mathewhe/aqua_rat huggingface dataset:
Question: The cost to park a car in a certain parking garage is $10.00 for up to 2 hours of parking and $1.75 for each hour in excess of 2 hours. What is the average (arithmetic mean) cost per hour to park a car in the parking garage for 9 hours?
(A)  $1.09
(B)  $1.67
(C)  $2.225
(D)  $2.47
(E)  $2.50
Rationale: Total cost of parking for 10 hours = 10$ for the first 2 hours and then 1.75 for (9-2) hours = 10+7*1.75 = 22.25
Thus the AVERAGE parking price = 22.25/9 = 2.47 $
D is the correct answer.
Answer: (D)  $2.47
Question: A work which could be finished in 9 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 18
(B) 20
(C) 22
(D) 24
(E) 26
Rationale: Explanation:
x ------- 9
(x + 10) ---- 6
x * 9 = (x + 10)6
x = 20
Answer: B
Answer: (B) 20
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability u that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: In order to determine the probability u that the World Series will last less than 7 games, we can first determine the probability that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Answer: (D)  68.75%
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
(A) 1/38
(B) 1/36
(C) 1/37
(D) 1/39
(E) 1/32
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B
Answer: (B) 1/36
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?
(A) 80 km/hr
(B) 66 km/hr
(C) 60 km/hr
(D) 67 km/hr
(E) 22 km/hr
Rationale: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/6 = 3x => x = 100/9
So, speed of the faster train = 200/9 = 200/9 * 18/5 = 80 km/hr.
Answer:A
Answer: (A) 80 km/hr
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.83. How much was lent at 5%?
(A) 299
(B) 566
(C) 678
(D) 700
(E) 8277
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83
5x/100 + 90 – 6x/100 = 83
x/100 = 7
=> x =700
Answer:D
Answer: (D) 700
Question: The quantities S and T are positive and are related by the equation S=K/T, where k is a constant. If the value of S increases by 30 percent, then the value of T decreases by what percent?
(A) 25%
(B) 33 ¹/₃%
(C) 50%
(D) 66 ²/₃%
(E) 20%
Rationale: We can assign numbers:
lets say S = 2, K = 6 (constant) and T = 3 (so that S=K/T)
Now increasing S by 30% gives S=5, K remains constant, so T = 2 (6/2=3)
decrease in T= 1, percent decrease in T = (1/5)*100 =20%
Answer E
Answer: (E) 20%
Question: Arjun and Sajal are friends . each has some money. If Arun gives Rs. 30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives Rs. 10 to Arjun, the Arjun will have thrice as much as is left with Sajal. How much money does Arjun have?
(A) 62 Rs
(B) 63 Rs
(C) 64 Rs
(D) 72 Rs
(E) 68 Rs
Rationale: If arun had x rs , and sejal had y rs, then
2*(x-30) = y+30 or 2x-60= y+30 or y= 2x-90
and
x+10 = 3*(y-10)= 3*(2x-90-10)=6x-300
or
5x=310
x= 310/5 = 62 Rs with Arjun
ANSWER:A
Answer: (A) 62 Rs
Question: In a camp, there is a meal for 90 men or 180 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal ?
(A) 16
(B) 20
(C) 13
(D) 15
(E) 17
Rationale: Explanation :
There is a meal for 180 children. 150 children have taken the meal.
Remaining meal is to be catered to 30 children.
Now, 180 children = 90 men
So, 30 Children = (90/180) * 30 = 15 men
Answer : D
Answer: (D) 15
Question: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I.	x = z
II.	x > y > z
III. x > y
(A) I and II
(B) I only
(C) II only
(D) III only
(E) None
Rationale: 3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
III correct.
We can't say much about z though;
x=-5; y=-100; z=-95
II and I incorrect.
Ans:D
Answer: (D) III only
Question: An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same distance in 4 2/3 hours, it Must travel at a speed of
(A) 440
(B) 540
(C) 640
(D) 740
(E) 250
Rationale: Speed of aeroplane = 420 Kmph
Distance travelled in 6 hours
= 420 * 6 = 2520 Km
Speed of aeroplane to acver 2520 Km in 14/3
= 2520*3/14 = 540 Km
Answer B.
