mathewhe/aqua_rat huggingface dataset:
Question: From a group of 19 astronauts that includes 10 people with previous experience in space flight, a 3-person crew is to be selected so that exactly 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
(A) 380
(B) 370
(C) 350
(D) 360
(E) 340
Rationale: number of astronauts with previous experience = 10
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group
(10C1)*(9C2)
=10*36= 360
Answer : D
Answer: (D) 360
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 7 kmph
(B) 5 kmph
(C) 3 kmph
(D) 8 kmph
(E) 2 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer: D
Answer: (D) 8 kmph
Question: the sum of series represented as
1/(1*5) + 1/(5*9) + 1/(9*13) +..... + 1/(221*225) is
(A) 28/221
(B) 56/221
(C) 56/225
(D) 54/225
(E) none of these
Rationale: 1/(1*5) + 1/(5*9) + 1/(9*13) +..... + 1/(221*225)
=(1/4)*[(5-1)/(1*5) + (9-5)/(5*9) + (13-9)/(9*13) +..... + (225-221)/(221*225)]
=(1/4)*[(1- 1/5)+(1/5 - 1/9)+(1/9 -1/13)+...(1/221 -1/225)]
=(1/4)*(1- 1/225)
=(1/4)*(224/225)
=56/225
ANSWER:C
Answer: (C) 56/225
Question: Before leaving for his business trip, Chad asks his assistant to choose and pack five shirts from his closet, which currently contains eight shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the shirts packed but the blue shirt will not?
(A) 1/5
(B) 3/7
(C) 5/14
(D) 9/28
(E) 15/56
Rationale: The total number of ways to choose 5 shirts from 8 is 8C5 = 56
The number of ways to choose a pink shirt plus 4 shirts from 6 is 6C4 = 15
P(a pink shirt but not a blue shirt) = 15/56
The answer is E.
Answer: (E) 15/56
Question: By using the numbers 0, 2, 3, 5 and 4 only once, how many five digit numbers can be made that are divisible by 8?
(A) 18
(B) 24
(C) 48
(D) 16
(E) 52
Rationale: A number to be divisible by 8 must end with 8, 16, 24,32,40...
So, there are the following cases possible:
035-24 --> the first three digits can be arranged in 3=6 ways.
054-32--> the first three digits can be arranged in 3=6 ways.
235-40--> the first three digits can be arranged in 3=6 ways.
Total = 6+6+6 = 18.
Answer: A.
Answer: (A) 18
Question: Of the following values of n, the value of (-1/7 )^(-n) will be greatest for n =
(A) 3
(B) 2
(C) 0
(D) -2
(E) -3
Rationale: imo -2
(-17)^-2=
1/(1/49)=49
oops i meant 2
B
Answer: (B) 2
Question: The average age of A and B is 40 years. If C were to replace A, the average would be 38 and if C were to replace B, the average would be 52. What are the age of A, B and C?
(A) 40, 38, 52
(B) 40, 20, 26
(C) 36, 80, 20
(D) 54, 26, 50
(E) None of the above
Rationale: Given A + B = 80â€¦(i)
C + B = 76 â€¦ (ii)
A + C = 104â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C = 130 â€¦(iv)
from (i) and (iv), we get
C = 50 years
âˆ´ B = 26 years and A = 54 years
Answer D
Answer: (D) 54, 26, 50
Question: Steve traveled the first 2 hours of his journey at 55 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
(A) 60 mph
(B) 56.67 mph
(C) 70 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Distance traveled in 2 hours = 2 * 55 = 110 m
Distance traveled in 3 hours = 3 * 80 = 240m
Total distance covered = 240 + 110 = 350m
Total time = 2 + 3 =5 h
Hence avg speed = total distance covered / total time taken
= 350/5 = 70mph
Answer: C
Answer: (C) 70 mph
Question: The sum of ages of 5 children born 2 years different each is 40 years. What is the age of the Elder child?
(A) 12
(B) 9
(C) 10
(D) 16
(E) 17
Rationale: Let the ages of children be x, (x + 2), (x + 4), (x + 6) and (x + 8) years.
