mathewhe/aqua_rat huggingface dataset:
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: Given two fair dice, what is the probability W that the sum of their numbers is 4 if exactly one die shows a 3?
(A) a) 2/11
(B) b) 1/18
(C) c) 3/11
(D) d) 2/39
(E) e) 1/5
Rationale: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.the probability W that the sum of their numbers is 4 if exactly one die shows a 3
2/11 would be the answer if 'at least one of the die shows a 3'.A
Answer: (A) a) 2/11
Question: If a is a positive integer, which of the following could NOT be the square of a?
(A)  5,008,644
(B)  5,004,169
(C)  4,999,696
(D)  4,995,225
(E)  4,990,752
Rationale: A number ending with 2 can never be a perfect square.
Units digit of a perfect square must be:
1,4,9,6,5
Answer E)
Answer: (E)  4,990,752
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire?
(A) 2
(B) 1
(C) 4
(D) 3
(E) 5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 96,000 m : C is the circumference
C = 4 meters
correct answer C
Answer: (C) 4
Question: An design manager has 10patterns of chairs & 7patterns of tables. In how many ways can he make a pair of table & chair?
(A) 70
(B) 40
(C) 80
(D) 90
(E) 100
Rationale: He has has ten patterns of chairs and eight patterns of tables
Hence, A chair can be arranged in 10 ways and
A table can be arranged in 7 ways
Hence one chair and one table can be arranged in 10 x 7 ways = 70 ways
A
Answer: (A) 70
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 2879
(C) 289
(D) 279
(E) 2928
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer:A
Answer: (A) 3630
Question: Two brothers were expected to return here on the same day. Rajat returned 3 days earlier but Rohit returned 4 days later. If Rajat returned on Tuesday, what was the expected day when both the brothers were to return home and when did Rohit Return?
(A) Wednesday, Sunday
(B) Thursday, Monday
(C) Friday, Tuesday
(D) Monday, Friday
(E) none
Rationale: Rajat returned on Tuesday -i.e. 3 days earlier
so actual day to return home is Friday.
Rohit returned after days so Tuesday.
ANSWER:C
Answer: (C) Friday, Tuesday
Question: The flow of water through a drainage pipe was monitored for a 3-hour period. In the second hour, the rate of flow was 36 gallons per hour, which was 50 percent faster than the rate of flow for the first hour. If 25 percent more water flowed through the pipe in the third hour than it did in the second, how many gallons of water flowed through the pipe during the entire three hours?
(A) 106.25
(B) 105.5
(C) 105.75
(D) 106
(E) 105.0
Rationale: Rate of flow of water in second hour = 36 gallons per hour
Rate of flow of water in first hour = 36/(3/2) = 24 gallons per hour
Rate of flow of water in third hour = (125/100)* 36 = (5/4) * 36 = 45 gallons per hour
Number of gallons of water that flowed through the pipe during the entire 3 hours = 24+36+45 = 105 gallons
Answer E
Answer: (E) 105.0
Question: How many seconds will a 700 meter long train moving with a speed of 63 km/hr take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
(A) 48
(B) 36
(C) 42
(D) 11
(E) 18
Rationale: Explanation:
Here distance d = 700 mts
speed s = 63 - 3 = 60 kmph = 60 x 5/18 m/s
time t = = 42 sec.
Answer: C
Answer: (C) 42
Question: Suppose five circles, each 4 inches in diameter, are cut from a rectangular strip of paper 12 inches
long. If the least amount of paper is to be wasted, what is the width of the paper strip?
a=sqrt(3)
(A)  5
(B)  4 +2a
(C)  8
(D)  4(1+ a)
(E)  not enough information
Rationale: Also if we dont go by 30:60:90 rule, we can arrive at the length of by pythagoras theorem.
(AC)^2 + (BC)^2 = AB^2
(AC)^2 + 2^2 = 4^2
AC = 2 root b.
so the width of paper = 2 + 2 + 2 root 3 --> 4 + 2 root 3.
which is B.
Answer: (B)  4 +2a
Question: In how many ways the letters of the word RAIMBON be arranged?