Answer: (B) 540
Question: A sum of Rs. 1190 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
(A) Rs. 120
(B) Rs. 210
(C) Rs. 240
(D) Rs. 300
(E) None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 1190
=> 17x/12 = 1190
=> 1190 x 12/ 17 = Rs.840
Hence, B’s share = Rs. (840/4) = Rs. 210.
Answer B
Answer: (B) Rs. 210
Question: John bought 9.25m of cloth for $397.75. Find the cost price per metre.
(A) 46
(B) 47
(C) 58
(D) 56
(E) 43
Rationale: Cloth bought by John = 9.25 m
Cost of 9.25 m = $397.75
Cost per metre = 397.75 ÷ 9.25
The cost of the cloth per metre = $ 43
Answers: E
Answer: (E) 43
Question: Initially, the boys and girls in a classroom were in the ratio of 2:3. Then, 4 boys entered the room and 3 girls left the room. Then, the number of girls tripled. Now there are 24 boys in the room. How many girls are currently in the room?
(A) 12
(B) 40
(C) 15
(D) 34
(E) 81
Rationale: Working backwards: 24 boys - 4 boys = 20 boys in the room initially.
From ratio boys:girls = 2:3 = 1:3/2 we have:
girls in the room initially = (3/2)(20) = 30.
From this we work forward: (3)(30 girls - 3 girls) = 81 girls in the room.
Answer: E
Answer: (E) 81
Question: If six persons sit in a row, then the probability that three particular persons are always together is
(A) 1/20
(B) 3/10
(C) 1/5
(D) 4/5
(E) 2/5
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5
ANSWER:C
Answer: (C) 1/5
Question: The average weight of 10 boys increases by 3.5 kg when a new boy comes in place of one of them weighing 50 kg. What might be the weight of the new boy?
(A) 85 kg
(B) 80 kg
(C) 75 kg
(D) 72 kg
(E) 65 kg
Rationale: Total weight increased = 10 x 3.5 kg = 35 kg.
Weight of new person = 50 + 35 kg =85 kg
Answer : A
Answer: (A) 85 kg
Question: Ashly and Vinnie work on a sales staff with 8 other salespeople. If five members of the staff will be chosen at random to attend a sales workshop, what is the probability that both Ashly and Vinnie will be chosen?
(A) 1/10
(B) 3/28
(C) 2/9
(D) 1/4
(E) 1/2
Rationale: I did slightly different and hence obviously ended up with the answer 2/9.
I assumed that because Ashly and Winni have to be chosen, the remaining selection is 3 people from 8.
8C3/10C5= 2/9. Option C.
Answer: (C) 2/9
Question: If f(x) = 2*(x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?
(A) f(x)
(B) -2f(x)
(C) 1/f(x)
(D) -1/f(x)
(E) 2*f(x)
Rationale: f(1/x) = ((1/x)^4 - 1) / ((1/x)^2)
= ((1/x^4) - 1) / (1/x^2)
= ((1-x^4)/(x^4)) / (1/x^2)
= (1-x^4)/(x^2)
= - 2( (x^4) -1) / (x^2)
= -2*f(x)
Answer is B.
Answer: (B) -2f(x)
Question: If x > 0, x/10 + x/25 is what percent of x?
(A) 6%
(B) 14%
(C) 37 1/2%
(D) 60%
(E) 75 %
Rationale: Just plug and chug. Since the question asks for percents, pick 100. (but any number will do.)
100/10 + 100/25= 10+4 =14
14 is 14% of 100=B
Answer: (B) 14%
Question: I came across this problem in the GMATprep software and got it totally wrong!
A company consists of 6 senior and 4 junior staff officers. If a committee is created with 2 senior and 1 junior staff officers, how many possible committees are there?
(A) 12
(B) 44
(C) 56
(D) 60
(E) 200
Rationale: 6C2*4C1
=60 = D
Answer: (D) 60
Question: The present worth of Rs. 2310 due 2 years hence, the rate of interest being 15% per annum, is:
(A) 1689
(B) 1680
(C) 1682
(D) 1681
(E) 1686
Rationale: P.W. = Rs. 100 x 2310 = Rs. 1680.
100 + 15 x	5
2
Answer: B
Answer: (B) 1680
Question: What is the minimum value of z for which z^2 + z - 3/10 > 0 is not true?
