mathewhe/aqua_rat huggingface dataset:
Question: Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate Q in miles per hour for the entire trip?
(A) Q=26.7
(B) Q=30.0
(C) Q=40.0
(D) Q=53.3
(E) Q=60.0
Rationale: VERITAS PREPOFFICIAL SOLUTION
Correct Answer: C
Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.
Answer choice C is correct.
Answer: (C) Q=40.0
Question: A sum was put a simple interest at a certain rate for 3 years. Had it been put at 3% higher rate, it would have fetched Rs. 90 more. The sum is:
(A) s.750
(B) s.900
(C) s.1000
(D) s.1200
(E) s.1500
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x Ã— (R+3) Ã— 3/100âˆ’xÃ—RÃ—3/100=90
â‡’x Ã— 3Ã—3/100=90
â‡’x Ã— 3 /100=30
â‡’3x=3000
â‡’x=1000
Answer : Option C
Answer: (C) s.1000
Question: A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 128 in his diary to remember his PIN. He also wrote out the way to calculate 128 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 128".
Once, Prafull saw his diary in which Pinaki wrote this number 128. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
(A) 867
(B) 869
(C) 871
(D) 873
(E) None
Rationale: Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =128.
Thus, (996 × x)/997=128.
=>x= 869.
Answer : B
Answer: (B) 869
Question: Pipe A can fill a tank in 5 hours, pipe B in 5 hours and pipe C in 10 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 5
(B) 4
(C) 3
(D) 1
(E) 2
Rationale: Part filled by A + B + C in 1 hour = 1/5 + 1/5+ 1/10= 1/2
All the three pipes together will fill the tank in 2 hours.
Answer: E
Answer: (E) 2
Question: 189. The inside dimensions of a rectangular wooden box
are 8 inches by 10 inches by 12 inches. A cylindrical
canister is to be placed inside the box so that it stands
upright when the closed box rests on one of its six
faces. Of all such canisters that could be used, what is
the radius, in inches, of the one that has maximum
volume?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  8
Rationale: Since the radius is squared, the biggest volume cylinder will have the biggest possible radius. To achieve that, let the smaller dimension of the rectangular box be the height. So, it will have 12x10 width x length. The biggest cylinder must fit both dimensions, so it must have at most a diameter of 10, so the radius will be 5.
C
Answer: (C)  5
Question: A snail, climbing a 24 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall?
(A) 12
(B) 16
(C) 17
(D) 20
(E) 21
Rationale: total transaction in two days = 4-2 = 2 feet
in 20 days it will climb 20 feet
on the 21st day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =21
E
Answer: (E) 21
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 76
(B) 29
(C) 26
(D) 19
(E) 11
Rationale: Explanation:
Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 x 10 = 320.
Now increase in avg = 4runs. So, new avg = 32+4 = 36runs
Total runs = new avg x new no. of innings = 36 x 11 = 396
Runs made in the 11th inning = 396 - 320 = 76
Answer: A
Answer: (A) 76
Question: A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
(A) 40x
(B) 75x
(C) 48x
(D) 24x
(E) x/75
Rationale: The larger rim must circulate for the same number of inches the smaller rim does.
C = (pi)d
C(small): (pi)*28
C(large): (pi)*42
Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*28*60 = (pi)*(1680) inches
(pi)*(1680) = (pi)*(42)(x)
pi*(40) = pi*(x)
40=x
Answer: A. 40x
Answer: (A) 40x
Question: The original price of a suit is $150. The price increased 20%, and after this increase, the store published a 20% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 20% off the increased price, how much did these consumers pay for the suit?
(A) $130
(B) $136
(C) $144
(D) $150
(E) $160
Rationale: 0.8*(1.2*150) = $144
The answer is C.
Answer: (C) $144
Question: For each 6-month period during a light bulb's life span, the odds of it not burning out from over-use are half what they were in the previous 6-month period. If the odds of a light bulb burning out during the first 6-month period following its purchase are 1/4, what are the odds of it burning out during the period from 6months to 1 year following its purchase?
(A) 5/27
(B) 2/9
(C) 1/2
(D) 4/9
(E) 2/3
Rationale: P(of not burning out in a six mnth period)=1/2 of P(of not burning out in prev 6 mnth period)
P(of burning out in 1st 6 mnth)= 1/4
--->P( of not burning out in 1st 6 mnth)=1-1/4=3/4
---->P(of not burning out in a six mnth period)=1/2 *3/4=3/8--->P(of burning out in a six mnth period)=1-1/3=2/3
now
P( of burning out in 2nd six mnth period)=P( of not burning out in 1st six mnth)*P(of burning out in a six mnth)
=3/4 * 5/8=1/2
Ans D
Answer: (D) 4/9
Question: If three eighth of a number is 141. What will be the approximately value of 32.08% of this number?