(A) 4540
(B) 4740
(C) 5040
(D) 6432
(E) 7794
Rationale: Total ways of arranging the letters = 7! = 5040 ways.
C)
Answer: (C) 5040
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.165. Find the unknown rate of two towels?
(A) A)400
(B) B)450
(C) C)500
(D) D)550
(E) E)600
Rationale: 10 * 150 = 1650
3 * 100 + 5 * 150 = 1050
1650 – 1050 = 600
E
Answer: (E) E)600
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 80 ps per meter is?
(A) 287
(B) 369
(C) 125
(D) 200
(E) 361
Rationale: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 0.80
= Rs.200
Answer:D
Answer: (D) 200
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 13 units?
(A) 140 sq.units
(B) 170 sq.units
(C) 190 sq.units
(D) 940 sq.units
(E) 182 sq.units
Rationale: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 13 = 182 sq.units
Answer: Option E
Answer: (E) 182 sq.units
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 78 2/11%
(B) 18 2/11%
(C) 88 2/11%
(D) 58 2/11%
(E) 68 2/11%
Rationale: Explanation:
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer:B
Answer: (B) 18 2/11%
Question: The ages of Charlie and Vaibhav are in the proportion of 3 : 5. After 9 years, the proportion of their ages will be 3 : 4. Then the current age of Vaibhav is:
(A) 15 years
(B) 16 years
(C) 135 years
(D) 21 years
(E) 18 years
Rationale: A
15 years
Charlie’s age = 3A and
Vaibhav’s age = 5A
{ (3A + 9)/(5A + 9) }=3/4
=> 4 (3A + 9) = 3 (5A + 9)
=> A = 3
Therefore, Vaibhav’s age = 15 years.
Answer: (A) 15 years
Question: A tank is 25 m long, 12 m wide and 6 m deep. What is the cost of plastering its walls and bottom at the rate of 75 paise per sq.m?
(A) 558
(B) 502
(C) 516
(D) 612
(E) 700
Rationale: TOTAL SURFACE S = 2LW + 2LH + 2WH
=(25 * 12) + (2 * 25 * 6 ) + ( 2 * 12 * 6 )
= 300 + 300 + 144
=744 M2
THEREFORE COST OF PLASTERING = 744 * 75 = 5800 PAISE = 558
ANSWER A
Answer: (A) 558
Question: Look at this series: 14, 28, 20, 40, 32, 64, ... What number should come next?
(A) 56
(B) 44
(C) 26
(D) 48
(E) 49
Rationale: A
56
This is an alternating multiplication and subtracting series: First, multiply by 2 and then subtract 8.
Answer: (A) 56
Question: If a is a digit in the number (a5,608 + 584)/88 = an integer, what is the value of a?
(A) 2
(B) 1
(C) 3
(D) 7
(E) 9
Rationale: (a5,608 + 584)/88 = a6,192/88
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
192/8 = 24 => So, we want divisible by 11.
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a619-2 => a61-7 => a5-4 => a1 => 11/11.
So a = 1.
Answer: B
Answer: (B) 1
Question: Determine the equation for the line parallel to r ≡ x + 2y − 2= 0 that passes through the point A = (1, 3).
(A) x + 2y = 0
(B) 2y − 7= 0
(C) x + 2y − 7= 0
(D) x − 7= 0
(E) x - 2y + 7= 0
Rationale: the equation for the line parallel to r ≡ x + 2y − 2= 0 is
x + 2y + K= 0
1 + 2• 3 + k = 0
k = −7
x + 2y − 7= 0
ANSWER C x + 2y − 7= 0
Answer: (C) x + 2y − 7= 0
Question: In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th term in sequence S?
(A) 3(2^13)
(B) 9(2^15)
(C) 21(2^14)
(D) 9(2^14)
(E) 21(2^13)
Rationale: The terms in the sequence can be shown as
a(n) = 2* a(n-1)
So, the sequence will look like: 3, 2*3, (2^2) *3,...
And the nth term will be given as 2^(n-1) *3
Therefore, a(14) = (2^13)*3,
Answer : A
Answer: (A) 3(2^13)
Question: David gets on the elevator at the 11th floor of a building and rides up at the rate of 57 floors per minute. At the same time, Albert gets on an elevator at the 51st floor of the same building and rides down at the rate of 63 floors per minute. If they continue travelling at these rates, then at which floor will their paths cross ?