(A)  -5/2
(B)  -3/5
(C)  -1/5
(D)  1/4
(E)  1/5
Rationale: I think B -3/5 is the best ans...
Answer: (B)  -3/5
Question: If k is an integer and 0.0010101 x 10^k is greater than 100, what is the least possible value of k?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 0.0010101 * 10^k > 100
We need to move the decimal point to the right 5 places to get 101.01
This is equivalent to multiplying by 10^5.
The answer is D.
Answer: (D) 5
Question: A fraction becomes 4 when 1 is added to both the numerator and denominator, and it becomes 7 when 1 is subtracted from both the numerator and denominator. The numerator of the given fraction is :
(A) 2
(B) 3
(C) 7
(D) 15
(E) 17
Rationale: Explanation:
Let the required fraction be a/b
Then a+1/b+1=4⇒a−4b=3
and a−1/b−1=7⇒a−7b=−6
Solving these equations we get,
a=15
b=3
Correct Option: D
Answer: (D) 15
Question: IF 2+3=31 ; 3+5=134 ; 5+7=368 Then 7+11=?
(A) 1250
(B) 1360
(C) 1270
(D) 1380
(E) 1290
Rationale: 2^2 + 3^3= 4 + 27 = 31
3^2 + 5^3= 9 + 125 = 134
5^2 + 7^3= 25 + 343 = 368
and
7^2 + 11^3= 49 + 1331 = 1380
ANSWER:D
Answer: (D) 1380
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 700 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
(A) 511
(B) 546
(C) 552
(D) 562
(E) 570
Rationale: Number of newborns that can die in first month = 1/10 * 700 = 70
Survived = 630
Number of newborns that can die in second month = 1/10 * 630 = 63
Survived = 567
Number of newborns that can die in third month = 1/10 * 567 = 56
Survived = 511
Answer:A
Answer: (A) 511
Question: If 250!/10^n is an integer, what is the largest possible value of n?
(A) 65
(B) 66
(C) 62
(D) 69
(E) 97
Rationale: The question actually asks the highest power of 10 which divides 250! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
250 factorial will have 62 as -
250/5 = 50
50/5 = 10
10/5 =2
So answer will be (C) 62
Answer: (C) 62
Question: Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:
(A) 28 sec
(B) 36 sec
(C) 48 sec
(D) 52 sec
(E) 56 sec
Rationale: Relative speed = (60+ 90) km/hr
= 150x5/18
= 120/3 m/sec
Distance covered = (1.10 + 0.9) km = 2 km = 2000 m.
Required time = 2000 x 3/125 = 48 sec.
Answer : C.
Answer: (C) 48 sec
Question: Nobel played a cricket series. His 7 innings score as {50, 75, 90, 115 120, 135, 150 }, find the mean and median of cricket scores of Nobel respectively ?
(A) 105,115
(B) 100,120
(C) 143,90
(D) 115,105
(E) 100,130
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (50+ 75+ 90+ 115+ 120+ 135+ 150 )/7 = 105
Median = 115
Option A
Answer: (A) 105,115
Question: In how many different ways can the letters of the word 'BANANA' be arranged?
(A) 10 ways
(B) 120 ways
(C) 30 ways
(D) 60 ways
(E) 40 ways
Rationale: Totally there are 6 letters on the word BANANA. it contains 1B,3A,2N.
The no of ways is 6!/3!2!=120 ways.
ANSWER:B
Answer: (B) 120 ways
Question: The average age of a group of people were 60 person aged 40 exits the group and average increases to 65. How many people were in the group initally?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Let n be the number of people in the group
the new average;
65=60n-40/(n-1) => 65n-65=60n-40 => 5n=25 => n=5
Answer: C
Answer: (C) 5
Question: What is the dividend. divisor 18, the quotient is 9 and the remainder is 5?
(A) A)130
(B) B)134
(C) C)148
(D) D)158
(E) E)167
Rationale: D = d * Q + R
D = 18 * 9 + 5
D = 162 + 5
D = 167
Answer E
Answer: (E) E)167
Question: Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight?
