mathewhe/aqua_rat huggingface dataset:
Question: In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when a boy gets any no. of prizes?
(A) 45
(B) 70
(C) 64
(D) 56
(E) 67
Rationale: Ans.(C)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 4 ways, i.e. (4 x 4 x 4) ways = 43 ways = 64 ways Or nr ways = 43 ways = 64 ways
Answer: (C) 64
Question: 4,5,9,18,34,?
(A) 49
(B) 59
(C) 48
(D) 50
(E) 52
Rationale: 5-4=1
9-5=4
18-9=9
34-18=16
so, 34+25=59
ANSWER:B
Answer: (B) 59
Question: Pipe A can fill a tank in 8 hours, pipe B in 16 hours and pipe C in 48 hours. If all the pipes are open,in how many hours will the tank be filled ?
(A) 4.7
(B) 4.5
(C) 4.6
(D) 4.8
(E) 5
Rationale: 1/8+1/16+1/48=10/48=1/4.8. so 4.8 hrs
ANSWER:D
Answer: (D) 4.8
Question: A certain amount earns simple interest of 1750 after 7 years Had the interest been 2% more, how much more interest would it have earned?
(A) 35
(B) 245
(C) 350
(D) Cannot be determined
(E) None of these
Rationale: We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.
Answer D
Answer: (D) Cannot be determined
Question: A car runs at the speed of 30 km per hour when not serviced and runs at 120 kmph when serviced. After servicing the car covers a certain distance in 8 hours. How much time will the car take to cover the same distance when not serviced?
(A) 18 hours 12 minutes
(B) 32 hours
(C) 28 hours 15 minutes
(D) 17 hours 12 minutes
(E) None
Rationale: Explanation :
Time = 120*8 / 30 = 32 hours
Answer â€“ B
Answer: (B) 32 hours
Question: For any numbers a and b, a#b = ab(4 − b). If a and a#b both represent positive numbers, which of the following could be a value of b?
(A) 3.2.1
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: a#b positive then b may be positive or negative. if positive then b< 4 may be 3,2 or 1 and if negative then it is more than or equal to -negative . ab will be -ve which is not possible as a and a#b should be positive.
ans 3,2 and 1
A
Answer: (A) 3.2.1
Question: A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 111.12
(B) 111.67
(C) 111.64
(D) 111.11
(E) 101.12
Rationale: A runs 1000 m while B runs 900 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/900 = 8000/9 = 888.88 m.
B can give C = 1000 - 888.88 = 111.12 m.
Answer:A
Answer: (A) 111.12
Question: 10% of (50% of $500) is?
(A) $15
(B) $20
(C) $25
(D) $30
(E) $22
Rationale: 10% of (50% of $500) = 10/100 (50/100 * 500) = $25
Answer is C
Answer: (C) $25
Question: Let's say in a lottery John have a 4% chance of winning the jackpot.
All lined up and 1st four people on the line lose. John is 5th in the row.
What's the chance of John winning now?
(A) 5%
(B) 4%
(C) 6%
(D) 3%
(E) 7%
Rationale: B
The winning chance probability is still 4% as the outcome of Samuel winning the lottery is a separate event from the 1st four losing it.
Answer: (B) 4%
Question: A,B,C invested some money such that capital of C is half of B and capital of B is half of A. If they get a profit of Rs.7000 then profit share of B is
(A) Rs.3000
(B) Rs.2000
(C) Rs.2500
(D) Rs.3500
(E) Rs.3600
Rationale: Ratio of their capital ie c:b:a=1:2:4
Hence b's share of profit =2/(7) *7000=2000
ANSWER:B
Answer: (B) Rs.2000
Question: The average monthly salary of 24 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 400. What is the manager's monthly salary ?
