mathewhe/aqua_rat huggingface dataset:
Question: Roger can read a book in k minutes. What part of the book can he read in 6 minutes? (k>8)
(A) 8+k
(B) 8/k
(C) k/8
(D) (k+ 8)/k
(E) (k-8) / k
Rationale: Let's sayk = 24
That is, it takes 24 minutes to read the entire book.
So, in 8 minutes, Roger can read1/3of the book
So, we're looking for the answer choice that yields an OUTPUT of1/3whenk = 24
A) 8+24=32ELIMINATE
B) 8/24=1/3KEEP
C)24/8 =3ELIMINATE
D) (24+ 8)/24=32/24 = 4/3ELIMINATE
E) (24-8) /24=16/24 = 2/3ELIMINATE
Answer:D
Answer: (D) (k+ 8)/k
Question: Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other?
(A) 1:2
(B) 2:1
(C) 1:3
(D) 3:1
(E) 1:4
Rationale: root (b):root(a)
2:1
ANSWER:B
Answer: (B) 2:1
Question: The greatest number of four digits which is divisible by 18, 25, 40 and 75 is:
(A) 9000
(B) 9400
(C) 9600
(D) 9800
(E) 9200
Rationale: Greatest number of 4-digits is 9999.
L.C.M. of 18, 25, 40 and 75 is 1800.
On dividing 9999 by 1800, the remainder is 999.
Required number (9999 - 999) = 9000.
Answer: Option A
Answer: (A) 9000
Question: Last year, Company X made q dollars in profit. two Thrid of the profit went to the company’s founder. The rest was split evenly among his Three other partners. In terms of q, how much did each of the other partners receive?
(A) q/9
(B) q/5
(C) q/6
(D) q/7
(E) q/8
Rationale: Profit = q
Profit to company founder = 2q/3
Profit to other partners = q/3
Number of other partners = 3
Profit to each partner = (q/3)/3 = q/9
Answer: A
Answer: (A) q/9
Question: Johnny makes $3.25 per hour at his work. If he works 8 hours, how much money will he earn?
(A) $30
(B) $54
(C) $26
(D) $12
(E) $9.60
Rationale: 3.25*8=26. Answer is C.
Answer: (C) $26
Question: The circumferences of the fore and hind-wheels of a carriage are 2 2/5 and 3 3/7 meters respectively. A chalk mark is put on the point of contact of each wheel with the ground at any given moment. How far will the carriage have travelled so that their chalk marks may be again on the ground at the same time?
(A) 18 metres
(B) 16 metres
(C) 38 metres
(D) 42 metres
(E) 24 metres
Rationale: A little reflection will show that chalk marks will touch the ground together for the first time after the wheels have passed over a distance which is the LCM of 2 2/5 metres and 3 3/7 metres.LCM of 12/5 metres and 24/7 metres =24 metres.
Answer is E
Answer: (E) 24 metres
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 675meters, after what time will they meet at the starting point?
(A) 20sec
(B) 15sec
(C) 45sec
(D) 50sec
(E) 1min
Rationale: They meet every 675/7+8 = 45sec
Answer is C
Answer: (C) 45sec
Question: Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 2 km apart, if they walk in the same direction?
(A) 5hours
(B) 6hours
(C) 1hours
(D) 10hours
(E) 12hours
Rationale: To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 2 =1 hours
Answer is C
Answer: (C) 1hours
Question: A sum of money becomes triple itself in 5 years at simple interest. How many years will it become six times at the same rate?
(A) 12 1/2 years
(B) 12 1/6 years
(C) 12 7/2 years
(D) 12 1/4 years
(E) 22 1/2 years
Rationale: 100 ---- 200 ---- 5
200 ---- 5
100 ---- 2 1/2
------------------
600 ---- 12 ½ years
Answer: A
Answer: (A) 12 1/2 years
Question: There is food for 760 men for 22 days. How many more men should join after two days so that the same food may last for 16 days more?
(A) 122
(B) 140
(C) 199
(D) 188
(E) 190
Rationale: 760 ---- 22
760 ---- 20
x ----- 16
x*16 = 760*20
x = 950
760
-------
190
Answer: E
Answer: (E) 190
Question: A certain bag contains 100 balls â€” 20 white, 30 green, 10 yellow, 37 red, and 3 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple?
(A) 0.9
(B) 0.75
(C) 0.6
(D) 0.8
(E) 0.5
Rationale: According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (20 + 30 + 10)/100 = 60/100 = 0.6.