Then, x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 40
5x = 20
x = 4.
x+8= 4+8= 12
Answer : A
Answer: (A) 12
Question: What is the difference between the largest and the smallest number written with 7, 7, 0, 7?
(A) 6893
(B) 6993
(C) 6093
(D) 693
(E) None
Rationale: 7770
7077
-------------
693
ANSWER:D
Answer: (D) 693
Question: If "PROMPT" is coded as QSPLOS ,then "PLAYER" should be
(A) FKSKJH
(B) DSKUIW
(C) SHOUSA
(D) QMBXDQ
(E) SUISDUH
Rationale: Explanation:
1st 3 letters are denoted by its next alphabet and the next 3 letters are denoted by its previous alphabets.
Answer: D
Answer: (D) QMBXDQ
Question: If a: b = 1:4, b:c = 13:9, c:d = 5:13, find a:d?
(A) 5/46
(B) 7/36
(C) 1/36
(D) 5/36
(E) 5/37
Rationale: a/d = (1/4)*(13/9)*(5/13) => 5/36
ANSWER:D
Answer: (D) 5/36
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 2/3
(C) 3/5
(D) 5/7
(E) 7/8
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Answer: (A) 1/2
Question: In the following question, a matrix of certain characters is given.These characters follow a certain trend, row-wise or column wise.Find out this trend and choose the missing character accordingly.
(A) 12
(B) 372
(C) 38
(D) 37
(E) 39
Rationale: Explanation:
In the first row, 72 ÷ (24/2) = 72 ÷ 12 = 6.
In the second row, 96 ÷ (16/2) = 96 ÷ 8 = 12.
Let the missing number in the third row be y.
Then, 108 ÷ (y/2) = 18 or y/2 = 108/18 = 6 or y = 12.
Answer: A) 12
Answer: (A) 12
Question: A man swims downstream 36 km and upstream 26 km taking 2 hours each time, what is the speed of the man in still water?
(A) 9
(B) 18.4
(C) 15.5
(D) 16.7
(E) 13.4
Rationale: 36 --- 2 DS = 18
? ---- 1
26 ---- 2 US = 13
? ---- 1 M = ?
M = (18 + 13)/2 = 15.5
Answer: C
Answer: (C) 15.5
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.6300. How much third person will get?
(A) 2400
(B) 2429
(C) 2980
(D) 2707
(E) 2800
Rationale: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 6300 = 2800
Answer:E
Answer: (E) 2800
Question: A local club has between 24 and 57 members. The members of the club can be separated into groups of which all but the final group, which will have 3 members, will have 4 members. The members can also be separated into groups so that all groups but the final group, which will have 3 members, will have 5 members. If the members are separated into as many groups of 6 as possible, how many members will be in the final group? (Source: Bell Curves)
(A) 6
(B) 5
(C) 3
(D) 2
(E) 1
Rationale: Case 1: Final group = 3; Rest of the group = 4A; Number of members = 4A + 3
Case 2: Final group = 3; Rest of the group = 5B; Number of members = 5B + 3
4A + 3 = 5B + 3
4A = 5B --> Possible values = 20, 40, 60, ........ --> But only 40 satisfies the given conditions
Number of members = 40 + 3 = 43
When divided into groups of 6, final group will have 1 member (6*7 + 1).
Answer: E
Answer: (E) 1
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 22772
(B) 20982
(C) 26882
(D) 11750
(E) 28812
Rationale: 200 + 130 = 330
800 - 330 = 470
200 ---- 5000
470 ---- ? => 11750.Answer: D
Answer: (D) 11750
Question: A cake shop has a surplus of cupcakes and prices them at 15% below the wholesale price of $3. A customer comes in with a coupon for 10% off a dozen cupcakes. How much does that customer pay for a dozen cupcakes?
(A) $27.56
(B) $28.52
(C) $30.60
(D) $27
(E) $27.54
Rationale: Wholesale cost of cupcakes = $3
Cupcakes were priced at 15% below $3 = $2.55
Cost of a dozen cupcakes = 12 * 2.55 = $30.60
% discount given by coupon = 10%
Customer paid = .9 * 30.6 = $27.54
Answer E
Answer: (E) $27.54
Question: Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much R does she have in her account after two years?