(A) Rs. 11,522
(B) Rs. 11,500
(C) Rs. 11,128
(D) Rs. 11,228
(E) Rs. 11,129
Rationale: Manager's monthly salary
= Rs. (1900 x 25 - 1500 x 24)
= Rs. 11,500
Answer: B
Answer: (B) Rs. 11,500
Question: If x is a positive integer such that x3 + 8x2 + 12x-385 = 0, then x is
(A) less than 6
(B) between 7 and 11
(C) between 12 and 20
(D) between 22 and 34
(E) larger than 50
Rationale: Let f(x) = x3 +8x2 +12x􀀀385. Since
f(6) = 63 +862 + 126-385 = 62(6 +8 +2)-385 = 36 16 - 385 > 0
and f(0) = -385 < 0, there must be some t 2 (0; 6) for which f(t) = 0. Therefore, f(x)
has a positive real root between 0 and 6. Descartes' Rule of Signs implies that there is
only one positive real root, so the answer must be (a). Or one can observe that f(5) = 0
to obtain the answer.
correct answer A
Answer: (A) less than 6
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/458
(B) 12/456
(C) 12/455
(D) 12/453
(E) 12/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer:C
Answer: (C) 12/455
Question: A bicycle wheel has a diameter of 0.81m. How many complete revolutions does it make in 1km?
(A) 246
(B) 448
(C) 393
(D) 710
(E) 223
Rationale: 1 revolution = 3.14 * diameter.
Number of revolutions in 1km = 1000m / ( 3.14 * 0.81m ) = 393.2. Hence 393 complete revolutions.
Answer C
Answer: (C) 393
Question: We have 8 people and 5 chairs. In how many ways chairs can be occupy?
(A) 1200
(B) 1450
(C) 1680
(D) 1912
(E) 900
Rationale: no. of ways they can be occupy = 8*7*6*5 = 1680
Answer is C
Answer: (C) 1680
Question: there r 5 papers Ratio of marks obtained in each subject is 6:7:8:9:10. Total marks obtained is 60%. 50% is pass marks. In how many subjects did he get above 50%.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Total marks in 5 papers = 60% (i.e., 60*5 = 300)
6x+ 7x+ 8x+ 9x+ 10x =60/100(500)
Put x= 8 for solving,
6x= 48; 7x = 56; 8x = 64 ; 9x = 72; 10x = 80
Marks are 6:7:8:9:10 = 48+56+64+72+80
= 300
So, 4 subjects he got 50% above
ANSWER:D
Answer: (D) 4
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:
(A) Rs. 5400
(B) Rs. 7200
(C) Rs. 8400
(D) Rs. 9600
(E) None of these
Rationale: Explanation:
Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
ANSWER IS C
Answer: (C) Rs. 8400
Question: Dara ran on a treadmill that had a readout indicating the time remaining in her exercise session. When the readout indicated 24 min 18 sec, she had completed 10% of her exercise session. The readout indicated which of the following when she had completed 40% of her exercise session?
(A) 10 min 48 sec
(B) 14 min 52 sec
(C) 14 min 58 sec
(D) 16 min 6 sec
(E) 16 min 12 sec
Rationale: 90% of the exercise should be completed in 24min 18 sec (1458 sec)
When she completes 40% of her exercise timer should show the time remaining for 60% of her exercise.
If 90% requires 1458 sec then 60% requires --> (60 * 1458)/90 = (2/3)*(1458) = 2 * 486 = 972 secs
Required answer = 972/60 = 16 min 12 sec
Answer: E
Answer: (E) 16 min 12 sec
Question: Mike weighs twice as much as Mary. Mike's weight is 150% of Michelle's weight. Alan weighs 20% more than Charlie. Charlie weighs 170% of Mary's weight. Which of these 5 people weighs the highest?
(A) Mary
(B) Mike
(C) Michelle
(D) Alan
(E) Charlie
Rationale: Mary < Michelle < Mike
Charlie < Alan
Let x be Mary's weight.
Mike's weight is 2x and Alan's weight is 1.2*1.7x = 2.04x.
The answer is D.
Answer: (D) Alan
Question: Rahim bought 65 books for Rs.1150 from one shop and 50 books for Rs.920 from another. What is the average price he paid per book ?