(A) 19
(B) 28
(C) 30
(D) 37
(E) 35
Rationale: Explanation:
Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 - 63x 120x = 40
x =	1/3
Number of floors covered by David in (1/3) min. = (1/3x 57	)=19.
So, their paths cross at (11 +19) i.e., 30th floor.
ANSWER IS C
Answer: (C) 30
Question: Q-2: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 3?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: CONCEPT: A number will be divisible by 3 if sum of all the digits of the number is divisible by 3
Here the Possible sum of the two distinct digits can be 3, 6, 9 and 12 only in order to satisfy the given condition
If sum of Digits = 3, No. = 12, 21 --- 2 Cases
If sum of Digits = 6, No. = 15, 24, 42, 51 --- 4 Cases
If sum of Digits = 9, No. = 27, 36, 45, 54, 63, 72 --- 6 Cases
If sum of Digits = 12, No. = 57, 75 --- 2 Cases
Total Cases = 2+4+6+2 = 14 cases
Answer: option E
Answer: (E) 14
Question: If 15 men can build a wall of forty two metres long in 5 days, what length of a similar wall can be built by 25 men in 4 days
(A) 48 metres
(B) 56 metres
(C) 60 metres
(D) 62 metres
(E) None of these
Rationale: Explanation :
Solution: Let the required length be x metres.
More men, more length built (Direct proportion)
Less days, less length built (Direct proportion)
men 15 : 25
days 5 : 4
.'.(15*5*x) = (25*4*42)
x = 56 metres.
Answer : B
Answer: (B) 56 metres
Question: A company makes a profit equal to 25% of its sales. The profit is shared equally among the 4 owners of the company. If the company generates sales of $5,000,000, how much money does each one of the owners get?
(A) $ 112,500
(B) $ 212,500
(C) $ 312,500
(D) $ 412,500
(E) $ 512,500
Rationale: The profit made on sales of $5,000,000 is given by
25% * $5,000,000 = $ 1,250,000
The profit made by each one of the 4 owners is given by
$ 1,250,000 / 4 = $ 312,500
correct answer C
Answer: (C) $ 312,500
Question: A jar contains only red, yellow, and orange marbles. If there are 3 red, 6 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the probability that 2 yellow, 1 red, and no orange marbles will be chosen?
(A) 1/60
(B) 1/45
(C) 2/45
(D) 3/22
(E) 5/22
Rationale: I started by finding the 2 probabilities, without calculation, like this:
P(YYR)
P(YRY)
P(RYY)
I calculated the first one and ended in 1/22. I looked at the answer choices at this point and saw answer D: 3/22.
This helped me realise that for the 3 possible orderings the probabbility is the same. So, it should be (1/22)*(6), which indeed is 6/22.
E
Answer: (E) 5/22
Question: Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is white
(A) 1
(B) 2/3
(C) 1/3
(D) 4/3
(E) 5/3
Rationale: Explanation:
Total cases = 10 + 20 = 30
Favourable cases = 20
So probability = 20/30 = 2/3
Answer: Option B
Answer: (B) 2/3
Question: f n = 3^8 - 2^8, which of the following is not a factor of n?
(A) 5
(B) 65
(C) 13
(D) 97
(E) 35
Rationale: = (3^4 -2^4) (3^4+2^4)
number is not divisible by 35
=97*13*5
E
Answer: (E) 35
Question: If k^3 is divisible by 60, what is the least possible value of integer k?
(A) 12
(B) 30
(C) 60
(D) 90
(E) 120
Rationale: 60 = 2^2*3*5
Therefore k must include at least 2 * 3 * 5 = 30.
The answer is B.
Answer: (B) 30
Question: Denominator of a number is 4 less than the numerator. If 6 is added to the numerator, it becomes 3 times the denominator. Find the denominator.