(A) 70
(B) 80
(C) 100
(D) 110
(E) 120
Rationale: Explanation:
x * 3/8 = 141 => x= 376
376 * 32.08/100 = 120
E)
Answer: (E) 120
Question: After giving a discount of rs.50 the shopkeeper gets a profit of 20%,if the cost price is rs.500.find the marked price%?
(A) 450
(B) 500
(C) 650
(D) 600
(E) 650
Rationale: cost price=500
s.p=500*120/100=600
disc=50
so...mark price=600+50=650......
ANSWER:E
Answer: (E) 650
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 20 km in 20 hours. How much time he would have saved if the direction of tide has not changed?
(A) 2
(B) 8
(C) 1
(D) 6
(E) 16
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 20 km in 4 hours.
But he took 20 hours.
He would have saved 20 â€“ 4 = 16 hours.
Answer: E
Answer: (E) 16
Question: The ratio of the volumes of two cubes is 729 : 1331. What is the ratio of their total surface areas?
(A) 81:121
(B) 81:128
(C) 81:113
(D) 81:112
(E) 81:119
Rationale: Ratio of the sides
= ³√729 : ³√1331
= 9 : 11
Ratio of surface areas
= 92 : 112
= 81:121
Answer:A
Answer: (A) 81:121
Question: A bag contains 1` red jellybeans and 10 blue jellybeans. If 3 jellybeans are removed one at a time, at random and are not replaced, what is the probability that all 3 jellybeans removed from the bag are blue?
(A) 9/100
(B) 2/19
(C) 1/8
(D) 3/20
(E) 3/10
Rationale: Method-1
10 red jellybeans and 10 blue jellybeans
Total Outcomes = No. of ways to choose 3 Jelly bean at random out of a total 20 jellybeans = 20C3 = 1140
Favourable Outcomes = No. of ways to choose 3 Jelly bean such that they are all Blue out of 10 Blue = 10C3 = 120
Probability = Favourable Outcomes / Total Outcomes = 10C3 / 20C3
Probability = 120 / 1140 = 1/8
Answer: option B
Method-2
Probability of First jelly bean to be Blue = 10/20 [Total 10 Blue out of total 20 jellybeans]
Probability of Second jelly bean to be Blue = 9/19 [Total 9 Blue remaining out of total 19 jellybeans remaining]
Probability of Third jelly bean to be Blue = 8/18 [Total 8 Blue remaining out of total 18 jellybeans remaining]
Required Probability = (10/20)*(9/19)*(8/18) = 2/19
Answer: option C
Answer: (C) 1/8
Question: If 60% of a number is greater than 30% of 10 by 27, what is the number?
(A) 50
(B) 100
(C) 30
(D) 75
(E) 5
Rationale: Explanation:
60/100 * x - 30/100 * 10 = 27
60/100 * x - 3 = 27
60/100 * x = 30
x = 30 * 100 / 60
x = 50
Answer: Option A
Answer: (A) 50
Question: Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 79th number in this set?
(A)  605
(B)  608
(C)  613
(D)  616
(E)  629
Rationale: The set S = {5, 13, 21, 29, ..................... }
1st Number = 8 * 0 + 5 = 5
2nd Number = 8 * 1 + 5 = 13
3rd Number = 8 * 2 + 5 = 21
79th Number = 8 * (79-1) + 5 = 629
Answer = E
Answer: (E)  629
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
(A) 125/129
(B) 125/129
(C) 125/126
(D) 125/120
(E) 125/122
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer:C
Answer: (C) 125/126
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
(A) 2888
(B) 2790
(C) 1210
(D) 2756
(E) 2991
Rationale: π (232 – 122)
= 1210
Answer: C
Answer: (C) 1210
Question: four out of Eight employees are capable of doing a certain task. Sixty percent of the five employees, including the four who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?
(A) 43.33%
(B) 33.33%
(C) 13.33%
(D) 38.33%
(E) none
Rationale: Given 50% of 8 employees including 4 who are capable of doing task.