(A) 11
(B) 18
(C) 99
(D) 787
(E) 12
Rationale: Average price per book = (1150 + 920) / (65 + 50)
= 2070 / 115
= Rs.18
Answer:B
Answer: (B) 18
Question: At what price must an article costing Rs.66.5 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 87.5
(B) 89.5
(C) 82.3
(D) 82.1
(E) 92.4
Rationale: CP = 66.5
SP = 66.5*(125/100) = 83.125
MP*(95/100) = 59.375
MP = 87.5
Answer:A
Answer: (A) 87.5
Question: What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage?
(A) 96.9
(B) 96.3
(C) 95.2
(D) 96.7
(E) 96.21
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-5+1/5
95.2
Thus the CP is Rs 95.2.
ANSWER: C
Answer: (C) 95.2
Question: A take twice as much time as B or thrice as much time to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in?
(A) 19
(B) 12
(C) 11
(D) 19
(E) 114
Rationale: Suppose A, B and C take x, x/2 and x/3 respectively to finish the work.
Then, (1/x + 2/x + 3/x) = 1/2
6/x = 1/2 => x = 12
So, B takes 6 hours to finish the work.
Answer: B
Answer: (B) 12
Question: Of the 40 animals at the shelter, 20 percent are cats. How many dogs must be adopted in order to bring the number of cats up to 50 percent of the animals in the shelter?
(A) 22
(B) 24
(C) 26
(D) 32
(E) 34
Rationale: Now, there are 8 cats (20% of 40) and 40-8=32 dogs at the shelter. We need there to be 8 cats and dogs, in this case there will be 50% cats and 50% dogs.
Therefore 32-8=24 dogs must be adopted.
Answer: B.
Answer: (B) 24
Question: A bus covers a certain distance at a speed of 54 kmph excluding stoppages and 45 kmph including stoppages.for how many minutes does the bus stop per hour?
(A) 5 min.
(B) 10 min.
(C) 15 min.
(D) 20 min.
(E) 30 min.
Rationale: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km =	9/54	x 60	min	= 10 min.
ANSWER:B
Answer: (B) 10 min.
Question: In a lottery, there are 11 prizes and 55 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 1/2
(B) 1/4
(C) 1/6
(D) 1/8
(E) 1/10
Rationale: P(winning a prize) = 11 / (11+55) = 11/66 = 1/6
The answer is C.
Answer: (C) 1/6
Question: Nitin's age was equal to square of some number last year and the following year it would be cube of a number. If again Nitin's age has to be equal to the cube of some number, then for how long he will have to wait?
(A) 10 years
(B) 38 years
(C) 39 years
(D) 64 years
(E) 52 years
Rationale: Explanation:
Clearly, we have to first find two numbers whose difference is 2 and of which the smaller one is a perfect square and the bigger one a perfect cube.
Such numbers are 25 and 27.
Thus, Nitin is now 26 years old. Since the next perfect cube after 27 is 64,
so required time period = (64 - 26) years = 38 years.
Answer: B
Answer: (B) 38 years
Question: The probability of a team winning a match given Matt is playing the match is 0.75. The probability of the team winning a match given Matt is not playing the match is 0.5. The probability of Matt playing any match is 0.8.
If it is known that the team has won the last match, what is the probability that Matt played the match?
(A) 0.8321
(B) 0.7
(C) 0.8571
(D) 0.7531
(E) 0.8213
Rationale: Out of 100 matches:
Matt is plays in 80 and not plays in 20.
Out of 80 matches Matt plays in, team wins 0.75*80 = 60.
Out of 20 matches Matt does not play in, team wins 0.5*20 = 10.
So, out of 100 matches 60 + 10 = 70 are won.
It is known that the team has won the last match. Out of 70 matches won, Matt is in 60: 60/70 = 0.8571...
Answer: C.
Answer: (C) 0.8571
Question: A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained $8400. Find the cost price of the Bike?