Answer is C
Answer: (C) 0.6
Question: A 2 digit known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
(A) 20
(B) 22
(C) 24
(D) 25
(E) 28
Rationale: Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.
C
Answer: (C) 24
Question: A retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 50 percent greater than the wholesale price. If the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent?
(A) 15
(B) 20
(C) 10
(D) 5
(E) 8
Rationale: Answer: D= 5.
Assume Rs. 100 to be the price at which the retailer buys from wholesaler.
50% increase makes Retail price = 150.
Now 30% decrease -> (1-30/100) * 150 = 105.
Now compared to the wholesale price of 100, 5% increase is what will have the same effect as increasing the wholesale price.
Answer: (D) 5
Question: The area of the largest circle that can be drawn inside a square of side 70 Cm in length is:
(A) 3600
(B) 2646
(C) 3850
(D) 4215
(E) 5205
Rationale: Radius of required circle = 35 Cm
its area = 22/7 × 35 × 35
110× 35= 3850 Cm(power)2
Answer is C.
Answer: (C) 3850
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
(A) 1.8
(B) 6.1
(C) 4.5
(D) 1.5
(E) 2.5
Rationale: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Answer: (D) 1.5
Question: If 5a + 7b = n, where a and b are positive integers, what is the largest possible value of n for which exactly one pair of integers (a, b) makes the equation true?
(A) 35
(B) 48
(C) 69
(D) 70
(E) 74
Rationale: 5*a1 + 7*b1 = n
5*a2 + 7*b2 = n
5*(a1 - a2) = 7*(b2 - b1)
since we are dealing with integers we can assume that a1 - a2 = 7*q and b2 - b1 = 5*q where q is integer, so whenever we get a pair for (a;b) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa, subtracting 7 from a and adding 5 to b.
Lets check how it works for our numbers, starting from the largest:
E)74 = 5*12 + 7*2 (a1 = 12, b1 = 2), subtract 7 fromaand add 5 tobrespectively, so a2 = 5 and b2 = 7, second pair - bad
D)70 = 5*7 + 7*5 (a1 = 7, b1 = 5), if we add 7 to a we will have to subtract 5 from b but b can't be 0, so - no pair, if we subtract 7 from a, we'll get a = 0 which also isn't allowed - no pair, thus this is the only pair for (a;b) that works,good!, thus
D is the answer
Answer: (D) 70
Question: If a survey shows that 36 citizens out of a sample of 300 support a particular Senate bill, what percent of the sample does not support the bill?
(A)  56%
(B)  64%
(C)  88%
(D)  82%
(E)  86%
Rationale: 36 out of 300 supports the bill and we are asked to find the percent who the does not support the bill.
36 out of 300 supports the bill = 12 out of 100 supports the bill ( taking in % terms )
12 out of 100 supports the bill = 88 (100-12) doesn't support the bill
So, answer is (C) 88%
Answer: (C)  88%
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit
(A) 70%
(B) 80%
(C) 90%
(D) None of above
(E) 60%
Rationale: Explanation:
Let C.P.= Rs. 100.
Then, Profit = Rs. 320,
S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 - 125) = Rs. 295
Required percentage = (295/420) * 100
= 70%(approx)
Answer: A
Answer: (A) 70%
Question: A solution of 100 litres contains milk and water in the ratio 5:x. If ten litres of water is added to the solution, the ratio becomes 3:2, find the value of x?
(A) 2.68
(B) 2.55
(C) 2.34
(D) 2.57
(E) 2.89
Rationale: Exp. Total new quantity = original sol + water =100+10 =110
New ratio = 3:2, New quantity of milk =3/5*110 = 66 Lit,
New quantity of water = 2/5*110= 44 Lit
Water present initially = (44-10) = 34 Lit
Ratio = 66/34 =5/x There for x = 2.57
Answer: D
Answer: (D) 2.57
Question: The tax on a commodity is diminished by 18% and its consumption increased by 15%. The effect on revenue is?
(A) 2%
(B) 8.7%
(C) 5.7%
(D) 6.7%
(E) 1%
Rationale: 100 * 100 = 10000
82 * 115 = 9430
-----------
10000-----------570
100-----------? => 5.7% decrease
Answer: C
Answer: (C) 5.7%
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 130 marks, the no of questions he attempts correctly is :
(A) 35
(B) 38
(C) 40
(D) 42
(E) 54
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 130
=> 5x = 190
=> x = 38
ANSWER IS B
Answer: (B) 38
Question: Jake, Lena, Fred, and Inna need to drive home from a corporate reception in an SUV that can seat 7 people. If only Inna or Jake can drive, how many seat allocations are possible?