(A) 2:9
(B) 2:7
(C) 1:6
(D) 1:4
(E) 1:3
Rationale: Ratio of A / Ratio of B = (Average Wt of Mixture - Wt of B)/(Wt of A - Average Wt of Mixture)
=> Ratio of A / Ratio of B = (4 - 3)/(10 - 4) = 1/6
So they should be mixed in the ratio 1:6
Answer - C
Answer: (C) 1:6
Question: At a circular table for eleven will sit nine adults and two small children. The two children will sit next to each other, and the two parents of the children will sit next to the children so that there is one parent on each side of the two children. If rotating their positions around the table is not considered changing the arrangement, in how many different ways can the eleven people be arranged around the table.
(A) 12,720
(B) 16,120
(C) 20,160
(D) 24,240
(E) 28,080
Rationale: Consider the two parents and two children as one unit.
Then there are seven adults and one family unit.
The number of ways 8 can form a line is 8!
Around a circular table, there would be 8 rotations so we divide this number by 8.
There are 7! ways for 8 to sit around the circular table.
Then the two children have two options and the two parents have two options.
Then the total number of ways is 7!*2*2= 20,160
The answer is C.
Answer: (C) 20,160
Question: In a set of integers, one-half of the numbers are multiples of 7 and one-third of the numbers are multiples of 3. If one-fifth of the numbers are multiples of both 3 and 7, then what percentage of the number are multiples of 7 but not multiples of 21?
(A) 9
(B) 15
(C) 30
(D) 33.3
(E) 60
Rationale: Say there are 210 number in the set (LCM of 2, 3, 5, and 7).
Multiples of 7 = 1/2*210 = 105;
Multiples of both 3 and 7, so multiples of 21 = 1/5*210 = 42.
Multiples of 7 but not 21 = 105 - 42 = 63.
The percentage = 63/210 = 3/10.
Answer: C.
Answer: (C) 30
Question: If the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 18
(B) 11.2
(C) 14
(D) 12
(E) 91
Rationale: 2 * 22/7 * 15 * x = 1056 => x
= 11.2
Answer: B
Answer: (B) 11.2
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) 1/23
Rationale: Explanation:
Total number of cases = 52
Favourable cases = 2
Probability = 2/56 = 1/26
ANSWER IS C
Answer: (C) 1/26
Question: if (64)^2 - (36)^2 = 10x, then x = ?
(A) 280
(B) 210
(C) 330
(D) 220
(E) 200
Rationale: a^2−b^2=(a−b)(a+b)
(64)^2 - (36)^2 = (64 - 36)(64 + 36) = 28 × 100
Given that (64)^2 - (36)^2 = 10x
=> 28 × 100 = 10x
=> x = 280
Answer is A
Answer: (A) 280
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 30 percent butterfat to obtain milk that is 20 percent butterfat?
(A) 6
(B) 8
(C) 14
(D) 16
(E) 28
Rationale: Equate the fat:
0.1x + 0.30*8 = 0.2(x + 8) --> x = 8.
Answer: B.
Answer: (B) 8
Question: If 2^4, 3^3, and 10^3 are factors of the product of 1,452 and w, where w is a positive integer, what is the smallest possible value of w?
(A) 198
(B) 288
(C) 363
(D) 360
(E) 484
Rationale: I will go with D (pending elements to match is 2^2*3^2*10^1 = 360
Answer: (D) 360
Question: In how many different ways can 4 physics, 4 math, and 4 chemistry books be arranged in a row so that all books of the same subject are together?
(A) 76,366
(B) 78,488
(C) 80,122
(D) 82,944
(E) 84,500
Rationale: Let's think of each subject as a group so there are 3 groups.
The number of ways to arrange these 3 groups is 3!
Within each subject the books can be re-arranged.
So we need to multiply 3! by 4!*4!*4! which is 3!*4!*4!*4! = 82,944
The answer is D.
Answer: (D) 82,944
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 3:2. The first number is:
(A) A)3
(B) B)98
(C) C)34
(D) D)35
(E) E)62
Rationale: (3x-9):(5x-9) = 3:2
x = 1 => 3x = 3
Answer:A
Answer: (A) A)3
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 6 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
(A) 2 hours
(B) 3 hours
(C) 5 hours
(D) 1 hour
(E) None of these
Rationale: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 6 hours, Tank A and B can effectively fill 1⁄12 × 6 = 1⁄2 of the tank.