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Let the Numerator be X and Denominator be Y. Then
=>X=Y+4 and 6+X=3*Y
=>6+Y+4=3*Y
=>2Y=10=>Y=5
Option C
Answer: (C) 5
Question: If 0.2 of a number is equal to 0.08 of another number, the ratio of the numbers is :
(A) 2 :3
(B) 3 :4
(C) 2 : 5
(D) 20 : 3
(E) 30:7
Rationale: 0.2A = 0.08B
-> A/B = 0.08/0.20 = 8/20 = 2/5
:. A : B = 2 : 5
ANSWER:C
Answer: (C) 2 : 5
Question: A cloth merchant has announced 25% rebate in prices. If one needs to have a rebate of Rs.40, then how many shirts, cash costing Rs.32, he should purchase ?
(A) 6
(B) 5
(C) 10
(D) 7
(E) 8
Rationale: Explanation:
Suppose the number of shirts = x.
Then, rebate = [25/100×32x]=8x
8x=40 or x = 5.
Correct Option : B
Answer: (B) 5
Question: A ranch has both horses and ponies. Exactly 5/6 of the ponies have horseshoes, and exactly 2/3 of the ponies with horseshoes are from Iceland. If there are 4 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
(A) 18
(B) 21
(C) 38
(D) 40
(E) 57
Rationale: 5/6*P have horseshoes, so P is a multiple of 6.
2/3*5/6*P = 5/9*P are Icelandic ponies with horseshoes, so P is a multiple of 9.
The minimum value of P is 18. Then H = P+4 = 22.
The minimum number of horses and ponies is 40.
The answer is D.
Answer: (D) 40
Question: Henry sold an item for Rs.7200/- and incurred a loss of 20%. At what price should he have sold the item to have gained a profit of 20%?
(A) 10600
(B) 10800
(C) 11000
(D) 11200
(E) 11400
Rationale: Explanation:
20% loss means SP = 80% of CP
:. CP = Rs.7200x100/80 = Rs.9000.
The SP for a gain of 20% = 9000+20% of 9000 = 9000+1800 =Rs10800.
Answer: Option B
Answer: (B) 10800
Question: Walking across campus, a student interviewed a group of students. 20% of the students took a finance class last semester, 45% took a marketing class last semester, and 45% took neither a finance nor a marketing class last semester. What percent of the students in the group took both a finance and a marketing class?
(A) 60%
(B) 50%
(C) 25%
(D) 15%
(E) 10%
Rationale: {Total} = {finance} + {marketing} - {both} + {neither}
100 = 20 + 45 - {both} + 45
{both} = 10%.
The answer is E.
Answer: (E) 10%
Question: Harkamal purchased 8kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) A)1000
(B) B)1055
(C) C)1065
(D) D)1075
(E) E)1095
Rationale: Cost of 8 kg grapes = 75 × 8 = 600.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 600 + 495 = 1095.
E)
Answer: (E) E)1095
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 10p, in terms of p?
(A) 10p
(B) 2p
(C) 5p
(D) 7p
(E) p^2
Rationale: Y=30p
other number is 10p
then GCF(30p,10P)=10P; A is the correct answer
Answer: (A) 10p
Question: Everyone shakes hands with everyone else in a room. Total number of handshakes is 120. Number of persons=?
(A) a.14
(B) b.12
(C) c.11
(D) d.15
(E) e.16
Rationale: In a room of n people, the number of possible handshakes is C(n,2) or n(n-1)/2
So n(n-1)/2 = 120 OR n(n-1)=240 OR n=16
Answer is (E)
Answer: (E) e.16
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 3168, how much was it in the beginning?
(A) A)3800
(B) B)4200
(C) C)4400
(D) D)4500
(E) E)4600
Rationale: X * (90/100) * (80/100) = 3168
X = 4400
ANSWER:C
Answer: (C) C)4400
Question: A dealer originally bought 90 identical batteries at a total cost of q dollars. If each battery was sold at 50 percent above the original cost per battery, then, in terms of q, for how many dollars was each battery sold?
(A) q/60
(B) 3q/2
(C) 145q
(D) q/90
(E) 145/q
Rationale: The cost of each battery was q/90.
Each battery was sold for 1.5q/90 = 3q/180 = q/60.
The answer is A.