(A) $10079.44
(B) R=$10815.83
(C) $12652.61
(D) $14232.14
(E) $20598.11
Rationale: PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
Answer: (B) R=$10815.83
Question: What is the ratio whose terms differ by 40 and the measure of which is 2⁄7?
(A) 16 : 56
(B) 14 : 56
(C) 15 : 56
(D) 16 : 72
(E) None of these
Rationale: Let the ratio be x: (x + 40).Then,
x/(x+40)=2/7 ⇒ 2x + 80 ⇒ x = 16.
∴ Required ratio = 16 : 56.
Answer A
Answer: (A) 16 : 56
Question: A group of boy scouts and girls scouts is going on a rafting trip. 52% of the scouts arrived with signed permission slips. If 40% of the scouts were boy scouts and 62.5% of the boy scouts arrived with signed permission slips, then what percentage of the children were girl scouts who arrived with signed permission slips?
(A) 27
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: We don't know how many scouts went on the trip, so let's assume 100 scouts went on the trip (since we only are concerned with percents in the answer)
40% were boy scouts so 40% of 100 = 40 were boy scouts
62.5% of the boy scouts brought their permission slips signed, so .625*40 = 25 boy scouts had signed slips
15 boy scouts did not
52% of all the scouts had signed slips, so .52*100 = 52 in total had signed slips
thus 52 - 25 = 27 girl scouts had signed slips
thus the percentage of scouts who were girl scouts arriving with signed permission slips is 27/100 = .27 = 27%
A
Answer: (A) 27
Question: A and B can together finish a work in 30 days. They worked at it for 20 days and then B let. The remaining work was done by A alone in 20 more days. B alone can do the entire work in
(A) 48 days
(B) 50 days
(C) 54 days
(D) 60 days
(E) 67 days
Rationale: A+B 's 1 day work = 1/30
A+B's 20 days work = 20*1/30 = 2/3
Remaining work left = 1-2/3 = 1/3
A does 1/3 work in ---> 20 days
A does 1 work in ---> x days
x = 3*20 = 60 days
A ll take 60 days to complete the whole work
A's 1 day work = 1/60
Therefore B's 1 day work = (A+B)'s 1 day work - A's 1 day work
=> 1/30 - 1/60
=1/60
So B's 1 day work = 1/60
B ll complete the entire work alone in 60 days
ANSWER:D
Answer: (D) 60 days
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. IN what ratio will the profit be shared at the end of 3 years?
(A) 3:4:9
(B) 3:4:7
(C) 3:4:5
(D) 3:4:1
(E) 3:4:2
Rationale: A:B:C = (40000 * 36) : (80000 * 12 + 40000 * 24) : (120000 * 24 + 40000 * 12)
= 144:192:336
= 3:4:7
Answer:B
Answer: (B) 3:4:7
Question: Three pipes, A, B, & C are attached to a tank. A & B can fill it in 20 & 30 minutes respectively while C can empty it in 15 minutes. If A, B & C are kept open successively for 4 minute each, how soon will the tank be filled?
(A) 2 hours
(B) 12 hours
(C) 3 hours
(D) 5 hours
(E) 6 hours
Rationale: in three minute 1/20+1/30-1/15=1/60 part is filled
12 min--------1/60 parts
x min--------- 1 part(full)
x=720 min =12 hours
ANSWER:B
Answer: (B) 12 hours
Question: A person was asked to state his age in years. His reply was , "Take my age 3 years hence, multiply it by 3 and subtract 3 times my age 3 years ago and you will know how old I am." What was the age of the person ?
(A) 18
(B) 92
(C) 27
(D) 26
(E) 19
Rationale: Explanation:
Let the present age of person be x years.
Then, 3(x + 3) - 3(x - 3 ) = x <=> (3x + 9) - (3x - 9) = x <=> x = 18..