Time taken to fill the remaining 1−(1/2) = 1/2 of the tank = (1/2)/(1/6) = 3 hours. Answer : Option B
Answer: (B) 3 hours
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 5 cm?
(A) 827 cm2
(B) 216 cm2
(C) 95 cm2
(D) 80 cm2
(E) 176 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (5)
= 95 cm2
Answer:C
Answer: (C) 95 cm2
Question: Albert invested an amount of $8000 in a fixed deposit scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?
(A) $8100
(B) $8820
(C) $8800
(D) $8810
(E) $8825
Rationale: Amount = 8000 x (1 + 5/100)^2)
= 8000 x 21/20 x 21/20
=8820.
Answer B)$8820
Answer: (B) $8820
Question: Two persons start running simultaneously around a circular track of length 600 m from the same point at speeds of 20 km/hr and 10 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
(A) 27 sec
(B) 87 sec
(C) 67 sec
(D) 72 sec
(E) 37 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 600 / (20 + 10)5/18 = 600 x 18 / 30 x 5 = 72 seconds.
Answer: D
Answer: (D) 72 sec
Question: The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 170 runs and his average excluding these two innings is 58 runs, find his highest score.
(A) 179
(B) 367
(C) 189
(D) 177
(E) 191
Rationale: Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 â€“ 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x â€“ 170
x + (x - 170) = 208
2x = 378
x = 189 runs
ANSWER: C
Answer: (C) 189
Question: At a speed of 50 miles per hour, a certain car uses 1 gallon of gasoline every 30 miles. If the car starts with a full 10 gallon tank of gasoline and travels for 5 hours at 50 miles per hour, the amount of gasoline used would be what fraction of a full tank?
(A) 3/25
(B) 5/6
(C) 7/12
(D) 2/3
(E) 25/36
Rationale: Gas used = (5 hours)*(50 miles/hour)*(1 gallon/30 miles) = 8+1/3 gallons
Portion used = (8+1/3) / 10 = 5/6
Ans B
Answer: (B) 5/6
Question: Nicky and Cristina are running a race. Since Cristina is faster than Nicky, she gives him a 36 meter head start. If Cristina runs at a pace of 6 meters per second and Nicky runs at a pace of only 3 meters per second, how many seconds will Nicky have run before Cristina catches up to him?
(A)  15 seconds
(B)  18 seconds
(C)  25 seconds
(D)  30 seconds
(E)  12 seconds
Rationale: used pluging in method
say t is the time for cristina to catch up with Nicky, the equation will be as under:
for Nicky=N=3*t+36
for Cristina=C=6*t
@t=12, N=72 C=72 right answer
ans:E
Answer: (E)  12 seconds
Question: Two sets of 3 consecutive positive odd integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
(A) 4
(B) 7
(C) 8
(D) 12
(E) it cannot be determined from the information given.
Rationale: A=(1,3,5), sum of this=9
B=(5,7,9), sum of this=21,
The differenct between 21-9=12
Hence,12 is the answer i.e.D
Answer: (D) 12
Question: How many real roots does the equation x^3y+16xy+64y=0 have if y < 0?
(A) 0
(B) 1
(C) 2
(D) 3
(E) Infinite
Rationale: x^3y+16xy+64y=0
=> y ( x^2 + 16x + 64) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-8
So although there are 2 factors , they are the same x=-8 .
The equations has 1 distinct real root .
Answer B
Answer: (B) 1
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) Rs.28,028
(B) Rs.28,002
(C) Rs.28,028
(D) Rs.28,000
(E) Rs.28,039
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer: D
Answer: (D) Rs.28,000
Question: If 244,312 football shoes need to be placed in boxes and each box can contain at most 5 pair of football shoes. How many pair of football shoes will be in the last unfilled box?
Options:
(A) 1football shoes
(B) 3 football shoes
(C) 4 football shoes
(D) 2 football shoes
(E) 9 football shoes
Rationale: The number of football shoes that can be placed in boxes of 5 football shoes is the first number that is divisible by 5 that occurs before 244,312.
In order to divide the sum in 5 parts, the amount must be divisible by 5
Divisibility rule of 5: the last digit is 5 or 0.
last digit of digits of 244,312 is 2 and 2 is not divisible by 5
Hence, we need to remove 2 to this number for it to be divisible by 5
Correct Option: D
Answer: (D) 2 football shoes