mathewhe/aqua_rat huggingface dataset:
Question: Darren bought 5 packs of white T-shirts and 3 packs of blue T-shirts for his basketball team. The white T-shirts come in packs of 6, and the blue T-shirts come in packs of 9. How many T-shirts did Darren buy in all?
(A) 77
(B) 57
(C) 34
(D) 65
(E) 21
Rationale: Step 1: Find the number of white T-shirts.
5 × 6 = 30
Step 2: Find the number of blue T-shirts.
3 × 9 = 27
Step 3: Find the total number of T-shirts.
30 + 27 = 57
Darren bought 57 T-shirts.
Answer is B.
Answer: (B) 57
Question: Three years ago, the ratio of ages of P and Q was 4:3. Six years from now, the ratio of their ages will be 7:6. What is P's age at present?
(A) 9
(B) 12
(C) 15
(D) 18
(E) 21
Rationale: 3(P-3)/4 = (Q-3). Then Q = 3(P-3)/4 + 3
6(P+6)/7 = Q+6
6(P+6)/7 = 3(P-3)/4 + 9
24P+144 = 21P + 189
3P = 45
P = 15
The answer is C.
Answer: (C) 15
Question: If 1+9+8=1, what is 2+8+9 ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: ONE + NINE + EIGHT = ONE (FIRST LETTER OF EACH WORD)
TWO + EIGHT + NINE = TEN (FIRST LETTER OF EACH WORD)
SO ANSWER IS 2+8+9 = 10
ANSWER:A
Answer: (A) 10
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 16
(B) 18
(C) 98
(D) 27
(E) 17
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Answer: (B) 18
Question: 1100 boys and 700 girls are examined in a test; 48% of the boys and 35% of the girls pass. The percentage of the total who failed is ?
(A) A)63.3%
(B) B)57.1%
(C) C)81.2%
(D) D)75.4%
(E) E)69.1%
Rationale: Total number of students = 1100+700 = 1800
Number of students passed = (48% of 1100+35% of 700) = 528+245 = 773
number of failures = 1027*100/1800 = 57.1%
Answer is B
Answer: (B) B)57.1%
Question: Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) 200
(B) 250
(C) 300
(D) 400
(E) 500
Rationale: Let z = 120% of z = 550
z+120/100z=550
11/5z=550
z=250
ANSWER B
Answer: (B) 250
Question: When two coins are tossed,Find the probability of getting all heads?
(A) 1/8
(B) 1/2
(C) 3/4
(D) 3/8
(E) 1/4
Rationale: When two coins are tossed,
S = {HH, HT, TH, TT} where H = Head and T = Tail
Let E = event of getting all heads
Then E = {HH}
so, P(E) = n(E)/n(S) =1/4
Answer: (E) 1/4
Question: Father is aged three times more than his son Suresh. After 8 years, he would be two and a half times of Suresh's age. After further 8 years, how many times would he be of Suresh's age?
(A) 2 times
(B) 2.(1/2)times
(C) 2(3/4) times
(D) 3 times
(E) 4 times
Rationale: F=4s
F+8 = 2.5(S+*0
solving these, F =32, S=8
After further 8 yrs,
F= 32+8+8=48
S=8+8+8=24 yrs
so 2 times.
ANSWER:A
Answer: (A) 2 times
Question: In a house, there are 4 birds, 3 dogs, and 18 cats living with the human family. If the total number of feet in the house are 74 more than the number of heads in the house, how many family members are there?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: Explanation: Let number of family members be x. Then, Total number of feet = 2 x 4 + 4 x 3 + 4 x 18 + 2x = 2x + 92. Total number of heads = 4 + 3 + 18 + x= 25 + x. Therefore (2x + 92) = (25+ x) + 74 or x = 7. Answer: D
Answer: (D) 7
Question: Two pipes P and Q can fill a cistern in 20 and 15 minutes respectively. Both are opened together, but at the end of 6 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/7
(B) 10 1/2
(C) 11 1/3
(D) 11 1/2
(E) 11 1/1
Rationale: 5/20+ x/15 = 1
x= 10 1/2.Answer: B
Answer: (B) 10 1/2
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 123
(B) 145
(C) 166
(D) 170
(E) 189
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold c bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2c
II. y > c
III. y > 3
(A) I only
(B) II only
(C) I and II
(D) II and III
(E) I, II, and III
Rationale: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(c-12) where c is the total number of bikes sold (when c>12).