(A) 30
(B) 42
(C) 120
(D) 240
(E) 960
Rationale: 4 people ,7 seats, only 2 can drive
if inna is in one seat remaining, 3 people can be arranged in 3p3 i.e 3! =6 ways
since any one can drive total ways = 6 *2= 12 ways
4 seats can be chosen out of remaining 6 seats in 6c3 ways = 6!/(3!*2!)= 20 ways
12*20=240
D
Answer: (D) 240
Question: Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).
(A) 2 hours 2 minutes
(B) 3 hours 5 minutes
(C) 4 hours 6minutes
(D) 5 hours 7 minutes
(E) 7 hours 9 minutes
Rationale: In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill
1/5 + 1/8 = 13 / 40 of a tank
Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving
(13/40) t = 1
t = 40 / 13 = 39/13 + 1/13 hours
= 3 hours and (1/13)*60 minutes
= 3 hours 5 minutes (rounded to the nearest minute)
correct answer B
Answer: (B) 3 hours 5 minutes
Question: John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John two hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
(A) 7
(B) 7 1/3
(C) 7 1/2
(D) 4
(E) 7 1/2
Rationale: John's speed - 15 miles/hr
Jacob's speed - 12 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 2 hour and 40min (until John's bike is repaired). Distance covered in 2 hour 40min (i.e 8/3hr) = 12x8/3 = 32 miles.
Now, when John starts riding back, the distance between them is 22 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-12 = 3 miles/hr.
Thus, to cover 22 miles at 3 miles/hr, John will take 22/3 = 7 1/3 hours
Answer B
Answer: (B) 7 1/3
Question: The average of first five prime numbers which are odd is?
(A) 15.5
(B) 15.7
(C) 15.2
(D) 7.8
(E) 15.1
Rationale: Sum of first 5 prime no. which are odd = 39
Average = 39/5 = 7.8
Answer:D
Answer: (D) 7.8
Question: Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 90 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
(A) 66
(B) 70
(C) 72
(D) 75
(E) 78
Rationale: Let the distance one way be x
Time from home to work = x/60
Time from work to home = x/90
Total time = 2 hrs
(x/60) + (x/90)= 2
Solving for x, we get x = 72
Time from home to work in minutes= (72)*60/60 = 72 minutes
Ans= C
Answer: (C) 72
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $750 (before payroll deductions)?
(A) 1600
(B) 1625
(C) 1650
(D) 1655
(E) 1675
Rationale: total pay = 40*$12.50 + $0.16*x = 760
x = 260 / 0.16 = 1625
The answer is B.
Answer: (B) 1625
Question: The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
(A) 10^9
(B) 10^8
(C) 10^7
(D) 10^6
(E) 10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
Make groups
2*5 = 10
3*17 = 50 (approximately)
7*13 = 100 (approximately)
11*19 = 200 (approximately)
So you make 7 zeroes (the 2 and the 5 also make a 0). When you multiply all these, the answer will be close to 10^7
ANSWER:C
Answer: (C) 10^7
Question: Dick and Jane each saved $1,000 in 1989. In 1990 Dick saved 15 percent more than in 1989, and together he and Jane saved a total of $2,000. Approximately what percent less did Jane save in 1990 than in 1989?
(A) 3%
(B) 5%
(C) 10%
(D) 15%
(E) 18%
Rationale: 1990
Dick saved = $ 1150
Jane saved = $ 850 (jane saved $150 less than she did the prior year)
Jane saved approximately $150/1000$ (15%) less in 1990
Answer: D
Answer: (D) 15%
Question: The average of 11numbers is 500. Out of 11numbers the average of first 6no. is 50, and last 6numbers is 60 then find 6th number?
(A) 95
(B) 80
(C) 110
(D) 120
(E) 72
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*50+6*60-11*50 = 110
Answer is C
Answer: (C) 110
Question: If w is 40 percent less than q, q is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
(A) 4%
(B) 18%
(C) 36%
(D) 40%
(E) 50%
Rationale: GIven w= 0.6q, q=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. E is the correct answer.
Answer: (E) 50%
Question: The greatest common factor of positive integers m and n is 9. What is the greatest common factor of (2m^2, 2n^2)?
(A) 9
(B) 81
(C) 162
(D) 324
(E) 405
Rationale: m = 9j and n = 9k, where the greatest common factor of j and k is 1.
2m^2 = 2*9*9*j^2 and 2n^2 = 2*9*9*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*9*9 = 162
The answer is C.