60% of 5 employeees
= 50/100 * 4
= 4 employees
===> 4 employees who are capable of doing the task and no one employee who is not capable.
percentage of employees assigned who are not capable
ANSWER:E
Answer: (E) none
Question: The largest four digit number which is a multiple of 8, 10,12 and 15 is:
(A) 9960
(B) 9950
(C) 9940
(D) 9930
(E) 9920
Rationale: lcm=120
9999/120=83
83*120=9960
ANSWER:A
Answer: (A) 9960
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were FIVE times the amount she spent per month, what should be the fraction of her salary that she spent each month?
(A) 1/4
(B) 3/4
(C) 12/17
(D) 15/17
(E) 1
Rationale: Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=5E=5(I-S)
=> 17S = 5I => Savings = 5/17 I
Hence Expenditure = 1-(5/17) = 12/17
Answer (C)
Answer: (C) 12/17
Question: A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 1/2
(B) 10/21
(C) 9/11
(D) 7/11
(E) 5/21
Rationale: Explanation :
Total number of balls = 2 + 3 + 2 = 7
Let S be the sample space.
n(S) = Total number of ways of drawing 2 balls out of 7 = 7C2
Let E = Event of drawing 2 balls , none of them is blue.
n(E) = Number of ways of drawing 2 balls , none of them is blue
= Number of ways of drawing 2 balls from the total 5 (=7-2) balls = 5C2
(âˆµ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)
P(E) = n(E)/n(S)=5C2/7C2=(5X4 /2X1) /(7X6 /2X1)=5X4/7X6 =10/21
ANSWER IS B
Answer: (B) 10/21
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b < 1
II. a/b > 0
III. ab < 1
(A) I only
(B) II only
(C) III only
(D) II and III only
(E) I and III only
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Answer: (D) II and III only
Question: Maya purchase 13 jars in a store then she returned 4 jars to store .Now how many jars she had?
(A) 5
(B) 11
(C) 19
(D) 9
(E) 4
Rationale: 13-4=9. Answer is D
Answer: (D) 9
Question: If KING is coded as 17 and MASS is coded as 29 Then DON is coded as
(A) 12
(B) 16
(C) 18
(D) None
(E) cannot be determined
Rationale: Explanation :
KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DON = 4+14+15=33 i.e(3*3)+(3*3)=18
Hence (C) is correct
Answer : C
Answer: (C) 18
Question: The average of four consecutive odd numbers is 12. Which is the lowest odd number?
(A) 9
(B) 3
(C) 5
(D) Cannot be determined
(E) None of these
Rationale: Let the four consecutive odd nos. be
2x – 3, 2x – 1, 2x + 1 and 2x + 3.
Now, 2x = 12 or, x = 6
Lowest odd no. = 2 × 6 – 3 = 9
Answer A
Answer: (A) 9
Question: Find the area of a parallelogram with base 18 cm and height 10 cm?
(A) 281
(B) 284
(C) 288
(D) 255
(E) 180
Rationale: Area of a parallelogram = base * height
= 18 * 10
= 180 cm2
Answer: E
Answer: (E) 180
Question: John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 4% and the mobile phone at a profit of 15%. Overall how much he make a profit.
(A) s. 90
(B) s. 620
(C) s. 600
(D) s. 650
(E) s. 690
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 15/100) = 8000 + 120
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 1200 = Rs. 600
As this is positive, an overall profit of Rs. 600 was made.
C
Answer: (C) s. 600
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
(A) Rs.7500
(B) Rs.7529
(C) Rs.7518
(D) Rs.7509
(E) Rs.7506
Rationale: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8
= Rs.7500
Answer:A
Answer: (A) Rs.7500
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 12 days and B in 18 days, then C alone can do it in?
(A) 21 days
(B) 15 days
(C) 12 days
(D) 9 days
(E) 6 days
Rationale: Explanation:
C = 1/4 - 1/12 – 1/18 = 1/9 => 9 days
Answer: D
Answer: (D) 9 days
Question: S is a set of 100 consecutive multiples of 8. If the smallest number in S is 108, then the greatest number in S is
(A) 998
(B) 297
(C) 999
(D) 902
(E) 900
Rationale: last term =first term +(total no. of terms-1)consecutive difference
S is a set of 100 consecutive multiples of 8. If the smallest number in S is 108, then the greatest number in S is
first term = 102 ; total terms =100 ; difference = 3
108+(99)8 = 900
Ans E
Answer: (E) 900
Question: What percent is 3% of 5% ?