C = cycles sold last week
CS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2CS
lets test all statements with C=0;
CS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with C=1;
CS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with X=6;
CS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Answer: (D) II and III
Question: A patient was given five pills which he is required to take one after every twenty minutes.
How long can the pills run for him?
(A) 1 hour
(B) 1 hour 20 minutes
(C) 1 hour 30 minutes
(D) 1 hour 35 minutes
(E) 1 hour 40 minutes
Rationale: Explanation:
He took the first pill at the zero minute.
He took the second pill after 20 minutes = 0+20=20
He took the third pill after 20 minutes = 20+20=40
He took the fourth pill after 20 minutes = 40+20=60
He took the fifth pill after 20 minutes = 60+20=80
Then it will last for 80 minutes or an hour and 20 minutes.
Answer B
Answer: (B) 1 hour 20 minutes
Question: A tradesman by means of his false balance defrauds to the extent of 10%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 20%
(B) 25%
(C) 27%
(D) 20%
(E) 21%
Rationale: g% = 10 + 10+ (10*10)/100
= 21%
ANSWER:E
Answer: (E) 21%
Question: There are 14 teams in a certain league and each team plays each of the other teams exactly once. What is the total number of games played?
(A) 91
(B) 98
(C) 105
(D) 112
(E) 119
Rationale: 14C2 = 91
The answer is A.
Answer: (A) 91
Question: A is twice as good workman as B, and together they complete a work in 20 days. In how many days can the work be complete by B alone?
(A) 35 days
(B) 65 days
(C) 45 days
(D) 60 days
(E) 95 days
Rationale: B=3A
60 days
D
Answer: (D) 60 days
Question: A bat is bought for Rs.400 and sold at a gain of 5% find its selling price?
(A) s.460/-
(B) s.480/-
(C) s.500/-
(D) s.420/-
(E) s.540/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
105 % ------> 420 (105 * 4 = 420)
Selling price = Rs.420/-
Option 'D'
Answer: (D) s.420/-
Question: The simple interest on a certain sum of money for 2 years at 10% per annum is half the compound interest on $100 for 2 years at 5% per annum. The sum placed on simple interest is ?
(A) $602.5
(B) $625.8
(C) $710.6
(D) $745
(E) $790.3
Rationale: C.I. = 100* (1 + 5/100)^2 - 100 = 100* 21/20 * 21/20 -100 = $120.5
Sum = 120.5*100/2*10 = $602.5
Answer is A
Answer: (A) $602.5
Question: The average runs of a cricket player of 8 innings was 24. How many runs must he make in his next innings so as to increase his average of runs by 8?
(A) 12
(B) 42
(C) 64
(D) 96
(E) 84
Rationale: Explanation:
Average after 9 innings = 32
Required number of runs = (32 * 9) – (24 * 8)
= 288 – 192 = 96
ANSWER D
Answer: (D) 96
Question: If a/b = 2, b/c = 3/2, c/d = 1/3, d/e = 2 and e/f = 2/3, then what is the value of abc/def ?
(A)  27/14
(B)  7/8
(C)  4/9
(D)  3/4
(E)  9/4
Rationale: Say a = 1. Then:
a/b = 2 --> b = 1/2;
b/c = 3/2 --> c = 1/3;
c/d = 1/3 --> d = 1;
d/e = 2 --> e = 1/2;
e/f = 2/3 --> f = 3/4.
abc/def = (1*1/2*1/3)/(1*1/2*3/4) = 4/9.
Answer: C.
Answer: (C)  4/9
Question: There are 6 girls and 6 boys. If they are to be seated in a row, what is the probability that no two boys sit together?
(A) A)1/12!
(B) B)6!5!/12!
(C) C)6!6!/12!
(D) D)2∗6!/12!
(E) E)none of these
Rationale: If girls are alternate, then only no 2 boys can be together.
So among 12 places, boys can be seated in 6 alternate places in 6! ways.
And girls can be seated in the remaining 6 places in 6! ways.
Therefore total number of ways = 6! * 6!
But there could be 2 such arrangements-->
1. When first place is filled by a girl
2. When first place is filled by a boy
Therefore total number of ways = 2*6! * 6!
Also total number of ways to fill 12 places = 12!
Hence probability =2∗6!6!/12!