Answer: (A) q/60
Question: The first term in a sequence is 1 and the second term is 10. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 29th term in the sequence?
(A) 3.5
(B) 5.5
(C) 10
(D) 10.5
(E) 29
Rationale: The third term is 5.5 since this is the average of 1 and 10.
Then the next terms will all be 5.5 since the average stays at 5.5
The answer is B.
Answer: (B) 5.5
Question: Billy makes $124 more than Kimberly in a week. Wynona makes 3 times as much as Billy and Kimberly put together in a week, which totals $2,436. How much would Billy, Kimberly, and Wynona make together in a month?
(A) $12,992
(B) $9,744
(C) $29,232
(D) $11,232
(E) None of the above
Rationale: b-k=124
3(b+k)=2,436 or b+k=812
Solving the 2 equations you get B=$468 and K=$344
So 4(468+344+2436)=$12,992
Correct Answer: A
Answer: (A) $12,992
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 13√4
(B) 13√2
(C) 23√2
(D) 12√4
(E) 13√9
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer: B
Answer: (B) 13√2
Question: If a number between 10 and 60 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
(A) 31/41
(B) 1041
(C) 14/41
(D) 27/41
(E) 16/51
Rationale: If tens digi is 6 ---> ones digit : 0
If tens digi is 5 ---> ones digit : 0, 1, 2, 3, 4
If tens digi is 4 ---> ones digit : 0, 1, 2, 3
If tens digi is 3 ---> ones digit : 0, 1, 2
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 60-10+1=51.
So the probability is 16/51.
The answer is (E).
Answer: (E) 16/51
Question: The average age of A and B is 50 years. If C were to replace A, the average would be 50 and if C were to replace B, the average would be 40. What are the age of A, B and C?
(A) 100,100, 80
(B) 50, 50, 40
(C) 40, 60, 40
(D) 50, 60, 40
(E) None of the above
Rationale: Given A + B = 100â€¦(i)
C + B = 100â€¦ (ii)
A + C = 80â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C = 140â€¦(iv)
from (i) and (iv), we get
C = 40years
âˆ´ B = 60 years and A = 40 years
Answer C
Answer: (C) 40, 60, 40
Question: If 50 apprentices can finish a job in 4 hours, and 30 journeymen can finish the same job in 7 hours, how much of the job should be completed by 10 apprentices and 15 journeymen in one hour?
(A) 17/140
(B) 29/180
(C) 26/143
(D) 1/5
(E) 39/121
Rationale: 50 apprentices can finish the job in 4 hours,thus:
10 apprentices can finish the job in 4*5 = 20 hours;
In 1 hour 10 apprentices can finish 1/20 of the job.
30 journeymen can finish the same job in 4,5 hours,thus:
15 journeymen can finish the job in 7*2 = 14 hours;
In 1 hour 15 journeymen can finish 1/14 of the job.
Therefore, in 1 hour 10 apprentices and 15 journeymen can finish 1/20+1/14=17/140 of the job.
Answer: A
Answer: (A) 17/140
Question: If x^4 > x^5 > x^3, which of the following could be the value of x?
(A) -3
(B) -2
(C) -2/3
(D) 2/3
(E) 3
Rationale: Let's break this question down into two parts. I: x4>x5x4>x5 and II: x5>x3x5>x3
Consider Part I:
x4>x5x4>x5
For this to be true, either xx is negative or it is a fraction less than 1
Consider Part II:
x5>x3x5>x3
If xx is negative, then for this to be true, xx has to be greater than -1.
If xx is a fraction less than 1, then for this part to be true, xx must also be negative.
In either case, xx can be represented by the inequality 0>x>−10>x>−1.
The only option that satisfies this condition is C (-2/3)
ANSWER:C
Answer: (C) -2/3
Question: A die is thrown three times. Events X and Y are defined as below:
X : 4 on the third throw
Y : 6 on the first and 5 on the second throw
What is the probability of X given that Y has already occurred.
(A) 1/7
(B) 1 by 6
(C) 2/3
(D) 2/5
(E) 3/5
Rationale: The sample space has 216 outcomes.