(A) 15%
(B) 1.5%
(C) 0.15%
(D) None of these
(E) Cannot be determined
Rationale: Answer
Required percent = [(3/100) / (5/100)] x 100]%
= [(3/100) x (100/5) x 100] %
= 60%
Correct Option: D
Answer: (D) None of these
Question: If N = 2^0.3 and N^b = 16, b must equal
(A) 3/80
(B) 3/5
(C) 4
(D) 5/3
(E) 40/3
Rationale: 30/100 = 3/10
N = 2 ^ 3/10
N^b = 2^4
(2^3/10)^b = 2^4
b = 40/3
Answer: E
Answer: (E) 40/3
Question: If sushi rows 27 km upstream and 81 km down steam taking 9 hours each, then the speed of the stream
(A) 12 kmph
(B) 13 kmph
(C) 22 kmph
(D) 20 kmph
(E) 15 kmph
Rationale: Speed upstream = 27/9 = 3 kmph
Speed down stream = 81/3 = 27 kmph
Speed of stream = ½ (27-3) = 12 kmph
ANSWER:A
Answer: (A) 12 kmph
Question: What is the number of integers from 1 to 500 (inclusive) that are divisible by neither 10 nor by 15?
(A) 170
(B) 250
(C) 300
(D) 560
(E) 420
Rationale: In 500 consecutive numbers, number of multiples of 10 = 500/10 = 50 (Ignore decimals)
In 500 consecutive numbers, number of multiples of 15 = 500/15 = 33
Number of multiples of 10*15 i.e. 150 = 500/150 = 3
Number of integers from 1 to 500 that are divisible by neither 10 nor by 15 = 500 - (50 + 33 - 3) {Using the concept of sets here) = 420
Answer is E
Answer: (E) 420
Question: In how many different number of ways a Committee of 3 person of can be selected from 5 men and 3 women such that at least 1 women is included in the committee
(A) 40
(B) 46
(C) 52
(D) 54
(E) 56
Rationale: 1W 2M 2W 1M 3W
= 3C1 × 5C2 + 3C2 × 5C1 + 3C3s
= 3 × (5 × 4)/2 + 3 × 5 + 1
= 30 + 15 + 1 = 46
Total 5M 3W
8C3 = 56
5C3 = 10
At least one women = total - with out women
At least one women = 56 - 10 = 46
B)
Answer: (B) 46
Question: For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 60?
(A) 10
(B) 15
(C) 8
(D) 12
(E) 20
Rationale: 4n+7 > 1
4n> -6
n > -(3/2)
n> -1.5 (n = -1, 0, 1 ,2 3........ upto infinity)
From second constraint
4n+7 < 60
4n< 53
n < 13. 25
n = (-infinity, .......-3, -2, -1, 0, 1, 2, .........upto 13)
Combining the two
-1.5 < n<13.25
n = 1 to 13 (48 integers)
and n = -1 and 0
so 15 integers.
B
Answer: (B) 15
Question: The average (arithmetic mean) of four different positive integers is 13. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 = 13
=> 5x + 2 + a = 52
=> 5x + a = 50
=> a = 50 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x=10
This gives us a=50 - 50 = 0
Therefore the minimum value that the fourth integer can have is 0. Option E
Answer: (E) 0
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1111. Find the cost of each ice-cream cup?
(A) 25
(B) 66
(C) 77
(D) 50
(E) 91
Rationale: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 1111
96 + 225 + 490 + 6x = 1111
6x = 300 => x = 50.
Answer: D
Answer: (D) 50
Question: Which of the following integers doesn't have a divisor greater than 1 that is the square of an integer?
(A) 12
(B) 36
(C) 100
(D) 61
(E) 72
Rationale: Prime Factorization
12=2*2*3=2^2*3. Includes a perfect square of 4.
36=2*2*3*3=2^2*3^2. Includes perfect squares of 4 and 9.
100=2*2*5*5=2^2*5^2. Includes the perfect squares 4 and 25.
61=61*1. 61 is prime, no perfect squares so a possibility.
72= 2*3*2*3*2=6^2*3. Includes perfect square of 36.
28=2*2*7=2^2*7. Includes a perfect square of 4.
All but 61 have a perfect square as a factor so the answer is D.
12=4*3. Perfect square of 4.
36=4*9. Perfect squares of 4 and 9.
100=4*25. Perfect squares 4 and 25.
61=61*1. No perfect squares.
72= 36*2. Perfect square of 36.