(A) 70000
(B) 60500
(C) 85000
(D) 60000
(E) 55000
Rationale: D
$60000
Answer: (D) 60000
Question: A solution of 66 litres contains milk and water in the ratio 7:x. If four litres of water is added to the solution, the ratio becomes 3:2, find the value of x?
(A) 8
(B) 5
(C) 3
(D) 4
(E) 2
Rationale: Exp. Total new quantity = original sol + water =66+4 =70
New ratio = 3:2, New quantity of milk =3/5*70 = 42 Lit,
New quantity of water = 2/5*70 = 28 Lit
Water present initially = (28-4) = 24 Lit
Ratio = 42/24 =7/4 There for x = 4
Answer: D
Answer: (D) 4
Question: Unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5. Choose exact number of cubes that can completely fill the box.
(A) 750
(B) 850
(C) 950
(D) 1050
(E) None of the above
Rationale: Let the dimensions of the box be, length=5*a, breadth=5*(a+1), height=5*(a+2)
Hence, volume=5*5*5*a*(a+1)*(a+2)
Among any 3 consecutive positive integers, we will either have (a number that is divisible by both 23) or (a number divisible by 2 and another number divisible by 3).
Volume= multiple of (125*2*3)
750=125*2*3
Answer:A
Answer: (A) 750
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 28,000 is made?
(A) 328897
(B) 120000
(C) 877888
(D) 124000
(E) 188871
Rationale: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 28,000 is made = 96,000 + 28,000 = Rs. 1,24,000
Answer: D
Answer: (D) 124000
Question: The difference between the two digit number and the number obtained by interchanging its digits is 54. The difference between the digits is?
(A) 4
(B) 6
(C) 1
(D) 7
(E) 8
Rationale: (10x + y) – (10y + x) = 54
x – y = 6
ANSWER:B
Answer: (B) 6
Question: Thirty percent of the women in a college class are science majors, and the non-science majors make up 60% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 35%
(B) 45%
(C) 55%
(D) 65%
(E) 75%
Rationale: Science majors make up 0.4 of the class.
60% of the class are women and 0.3*0.6 = 0.18 of the class are female science majors.
Then 0.22 of the class are male science majors.
0.4x = 0.22
x = 0.55 = 55%
The answer is C.
Answer: (C) 55%
Question: Two trains start simultaneously from opposite ends of a 150-km route and travel toward each other on parallel tracks. Train X, traveling at a constant rate, completes the 150-km trip in 4 hours. Train Y, travelling at a constant rate, completes the 150-km trip in 3.5 hours. How many kilometers had Train X traveled when it met Train Y?
(A) 68
(B) 70
(C) 72
(D) 74
(E) 76
Rationale: If the two trains cover a total distance D, then Train X travels (7/15)*D while Train Y travels (8/15)*D. If the trains travel 150 km to the meeting point, then Train X travels (7/15)*150 = 70 km. The answer is B.
Answer: (B) 70
Question: Some items were bought at 6 items for Rs. 5 and sold at 5 items for Rs. 6. What is the gain percentage?
(A) 44%
(B) 42%
(C) 46%
(D) 48%
(E) 41%
Rationale: gain percentage =(6*6/5*5-1)100
=11/25*100=44%
Answer : A
Answer: (A) 44%
Question: In how many different ways can the letters of the word 'DANCING' be arranged in such a way that the vowels always come together?
(A) A)360
(B) B)480
(C) C)720
(D) D)1440
(E) of these
Rationale: The word 'DANCING' has 7 different letters.
When the vowels AI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters DNCNG (AI).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (EAI) can be arranged among themselves in 2! = 2 ways.
Required number of ways = (720 x 2) = 1440.
ANSWER:D
Answer: (D) D)1440
Question: How many even number in the range between 20 to 100 inclusive are not divisible by 3
(A) 28
(B) 30
(C) 31
(D) 33
(E) 46
Rationale: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
20,22,24...100
using AP formula, we can say 100 = 20 + (n-1) *2
or n=41.
For 6,
24,36...96
using AP formu24la, we can say 96 = 24 + (n-1) *6
or n=13.