Answer:E
Answer: (E) E)none of these
Question: A restaurant meal cost $38.75 and there was no tax. If the tip was more than 20 percent but less than 25 percent of the cost of the meal, then the total amount paid must have been between
(A) $40 and $42
(B) $39 and $41
(C) $38 and $40
(D) $37 and $39
(E) $46 and $48
Rationale: The total amount for the meal was between 38.75*1.2=46.5 and 38.75*1.25=~48.43. Only option which covers all possible values of the meal is E.
Answer: E
Answer: (E) $46 and $48
Question: A cloth, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:
(A) 20%
(B) 25%
(C) 28%
(D) 30%
(E) 35%
Rationale: length = x
decrease = xy = 80/100 * 90/100 y
xy - 18/25 xy
=7/25 xy
dec % = 7/25*1/xy*100 = 28
ANSWER C
Answer: (C) 28%
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 40 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
(A) j/140
(B) 7j/500
(C) 140j
(D) j/100+40
(E) 140j/100
Rationale: cost of 100 jackets = j dollars
each jacket costing 40% more is same as
all costing 40% more.
therefore over all price = 1.40j
price for each = 1.40j/100 => 14j/1000=7j/500
ANSWER:B
Answer: (B) 7j/500
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer:B
Answer: (B) 4
Question: If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 11/15 Find P(A|B)
(A) 11/4
(B) 2/3
(C) 3/2
(D) 4/5
(E) 4/7
Rationale: P(A|B) = P(A âˆª B)/P(B)
P(A|B) = (11/15)/(4/15) = 11/4.
A
Answer: (A) 11/4
Question: A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it take 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
(A) 1:3
(B) 3:8
(C) 6:3
(D) 8:3
(E) None
Rationale: Sol.
Let the man rate upstream be x kmph and that downstream be y kmph. Then,
Distance coverd upstream in 8 hrs 48 min. = Distance coverd downstream in 4 hrs.
⇒ [x 8 4/5] = (y * 4) ⇒ 44/5 x = 4y ⇒ y = 11/5 x.
∴ Required ratio = [y + x / 2] : [6x / 5 * 1/2] : [6x / 5 * 1/2]
= 8/5 : 3/5 = 8:3.
Answer D
Answer: (D) 8:3
Question: In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/4, then x + y =
(A)  6.5
(B)  7
(C)  8
(D)  11
(E)  12
Rationale: Line k passes through the origin and has slope 1/4 means that its equation is y=1/4*x.
Thus: (x, 1)=(4, 1) and (10, y) = (10,2.5) --> x+y=4+2.5=6.5
Answer: A.
Answer: (A)  6.5
Question: If s is the product of the integers from 70 to 80 inclusive, and if t is the product of the integers from 70 to 81 inclusive, what is 1/s + 1/t in terms of t?
(A) 32/t
(B) 42/t
(C) 52/t
(D) 62/2t
(E) 82/t
Rationale: Similarly in the actual problem
s =t/81. 1/s = 1/(t/81) or 1/s = 81/t
1/s + 1/t = 81/t + 1/t = 82/t
E
Answer: (E) 82/t
Question: Three candidates contested an election and received 1136, 7636 and 13000 votes respectively. What percentage of the total votes did the winning candidate get?
(A) 46%
(B) 60%
(C) 74%
(D) 63%
(E) 68%
Rationale: B
13000/(1136 + 7636 + 13000) = 60%.
Answer: (B) 60%
Question: If 3^x*4^y = 4,782,969 and x – y = 14, then x = ?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Since 4,782,969 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 14 and y = 0, then x = 14.
The answer is E.
Answer: (E) 14
Question: In the county of Veenapaniville, there are a total of 50 high schools, of three kinds: 25 public schools, 17 parochial schools, and 8 private independent schools. These 50 schools are divided between three districts: A, B, and C. District A has 18 high schools total. District B has 17 high schools total, and only two of those are private independent schools. If District C has an equal number of each of the three kinds of schools, how many private independent schools are there in District A?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: Total Private Schools = 8
Dist A: High Schools = 18 ==> Private Schools = ?
Dist B: High Schools = 17 ==> Private Schools = 2
Dist C: High Schools = 15 ==> Private Schools = 5
Therefore, 8 - 2 - 5 ==> 1
Answer A)
Answer: (A) 1
Question: 25 children are going to a picnic. What is the smallest number of cakes that must be brought to the picnic so that each child receives the same number of cakes?
