomes of A and B are in the ratio x: y and their expenditure are in the ratio of w: z. If both save an equal amount of $M each, what will be the income of A?
Correct Answer
E. M x (z – w)/(xz – wy)
Explanation
ANS: (E) (Let total income of both is $I. So A’s income = I x /(x + y) and B’s income = I y/(x + y) Also expenditure of A = income – saving = [I x /(x + y)] – M And expenditure of B = [I y /(x + y)] – M The ratio of expenditures is w : z So {[I x /(x + y)] – M} : {[I y /(x + y)] – M} = w : z Or [I x – M (x + y)] : [I y – M (x + y)] = w : z Or z [I x – M (x + y)] = w [I y – M (x + y)] Or I (xz – wy) = M (x + y) (z – w) Or I = M (x + y) (z – w) / (xz – wy) So A’s income = I x /(x + y) Or = M x (z – w)/(xz – wy))
11.
Tap A alone takes 30 minutes to fill up a tank, while tap B alone takes 45 minutes to fill up the same tank. Tap C which is at the bottom of the tank can alone empty it in 36 minutes. Another tap D is fixed at 1/2 level of the tank. What will be the possible time t taken by tap D to empty the tank alone, if the tank is half full and it remains half full always when all four taps are open?
Indicate all such values
Correct Answer(s)
B. T = 18 minutes
D. T = 26 minutes
E. T = 30 minutes
Explanation
ANS: B, D and E (Both A & B together can fill up the tank in 18 minutes (1/30 + 1/45 = 1/18) Now tap C & D should also be able to empty the tank in not more than 18 minutes for tank to remain at half level. So maximum time taken by D will be 36 minutes. (1/36 + 1/36 = 1/18) Now if C & D take less time to empty, then when all tapes are open then the level will go down from 1/2. But tap D is at 1/2 level, so it will stop working and only C will empty in 36 minutes while A & B will fill up in 18 minutes. So water level will go up & when the level is more than 1/2, then D will start working & level will start reducing. Ultimately it will settle at 1/2 level only when all tapes are ON. This will happen for any value of t < 36 minutes. Hence 0 < t < 36 minutes. So t will take any value less than 36 minutes.)
12.
In the xy-coordinate system above, the lined portion is bounded by straight lines. Which of the following is not the equation of one of the bounded lines?
Correct Answer
B. X = 0
Explanation
Ans: B (y = 0 is the horizontal line passing through origin, and is one of the bounded lines.
x = 0 is the vertical line passing through the origin and is not one of the bounded lines.
x = 1 and x = 2 are obviously the bounded lines.
x + y = 3 is the slanting line. To verify it, we know that (1, 2) and (2, 1) are the points on the line.
So putting the value of x = 1 in the equation, we get y = 2 and similarly for x = 2, we get y = 1.)
13.
If 3% of (m + n) is 15, where m & n are positive integers and m is a double digit number. What is the least possible value of n?
(Numeric entry)
Correct Answer
401
Explanation
ANS: 401 ((3/100) (m + n) = 15, so m + n = 500. For n to be the least, m must be greatest two digit number which is 99. So n = 500 – 99 = 401.)
14.
If X = M + 2N + 3O + 4P + 5Q + 6R, where M, N …. R are natural numbers. If no four of the 6 numbers are same, find the minimum value of X?
Correct Answer
A. 27
Explanation
ANS: (A) (X will be minimum, when R has the lowest value followed by Q, P … & M. Minimum possible value for natural number is 1 and also no four numbers can have same value, so for X to be minimum P, Q & R will have value 1 followed by O, N & M which will have value of 2.
So X = 2x (1 + 2 +3) + 1x (4 + 5 + 6) = 12 + 15 = 27.)
15.
If X/Y is +ve, then which of the followings must be true?Indicate all such expressions.
Correct Answer(s)
A. XY > 0
C. X < 0, Y < 0
Explanation
ANS: A and C (X/Y will be +ve only when both X & Y are of same sign either both +ve or both –ve.
Take A, XY will be > 0 only when either both are +ve or –ve, so A is true.
Take B, X – Y > 0 Or X > Y, X can be greater than Y even when both have different signs. So B is not true.
Now take C, both are –ve, that is, of same sign, so (III) is also true.
Hence A and C are the correct.)
16.
If 0 < X < 1, which is the greatest?
Correct Answer
B. 1/X^2
Explanation
ANS: (B) (If a number is between 0 & 1, then the value of the value of the number reduces as the power of the number is increased. A number will be greatest either when the numerator is the greatest or the denominator is the smallest. Here X^2 is the smallest, hence 1/ X^2 is the greatest.)
17.
Had the rate of deceleration of the 10^{th} hour continued, the speed would have become zero at ......
Correct Answer
B. 11 Hrs 20 Minutes
Explanation
ANS: B (The rate of deceleration of the 10th hour was 30 miles/hrs. At 10th hors, the speed was 40 miles/hrs, so with this rate the speed would have reduced to 10 miles/hrs at 11 hrs and would have become zero in further 20 minutes.)
18.
During which two hour slot, the distance travelled was maximum?
Correct Answer
A. 6 – 8 hrs
Explanation
ANS: A (During 6 – 8 hrs, distance travelled = 85 + 80 = 165 miles
During 5 – 7 hrs, distance travelled = 75 + 85 = 160 miles
During 3 – 5 hrs, distance travelled = 50 + 60 = 110 miles
During 4 – 6 hrs, distance travelled = 60 + 75 = 135 miles
During 7 – 9 hrs, distance travelled = 80 + 70 = 150 miles.)
19.
Function f is defined as, 2f(x) = f(x+1) – f(x-1). If f(0) = 1 and f(1) = 2, find the value of f(5)?(Numeric entry)
Correct Answer
70
Explanation
ANS. 70 (In the given equation put x=1, 2f(1) = f(2) – f(0), so f(2) = 5. Similarly f(3) =12, f(4) = 29 and f(5) =70.)
20.
If the difference between the mean and median of the numbers of a set is 1, then that number set may be?
Correct Answer
D. (0, 3, 3, 4, 8, 9)
Explanation
ANS. D (Numbers in set (D) have mean of 4.5 and median of 3.5)