Hence, only divisible by 2 but not 3 = 41-13 = 28. hence, Answer A
Answer: (A) 28
Question: The area of a square field is 64816 sq m. How long will a lady take to cross the field diagonally at the rate of 7.2 km/hr?
(A) 2 min
(B) 4 min
(C) 5 min
(D) 3 min
(E) 3.5 min
Rationale: Area of a square field = 64816 sq m
Let the side of square = a
a^2 = 64816
=> a = 254.59
Diagonal = (2)^(1/2) * a
= 1.414 * 254.59
=360
Speed of lady = 7.2 km / hour
= 7200 m / hour
= 120 m / min
Time taken by lady to cross the field diagonally = 360/120 = 3 min
Answer D
Answer: (D) 3 min
Question: What is the lowest possible common multiple of 2 distinct integers, each greater than 150?
(A) 151
(B) 152
(C) 302
(D) 151*151
(E) 151*152
Rationale: The least common multiple of two numbers greater than 150 is 2(151) = 302, where the two distinct integers are 151 and 302.
The answer is C.
Answer: (C) 302
Question: From a group of 6boys&4girls a Committee of 4 persons is to be formed. In how many different ways can it be done, so that the committee has at least 2 boys?
(A) 120
(B) 130
(C) 185
(D) 195
(E) 210
Rationale: The committee of 4 persons is to be so formed that it has at least 2 men. The different ways that we can choose to form such a committee are:
(i) 2m. 2w in 6C2 x 4 C1=6X5 - 2X1 X 3X3 2X1 =n an (ii) 3m. 1w in 6C3 x 4C1 =6X5X4 3X2X1 X4 _n - a ''''
(iii) 4m in 6C4 -2x1 = 15 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least 2 men. = 90 + 18 + 15 = 185
C
Answer: (C) 185
Question: A man sells an article at 5% profit. If he had bought it at 5% less and sold it for 1 less, he would have gained 10%. The cost price of the article is :
(A) 200
(B) 150
(C) 240
(D) 280
(E) None of these
Rationale: Let the CP of the article be x.
Then, SP = 105x⁄100
Now, new CP = 95x⁄100 and new SP = 105x⁄100 - 1
According to the question
105x/100−1−95/100=10×95x/100×100
∴ x = 200
Answer A
Answer: (A) 200
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
(A) 12/457
(B) 12/456
(C) 12/455
(D) 12/454
(E) 12/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
Answer: C
Answer: (C) 12/455
Question: A circle graph shows how the budget of a certain company was spent: 55 percent for salaries, 9 percent for research and development, 5 percent for utilities, 4 percent for equipment, 2 percent for supplies, and the remainder for transportation. If the area of each sector of the graph is proportional to the percent of the budget it represents, how many degrees of the circle are used to represent transportation?
(A) 18°
(B) 36°
(C) 54°
(D) 72°
(E) 90°
Rationale: The percent of the budget for transportation is 100 - (55+9+5+4+2)= 25%
100% of the circle is 360 degrees.
Then (25%/100%)*360 = 90 degrees
The answer is E.
Answer: (E) 90°
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) 23%
(B) 56%
(C) 70%
(D) 35%
(E) 20%
Rationale: C
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 = 420 - 125 = Rs. 295
Required percentage = 295/420 * 100 = 1475/21 = 70%
Answer: (C) 70%
Question: The digits of a two-digit number differ by six. Find the difference of the number and the number formed by reversing its digits?
(A) 54
(B) 45
(C) 87
(D) 78
(E) 95
Rationale: let the tens digit be x and ones digit be y
x-y =6
10x+y - (10y+x) = 9x-9y = 9 (x-y) = 9*6 = 54
ANSWER:A
Answer: (A) 54
Question: A 12% stock yielding 10% is quoted at:
(A) Rs. 83.33
(B) Rs. 110
(C) Rs. 112
(D) Rs. 120
(E) Rs. 140
Rationale: Income of Rs 10 on investment of Rs 100
Income of Rs 12 on investment of ?