Answer: (D) 61
Question: A card shop contains 10 birthday cards, 10 holiday cards, and 9 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be of the same type?
(A) 3/29
(B) 12/58
(C) 12/840
(D) 7/841
(E) 12/841
Rationale: It doesn't matter which type of card you choose, so:
Probability of choosing 1st card: 1
Probability of choosing 2nd card of the same type: 4/29
Probability of choosing 3rd card of the same type: 3/29
Multiply and you get 12/841
Answer E.
Answer: (E) 12/841
Question: Money invested at x%, compounded annually, triples in value in approximately every 112/x years. If $1500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?
(A) $3,750
(B) $5,600
(C) $13,500
(D) $15,000
(E) $22,500
Rationale: x=8%
112/x years=112/8=14 years
Now, money triples every 14 years
Therefore, in 14 yrs , if $1500 triples to $4500, in 28 years, it will again triple to $4500*3=$13,500
Answer C
Answer: (C) $13,500
Question: One-fifth of Ramu’s expenditure is equal to one-half of his savings. If his monthly income is Rs.6300 how much amount does he save?
(A) Rs.1550
(B) Rs.1800
(C) Rs.2000
(D) Rs.2350
(E) Rs.2450
Rationale: Let the saving be Rs. x
Therefore, Expenditure = Rs. (6300-x)
then, (6300-x)* 1/5 = x* 1/2
=> 1260- x/5 = x/2
=> 1260= x/2 + x/5
=> 7x/10 = 1260
x= 1800
ANSWER:B
Answer: (B) Rs.1800
Question: If 1⁄8 of 2⁄3 of 4⁄5 of a number is 12 then 30 per cent of the number will be
(A) 48
(B) 64
(C) 54
(D) 42
(E) None of these
Rationale: Let the number be x.
and 1⁄8 of 2⁄3 of 4⁄5 × x = 12
∴ 3x⁄10 = 54
Answer C
Answer: (C) 54
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/9%
(B) 33 1/6%
(C) 33 1/3%
(D) 33 8/3%
(E) 31 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3%
Question: How many numbers between 0 and 1370 have a prime tens digit and a prime units digit?
(A) 204
(B) 212
(C) 220
(D) 228
(E) 236
Rationale: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1300, there 16*13 = 208 such numbers.
From 1301 to 1370, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 208+12 = 220
The answer is C.
Answer: (C) 220
Question: A dishonest person wants to make a profit on the selling of milk. He would like to mix water (costing nothing) with milk costing 33 $ per litre so as to make a profit of 50% on cost when he sells the resulting milk and water mixture for 36$. In what ratio should he mix the water and milk?
(A) 1:20
(B) 1:10
(C) 3:8
(D) 3:4
(E) 3:2
Rationale: First of all, let's consider 1 liter of the stuff he is going to sell --- naive customers think it's pure milk, but we know it's some milk-water mixture. He is going to sell this liter of milk-water for $36.
This $36 should be a 50% increase over cost. Here, we need to think about percentage increases as multipliers.
Using multipliers
(cost)*1.50 = $36
cost = 36/1.5 = 360/12 = $24
If he wants a 20% increase over cost on the sale of one liter of his milk-water, the cost has to be $24.
Well, a liter of milk costs $33, so if he is going to use just $30 of milk in his mixture, that's 24/33 = 8/11 of a liter. If milk is 8/11 of the liter, then water is 3/11 of the liter, and the ratio of water to milk is 3:8. Answer choice(C)
Answer: (C) 3:8
Question: What percentage of numbers from 1 to 50 have squares that end in the digit 5?
(A) 1
(B) 14
(C) 10
(D) 21
(E) 22
Rationale: Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 5. Such numbers from 1 to 50 are 5,15,25,35,45.
Number of such numbers = 14.
Required percentage = (5/50 * 100) = 10%
ANSWER:C
Answer: (C) 10
Question: A polygon has 35 diagonals. How many sides does it have?
Self made
(A)  10
(B)  13
(C)  14
(D)  15
(E)  16
Rationale: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 35
n*(n - 3) = 70
Substitute n from the answer choices. n = 10
Answer: A
Answer: (A)  10
Question: Find the one which does not belong to that group ?
(A) 233
(B) 288
(C) 608
(D) 287
(E) 112
Rationale: Explanation:
The sum of the digits in 508, 328, 706 and 148 is 13, but not in 608.
Answer:C
Answer: (C) 608