Answer: A) 18
Answer: (A) 18
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are:
(A) Rs. 10,500, Rs. 13,500, Rs. 16,500
(B) Rs. 10,500, Rs. 13,500, Rs. 16,508
(C) Rs. 10,500, Rs. 13,500, Rs. 16,56
(D) Rs. 10,500, Rs. 13,500, Rs. 16,57
(E) Rs. 10,500, Rs. 13,500, Rs. 16,502
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
nual profit of Rs. 40,500 are:
Answer:A
Answer: (A) Rs. 10,500, Rs. 13,500, Rs. 16,500
Question: A student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let the number of people to choose from = n
No of people to be chosen = 2
The number of ways 2 people can be chosen from n people=nC2
Now, the two people selected can be arranged in 2! ways
Hence nC2*2!=90 which gives n=10
ANSWER:D
Answer: (D) 10
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 1
(B) 8
(C) 7
(D) 5
(E) 4
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: A, B and C's age is in ratio 2:5:7. Find their ages if the sum of their age is 70 years.
(A) 10 , 25 and 35
(B) 5, 20 and 35
(C) 8, 20 and 32
(D) 11, 23 and 27
(E) 10, 20 and 30
Rationale: Let the age of A, B and C be 2x, 5x and 7x.
2x + 5x + 7x = 70
14x = 70
x = 5
The ages are 10, 25 and 35.
Answer : A
Answer: (A) 10 , 25 and 35
Question: The price of 24 apples is equal to that of 28 oranges. The price of 45 apples and 60 oranges together is Rs.1350. The total price of 30 apples and 40 oranges is
(A) 850
(B) 900
(C) 750
(D) 950
(E) 800
Rationale: Let the price of one apple = a and price of one orange = b
Price of 24 apples is equal to that of 28 oranges
24a = 28b
=> 6a = 7b
⇒b=6a/7 -----(Equation 1)
price of 45 apples and 60 oranges together is Rs.1350
=> 45a + 60b = 1350
=> 3a + 4b = 90
⇒3a+4(6a)/7=90 (∵ Substituted the value of b from equation 1)
⇒a+4(2a)/7=30
=> 7a + 8a = 30 × 7 = 210
=> 15a = 210
⇒a=21015=423=14
b=6a7=(6×14)/7=6×2=12
Total price of 30 apples and 40 oranges
= 30a + 45b = (30 × 14) + (40 × 12) = 420 + 480 = 900
Answer is B.
Answer: (B) 900
Question: Two water pumps, working simultaneously at their respective constant rates, took exactly nine hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 times the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
(A) 12
(B) 14
(C) 15
(D) 16
(E) 18
Rationale: Let x be the rate of the slower pump. Then 1.5x is the rate of the faster pump.
Both pumps together can fill 1/6 of the pool each hour.
2.5x = 1/9
x = 1/22.5
1.5x = 1.5/22.5 = 1/15
The faster pump could fill the pool in 15 hours.
The answer is C.
Answer: (C) 15
Question: (1/5)^f * (1/4)^18 = 1/(2(10)^35). What is f?
(A) 17
(B) 18
(C) 34
(D) 35
(E) 36
Rationale: We need to arrive at a common base. -->
(5)^(-f) * 2^(-36) = 2^(-36)*5^(-35)
5^(-f)=5^(-35)
-f=-35
f=35=D
Answer: (D) 35
Question: The average of 17 numbers is 59. Average of the first 9 of them is 56 and that of the last 9 is 63. Find the 9th number?
(A) 64
(B) 68
(C) 65
(D) 66
(E) 67
Rationale: Sum of all the 17 numbers = 17 * 59 = 1,003Sum of the first 9 of them = 9 * 56 = 504Sum of the last 9 of them = 9 * 63 = 567So, the 8th number = 504 + 567 - 1,003= 68.Answer: B
Answer: (B) 68
Question: A grocer has a sales of Euro 6435, Euro 6927, Euro 6855, Euro 7230 and Euro 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Euro 6500?