(A) 35
(B) 40
(C) 15
(D) 75
(E) 9
Rationale: The number of children going to the picnic are 25
The answer will be D because only 75 is divisible by 25
Answer: (D) 75
Question: ? x 120 = 173 x 240
(A) 545
(B) 685
(C) 865
(D) 495
(E) 346
Rationale: Let y x 120 = 173 x 240
Then y = (173 x 240) /120
= 346.
ANSWER :E
Answer: (E) 346
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam.
(A) 11
(B) 23
(C) 25
(D) 77
(E) 81
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer: C
Answer: (C) 25
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 2
(B) 6
(C) 7
(D) 9
(E) 1
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:A
Answer: (A) 2
Question: Siddharth wants to borrow Rs.8000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.28.80
(B) s.21.29
(C) s.22.29
(D) s.21.26
(E) s.21.12
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.8,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 8,000{ [1 + 6/100]2 - 1 - 12/100}
= 8,000 {(1.06)2- 1 - 0.12} = 8,000(1.1236 - 1 - 0.12)
= 8,000 (0.0036) = 8 * 3.6 = Rs.28.80
Answer: A
Answer: (A) s.28.80
Question: A scale 6 ft. 8 inches long is divided into 4 equal parts. Find the length of each part.
(A) 17 inches
(B) 20 inches
(C) 15 inches
(D) 18 inches
(E) None of these
Rationale: Explanation:
Total length of scale in inches = (6*12) + 8 = 80 inches
Length of each of the 4 parts = 80/4 = 20 inches
ANSWER B
Answer: (B) 20 inches
Question: A gambler began playing blackjack with $110 in chips. After exactly 12 hands, he left the table with $320 in chips, having won some hands and lost others. Each win earned $100 and each loss cost $10. How many possible outcomes were there for the first 5 hands he played? (For example, won the first hand, lost the second, etc.)
(A) 10
(B) 18
(C) 26
(D) 32
(E) 64
Rationale: If X is number of wins and Y num of losses then
100X - 10Y = 210
10X-Y = 21......only when Y = 9 and X = 3 it satisfies....so we have 3 wins and 9 losses.
for first 5, we can have the following:
0 wins 5 losses = 1 way
1 win and 4 losses = 5C1 = 5
2 wins and 3 losses = 5C2 = 10
3 wins and 2 losses = 5C3 = 10
Add total ways = 26 ways
ANSWER:C
Answer: (C) 26
Question: . For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’s chances of winning. Let’s assume such rumors to be true and that in a match between Ghana and Bolivia; Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
(A) 59
(B) 88
(C) 77
(D) 26
(E) 18
Rationale: The probability that Paul correctly picks the winner = (A's Chances of winning)x(Pauls picking the winner corectly) + (A's chances of loosing) x (Paul picks wrongly) = 23×23+13×13=59
Answer:	A
Answer: (A) 59
Question: A certain quantity is measured on two different scales, the P-scale and the S-scale, that are related linearly. Measurements on the P-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the P-scale corresponds to a measurement of 100 on the S-scale?
(A)  20
(B)  36
(C)  48
(D)  60
(E)  84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that P increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, P will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: (C)  48
Question: Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:
(A) 6 2/3%
(B) 6 2/8%
(C) 6 4/3%
(D) 8 2/3%
(E) 2 2/3%
Rationale: S.P. = 102% of Rs. 600 = 102	x 600 = Rs. 612.
100
Now, P.W. = Rs. 612 and sum = Rs. 688.50.
T.D. = Rs. (688.50 - 612) = Rs. 76.50.
Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.
Rate = 100 x 76.50	%	= 16%
612 x	3
4
Answer: A
Answer: (A) 6 2/3%
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
(A) 2.4 km
(B) 2.5 km
(C) 3 km
(D) 3.6 km
(E) None
Rationale: Solution
Speed downstream = (5 + 1) kmph	= 6kmph.
Speed upstream = (5 -1) kmph	= 4 kmph.
Let the required distance be x km.
Then, x/6 + x/4 = 1
= 2x + 3x = 12
‹=›5x = 12
‹=›x = 2.4.
Answer A
Answer: (A) 2.4 km
Question: Set A contains three different positive odd integers and four different positive even integers. Set B contains two different positive odd integers and three different positive even integers. If one integer from set A and one integer from set B are chosen at random, what is the probability that the product of the chosen integers is even?
(A) 3/5
(B) 7/15
(C) 11/15
(D) 23/35
(E) 29/35
Rationale: There can be an odd product only if both integers are odd.
P(odd product) = 3/7*2/5 = 6/35
P(even product) = 1 - 6/35 = 29/35
The answer is E.