Now X =
(1,1,4) (1,2,4) ... (1,6,4) (2,1,4) (2,2,4) ... (2,6,4)
(3,1,4) (3,2,4) ... (3,6,4) (4,1,4) (4,2,4) ...(4,6,4)
(5,1,4) (5,2,4) ... (5,6,4) (6,1,4) (6,2,4) ...(6,5,4) (6,6,4)
Y = {(6,5,1), (6,5,2), (6,5,3), (6,5,4), (6,5,5), (6,5,6)}
and X n Y = {(6,5,4)}.
Now P(Y) = 6/216
and P (X n Y) = 1/216
Then P(X|Y) = (1/216)/(6/216) = 1/6.
B)
Answer: (B) 1 by 6
Question: What is the sum of all the numbers between 1 and 16, inclusive?
(A) 190
(B) 200
(C) 185
(D) 166
(E) 213
Rationale: All you have to do is add 1+2+3+4...+14+15+16, which is 190.
Final Answer:
A
Answer: (A) 190
Question: If the median of a list of numbers is m, the first quartile of the list is the median of the numbers in the list that are less than m. What is the first quartile of the list of numbers 42, 24, 30, 34, 26, 36, 33 and 35 ?
(A) 33
(B) 28
(C) 27
(D) 24
(E) 23
Rationale: It is given that a quartile is the middle number of all numbers less than median..
so lets arrange the number in ascending order- 42, 24, 30, 34, 26, 36, 33 and 35
24, 26, 30, 33, 34, 35, 36, 42...
numbers less than median are 24, 26, 30, 33..
the median of these numbers = center of 26 and 30 = 28
B
Answer: (B) 28
Question: If Re.250 amounts to Rs.400 over a period of 5 years. What is the rate of simple interest?
(A) 11%
(B) 12%
(C) 13%
(D) 10%
(E) 14%
Rationale: 150 = (250*5*R)/100
R = 12%
Answer:B
Answer: (B) 12%
Question: For the given equation x9+5x8−x3+7x+2=0,x9+5x8−x3+7x+2=0, how many maximum real roots are possible?
(A) 3
(B) 7
(C) 4
(D) 0
(E) 1
Rationale: f(x) = x9+5x8−x3+7x+2=0x9+5x8−x3+7x+2=0
In f(x), there are 2 changes of sign. So, there are two positive roots.
f(-x) = - x9+5x8−x3+7x+2=0x9+5x8−x3+7x+2=0
In f(-x), there are 3 changes of sign. So, there are three negative roots.
So, in all there are 5 real roots possible (2 positive and 3 negative) and as degree of the given equation is 9, there are total 9 roots. So, remaining 4 roots will be imaginary.
Answer:C
Answer: (C) 4
Question: The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.
(A) 5:25
(B) 4:25
(C) 3:15
(D) 7:15
(E) 6:15
Rationale: Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2
= 4x2: 25x2
= 4 : 25.
ANSWER B 4:25
Answer: (B) 4:25
Question: In how many ways R can the crew of a ten oared boat be arranged ,when of the ten persons available, 2 of whom can row only on the bow side and 3 of whom can row only on the stroke side?
(A) 1. 10!/(2! * 3!)
(B) 2. 10!/(8! * 7!)
(C) 3. 5!/(3! * 2!)
(D) 4. (5!)^3/(3! * 2!)
(E) 5. 5!/(8! * 7!)
Rationale: Ans is D.
Going by the assumtion that both the Bow side and Stroke side will have 5 person each.
Five(3+2) of them had allready been selected(according to their preference), so from the remaining 5 we have to select 2 for the stroke side or 3 for the bow side.
and the 5 crew of each side can be arranged in 5! ways.R
Hence answer is 5C3 * 5! * 5!= (5!)^3/ 3!2!.D
Answer: (D) 4. (5!)^3/(3! * 2!)
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $8.40?
(A) 426
(B) 430
(C) 443
(D) 530
(E) 486
Rationale: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 8.4$, we can buy as many as 5 packs of 100 (5 x 1.5$ = 7.5$). We then have 0.9 $ left. so we buy 30 individual envelopes. If we add up the numbers, we get 500+30=530 envelopes. Answer D
Answer: (D) 530