Answer: (C) 162
Question: Two pipes A and B can fill a tank in 5 hrs and 20 hrs respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 5 hr
(B) 4 hr
(C) 6 hr
(D) 3 hr
(E) 7 hr
Rationale: Explanation:
Pipe A can fill 1/5 of the tank in 1 hr
Pipe B can fill 1/20 of the tank in 1 hr
Pipe A and B together can fill 1/5+1/20=1/4 of the tank in 1 hr
i.e., Pipe A and B together can fill the tank in 4 hours
Answer: Option B
Answer: (B) 4 hr
Question: If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
Then 6 = ?
Hint: Its a logic Riddle not a mathematical riddle
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: A
1
As stated
1=6 => 6=1
Answer: (A) 1
Question: Which of the following is a prime number ??
(A) 33
(B) 81
(C) 32
(D) 93
(E) 11
Rationale: E
11
Clearly, 11 is a prime number.
Answer is E
Answer: (E) 11
Question: A city council will select 2 of 8 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
(A) 36
(B) 72
(C) 168
(D) 216
(E) 432
Rationale: OA C
8C2 * 6C1
using the combination formula to choose 2 from 8 and 1 from 6
Answer: (C) 168
Question: The angle between the minute hand and the hour hand of a clock when the time is 8:30
(A) 33
(B) 75
(C) 29
(D) 27
(E) 299
Rationale: Explanation:
Angle traced by hour hand in \inline \frac{17}{2} hrs = \inline \left ( \frac{360}{12}\times \frac{17}{2} \right )^{o} = 255
Angle traced by min hand in 30 min = \inline \left ( \frac{360}{60}\times 30 \right )^{o} = 180
\inline \therefore Required angle = (255 - 180) = \inline 75^{o}
Answer: B) 75
Answer: (B) 75
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s?
(A) 8
(B) 2
(C) − 2
(D) − 3
(E) − 5
Rationale: Given: x^2 − 2x − 15 = (x + r)( x + s)
Factor to get: (x - 5)(x + 3) = (x + r)( x + s)
Rewrite as: (x + -5)(x + 3) = (x + r)( x + s)
So, it's possible that r = -5 and s = 3
Here, r - s = (-5) - 3
= -8
Try REVERSING the factorization:
x^2 − 2x − 15 = (x + r)( x + s)
Factor to get: (x + 3)(x - 5) = (x + r)( x + s)
Rewrite as: (x + 3)(x + -5) = (x + r)( x + s)
So, it's possible that r = 3 and s = -5
Here, r - s = 3 - (-5)
= 8
Answer: A
Answer: (A) 8
Question: the sum of the ages of 5 children born at the intervals of 3 year each is 50 year. what is the age of the youngest child ?
(A) 4 year
(B) 8 year
(C) 10 year
(D) None of these
(E) 9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 ⇔ 5 x = 20 ⇔ x= 4.
∴ Age of the youngest child = x = 4 years. Answer A
Answer: (A) 4 year
Question: Working together, John and Jack can type 30 pages in one hour. If they would be able to type 35 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
(A) 3/2
(B) 2/1
(C) 5/2
(D) 4/3
(E) 1/3
Rationale: Lets say John types x pages an hour and Jack types y pages an hour.
We know that x+y=30
Jack increase speed by 25% means he will type 1.25y pages an hour.
So we get x+1.25y=35
We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.25y=5 so y=20 ... so x=10
(y/x)=2/1
Answer is (B)
Answer: (B) 2/1
Question: A man divides his property so that his son’s share to his wife’s and the wife’s share to his daughter are both in the ratio 3 : 1. If the daughter gets 10,000 less than the son, find the total worth of the property.
(A) 16,200
(B) 16,250
(C) 16,500
(D) 15,300
(E) None of these
Rationale: Let Son’s share = S;
Daughter’s share = D;
and Wife’s share = W.
Also, S : W = W : D = 3 : 1
∴ S : W : D = 9 : 3 : 1
then S = 9x , D = x
and 9x – x = 10,000 ⇒ x = 1250
∴ Total worth of the property = (9 + 3 + 1)x = 13x
= 13 × 1250 = 16,250
Answer B
Answer: (B) 16,250
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
(A) 70 lbs
(B) 40 lbs
(C) 30 lbs
(D) 50 lbs
(E) 60 lbs
Rationale: 100(x)(7/100)+(100(1-x)) (17/100)=100(10/100)
7x+17-17x=10
-10 x=-7
x=7/10
100lbs x (7/10) = 70 lbs
ANSWER:A
Answer: (A) 70 lbs
Question: A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?