Answer: (E) 29/35
Question: For each positive integer,the quantitySn is defined such thatSn+2=(Sn)^2 -S(n+2).in addition ,S2=1.then which of the following must be true.
(A) a)S4 +S3 +1=0
(B) b)(S1)^2 +S4 +2=0
(C) c) ifS1=-1thenS4 is also equal to-1.
(D) d) ifS4 =-7thenS1=-2.
(E) e) ifS1 =-3thenS4=-7
Rationale: Since all the answers include S4, let's start from there.
S4=S2^2-S3
S3=S1^2-S2
Substituting S3 into the first equation we get:
S4=S2^2-(S1^2-S2)
Since S2=1
S4=1-(S1^2-1)
S4=2-S1^2
We need S1^2 in order to calculate S4.
E) provides S1 and from there we can calculate S4:
S4=2-(-3)^2
S4=-7
Correct.
As a side note, I would be very careful with answers in the formif S4=x then S1=y(such as option D ), as we are dealing with S1^2 (not S1), S1 can have two different values and it can not be determined for sure which root is the right answer.
For example:
If S4=-7 then S1=3 :
if we substitute S4 with - 7 we get:
-7=2-S1^2
S1^2=9
now S1 can be +/-3 !!
E
Answer: (E) e) ifS1 =-3thenS4=-7
Question: Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 8, how many people got on at the first stop?
(A) 128
(B) 64
(C) 32
(D) 16
(E) 8
Rationale: 7 - > 1
6 - > 2
5 - > 4
4 - > 8
3 - > 16
2 - > 32
1 - > 64
because people get off after the first stop
=> the formula will be : 2^(n-1) where n is the stop number
in this case n = 5
=> 2^(8-1) = 2^7 = 128
=> answer is A
Answer: (A) 128
Question: Set A contains all the even numbers between 2 and 50 inclusive. Set B contains all the even numbers between 102 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 2500
(B) 5050
(C) 11325
(D) 6275
(E) 2550
Rationale: SET A: {2, 4, 6, 8,...., 50}. Set of first 25 consecutive positive even numbers.
SET B: {102, 104, 106,....., 150}. Another set of 25 consecutive even numbers starting from 102.
Difference between 1st term of set A and that of set B is 100. Difference between 2nd term of set A and that of set B is 100.
Each term in set B is 100 more than the corresponding term in set A.
So sum of the differences of all the terms is (100 + 100 + 100 + ....) = 25 * 100 = 2500.
Answer: (A) 2500
Question: A and B start a business jointly. A invests Rs.16000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
(A) 27778
(B) 12800
(C) 27888
(D) 29778
(E) 17781
Rationale: 16*8: x*4 = 5:2
x = 12.8 => Rs.12800
Answer: B
Answer: (B) 12800
Question: 200 hundred multiples of seven are chosen at random, and 500 multiples of eight are chosen at random. Approximately what percentage of the 700 selected numbers are odd?
(A) 14.29%
(B) 15.29%
(C) 16.29%
(D) 17.29%
(E) 18.29%
Rationale: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....
Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.
So approx. 50 % of the 200 multiples are odd i.e 100 multiples.
--> Similalrly, for 8 multiples are:8,16,24...
All are even so 0 % are odd.
Total odd= (100+0)/(200+500)= 100/700=1/7 = 14.29%
Answer A
Answer: (A) 14.29%
Question: A man can row his boat with the stream at 8 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 2 kmph
(C) 8 kmph
(D) 7 kmph
(E) 5 kmph
Rationale: DS = 8
US = 4
S = ?
S = (8 - 4)/2 = 2 kmph
Answer: B
Answer: (B) 2 kmph
Question: A, B and C rents a pasture for Rs.480. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 270
(B) 199
(C) 676
(D) 149
(E) 122
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 480= 149
Answer: D
Answer: (D) 149
Question: What is the median from the below series 92, 93, 88, 95, 88, 97, 87, and 98
(A) 80
(B) 82
(C) 92.25
(D) 98
(E) 100
Rationale: Ordering the data from least to greatest, we get:
87, 88, 88,92, 93, 95, 96, 98
The median quiz score was 92.25 (Four quiz scores were higher than 92.25 and four were lower.)
C
Answer: (C) 92.25
Question: What is the prime factors’ number of 18?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^1*3^2
prime factors’ number will be 1+2 =3.
Hence, answer is B.
Answer: (B) 3