= (12*100)/10=120
ANSWER:D
Answer: (D) Rs. 120
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 34
(B) 387
(C) 42
(D) 28
(E) 71
Rationale: Explanation:
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
{\color{Blue} \therefore } 125 : 150 :: 35 : x {\color{Blue} \Rightarrow } 125 x x = 150 x 35
{\color{Blue} \Rightarrow x=\frac{150\times 35}{125}}
{\color{Blue} \Rightarrow } x = 42.
Answer: C) 42
Answer: (C) 42
Question: The total car population in a Mumbai is 2,94,00 out of which 1,50,00 are made by Honda. Out of every 100 Honda cars, 98 are red in color, but only 53% of the total car population is red. Find the % of non-Honda cars that are red
(A) 4%
(B) 4.65%
(C) 6.125%
(D) 7.24%
(E) 7.45%
Rationale: Total Car.29.10 i.e., Honda +non Honda = 29400 Given: Whim. tractor .150W
Now,5346 of 2..00 = Honda +Red Non-Honda 29400 .:4 =15582 Thus...El Mall... 1.0 Now Honda 15582 flow, Non-. Honda =15582 - 15.582-14700=8B2 96 non-Honda =1=1.100 = 6.125%
C
Answer: (C) 6.125%
Question: A reduction of 20% in the price of salt enables a lady to obtain 25 kgs more for Rs.100, find the original price per kg?
(A) 6
(B) 1
(C) 5
(D) 4
(E) 7
Rationale: 100*(20/100) = 20 --- 25
? --- 1 => Rs.0.8
100 --- 80
? --- 0.8 => Rs.1
Answer: B
Answer: (B) 1
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 2/3 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 1/2
(B) 2/3
(C) 3/5
(D) 4/5
(E) 5/8
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (2x/3)(3y/4) = xy/2
The total number of boxes is xy + xy/2 = 3xy/2
The fraction loaded by the day crew is xy / (3xy/2) = 2/3
The answer is B.
Answer: (B) 2/3
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 14, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/40
(E)  3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 14 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is D.
Answer: (D)  3x/40
Question: If each side of a square is increased by 25%, find the percentage change in its area?
(A) 56.29%
(B) 56.25%
(C) 56.95%
(D) 53.25%
(E) 36.25%
Rationale: let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%
Answer: B
Answer: (B) 56.25%
Question: In how many ways can the letters of wordTREATMENTbe arranged such that all the Consonants always appear together?
(A) 9!
(B) 4!*6!
(C) 5!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (9 letters, 3 vowels e, a, e and 6 consonant t, r, t, m, n, t)
For all consonants together, consider them as 1 group {t, r, t, m, n, t} E A E --> this gives us 4! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 6! ways
Thus total arrangements with all consonants together = 4!*6! --> B is the correct answer.
Answer: (B) 4!*6!
Question: In right triangle ABC, AC is the hypotenuse. If AC is 40 and AB + BC = 60, what is the area of the triangle ABC?
(A) 225
(B) 450
(C) 25√2
(D) 500
(E) 200√2
Rationale: Square AB + BC = 60:
(AB)^2 + 2*AB*BC + (BC)^2 = 3600. Since (AC)^2 = (AB)^2 + (BC)^2 = 40^2 = 1600, then (AB)^2 + 2*AB*BC + (BC)^2 = 1600 + 2*AB*BC = 3600.
1600 + 2*AB*BC = 3600.
AB*BC = 1000.
The area = 1/2*AB*BC = 500.
Answer: D.
Answer: (D) 500
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 19%
(B) 11%
(C) 18%
(D) 218%
(E) 14%
Rationale: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP = Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer:C
Answer: (C) 18%
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $50,000?
(A) $38,796.
(B) $48,720.
(C) $38,976.
(D) $39,679.
(E) $36,796.
Rationale: 50,000 *1.16*.84=48,720
Answer B
Answer: (B) $48,720.