(A) 3
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: sax Work done by Afar 3 days : i
J
.. Remzming war — 1
.Work done by (A + B) for 1 day :
. Work done by a for 1 day
6 days
C
Answer: (C) 6
Question: The sum of first five prime numbers is?
(A) 11
(B) 18
(C) 26
(D) 28
(E) None of these
Rationale: Required sum = (2+3+5+7+11)=28.
Correct Option : D
Answer: (D) 28
Question: Naomi drives to the beauty parlor in 60 minutes. On the way back, her average speed is half the average speed as it was to the way to the parlor. How much time will it take Naomi to travel two round trips to the beauty parlor?
(A) 3 hours.
(B) 4 hours.
(C) 4 hours and 20 minutes.
(D) 5 hours and 50 minutes
(E) 6 hours.
Rationale: s1=2s2
since, speed is inversely proportional to time
we have,
s1/s2=2/1=t2/t1
therefore , the time taken for one trip = 60+120 = 180 minutes
total = 180*2 =360 minutes = 6 hours
ANSWER:E
Answer: (E) 6 hours.
Question: If the price of 20 toys is 540, then what will the price of 15 toys ?
(A) 144
(B) 405
(C) 117
(D) 287
(E) 112
Rationale: One toy price = 540/20 = 27
15 toy price = 15 * 27 = 405
Answer : B
Answer: (B) 405
Question: A clock loses two minutes every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
(A) 11:54:40 AM
(B) 11:56:24 AM
(C) 12:16:40 PM
(D) 11:22:24 AM
(E) 12:06:36 PM
Rationale: Clock loses: 2 minute in 3 hours = 16 minutes in 24 hours = 64 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;
Net gain in 10 days = 86.40 - 64 = 22.4 minutes.
11AM + 22.4 minutes = 11:22 and 4/10th of a minute or 24 seconds.
Answer: D.
Answer: (D) 11:22:24 AM
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
(A) 120
(B) 140
(C) 240
(D) 320
(E) 100
Rationale: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is
x+2x=3x. This must be equal to 360.
3x=360
x=360/3
x=120
Therefore, the salesman sold 120 kg in the morning and 2*120=240 kg in the afternoon.
Answer is C.
Answer: (C) 240
Question: If the bus had traveled 60 kmh faster than it actually did, the trip of 120 km would have lasted 1 hour less. Find the speed of the bus.
(A) 55 kmh
(B) 30 kmh
(C) 80 kmh
(D) 60 kmh
(E) 75 kmh
Rationale: Time = Distance/Speed
Difference in time = 1 hr
120/x - 120/(x + 60) = 1
Substitute the value of x from the options. --> x = 60 --> 120/60 - 120/120 = 2 - 1 = 1
Answer: D
Answer: (D) 60 kmh
Question: The sum of two numbers is 95. Their difference is 5. The bigger number is
(A) 20
(B) 50
(C) 30
(D) 35
(E) 45
Rationale: X + Y = 95
X - Y = 5
Adding 2X = 100 ==> X = 50 and Y = 95 - 50 = 45
Bigger number is X = 50
Answer B.
Answer: (B) 50
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
(A) 1/13
(B) 2/13
(C) 1/26
(D) 1/52
(E) None
Rationale: Solution
Here, n(S) = 52
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E)	= n(E) / n(S)
= 2/52
‹=›1/26.
Answer C
Answer: (C) 1/26
Question: Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers?
(A) a 17
(B) b) 34
(C) c) 35
(D) d) 45
(E) e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
C- 0 and 35
therefore the minimum range is 34, it cant be any lower however you play with the numbers.
B
Answer: (B) b) 34
Question: You buy a piece of land with an area of âˆš400, how long is one side of the land plot?
(A) 28
(B) 29
(C) 30
(D) 20
(E) 32
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 400.
Answer D
Answer: (D) 20
Question: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=12?
(A) –108
(B) 19
(C) 10
(D) 16
(E) 18
Rationale: #p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 12 ---> 8p= 152 ---> p = 19, B is the correct answer.
Answer: (B) 19
Question: If 2^z is a factor of 25!, which of the following could be the value of z?
I. 22
II. 23
III. 24
(A) I ​ only
(B) II only
(C) I​ and II
(D) I, II, and III
(E) None
Rationale: 25! contains all numbers from 1 to 25. To find the factor with the highest power of 2, we count the number of multiples of 2,4,8 and 16
Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22
A is the answer.
Answer: (A) I ​ only