(A) Euro 4691
(B) Euro 4591
(C) Euro 3591
(D) Euro 7791
(E) Euro 4991
Rationale: E
Euro 4991
Total sale for 5 months = Euro (6435 + 6927 + 6855 + 7230 + 6562) = Euro 34009.
Required sale = Euro [ (6500 x 6) - 34009 ]
= Euro (39000 - 34009)
= Euro 4991.
Answer: (E) Euro 4991
Question: The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
(A) 18 cm
(B) 20 cm
(C) 22 cm
(D) 24 cm
(E) 25 cm
Rationale: 2(l + b) = 5
b 1
2l + 2b = 5b
3b = 2l
b = 2 l
3
Then, Area = 216 cm2
l x b = 216
l x 2 l = 216
3
l2 = 324
l = 18 cm.
A
Answer: (A) 18 cm
Question: A room contains 100 people, 20 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 50
(B) 40
(C) 30
(D) 20
(E) 10
Rationale: (1) 100 total = 20% women ~ 20 women
(2) x left = 30% x women
(3) 100-x left in the room = 10%(100-x) women
--> (1)=(2) + (3)
--> 30% x + 10%(100-x) = 20
--> 20% x = 10
--> x = 50
Answer is A
Answer: (A) 50
Question: Prakash has 3 pairs of shoes; each pair is a different color. If Prakash randomly selects 2 shoes without replacement from the 6 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 1/5
(C) 1/9
(D) 1/10
(E) 1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 6 shoes = 6/6 = 1
Probability of selecting the next shoe (out of 6 available) having the same color = 1/5 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/5=1/5.
B is the correct answer.
Answer: (B) 1/5
Question: In an exam, B scored 60 percent, C scored 40 percent and D 59 percent. The maximum score awarded in the exam is 600. Find the average mark scored by all the three candidates?
(A) 316
(B) 318
(C) 320
(D) 322
(E) 324
Rationale: Average mark scored by all the three boys
= [60/100 (600) + 40/100 (600) + 59/100 (600)] / 3
= 318
Answer: B
Answer: (B) 318
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) 44 years
Rationale: current age = 26 years because Nitin's age was equal to square of some number ( 25= 5^2) last year and the following year it would be cube of a number (27= 3^3).
Next cube age will be 64 =4^3 which will come after 64-26 = 38 years.
ANSWER:B
Answer: (B) 38 years
Question: Akhil purchased 70kg vegetable at Rs. 420, then sold them at the rate of Rs. 6.50 per kg, find the profit percent.
(A) 8 1/3%
(B) 7 1/3%
(C) 6 1/3%
(D) 5 1/3%
(E) 4 1/3%
Rationale: Explanation:
Please note in this type of questions, get the value of 1 kg to solve this question, lets solve it.
C.P. of 1 Kg = 420/70 = Rs. 6
Selling Price = 6.50
Gain = Rs. 0.50
Gain%=.50/6∗100=8 1/3%
Option A
Answer: (A) 8 1/3%
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c-a=2
II. -abc is positive integer
III. (a+b+c)/3 is an integer
(A) I & III only
(B) II
(C) I and II
(D) II and III
(E) I, II and III
Rationale: If a, b, c are consequitive positive integers and a<b<c, which of the following must be true?
1. c-a=2
2. abc is an even integer
3. (a+b+c) /3 is an integer
1.
a=a
b=a+1
c=a+2
c-a=a+2-a=2.
Correct
2. -abc is positive integer.
positive * negative = negative
False.
3. (a+b+c) /3 is an integer
Again;
a=a
b=a+1
c=a+2
a+b+c=(a+a+1+a+2)=3a+3
3a is always divisible by 3
3 is divisible by 3.
Thus3a+3is also divisible by 3.
Rule:
if integer x is divisible by n
and
integer y is divisible by n
then; x+y must be divisible by n
Correct.
Ans :A
Answer: (A) I & III only
Question: What is the remainder when 263251 is divided by 9?
(A) 2
(B) 8
(C) 7
(D) 1
(E) 9
Rationale: Explanation:
If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.
2 + 6 + 3 + 2 + 5 + 1 = 19
The nearest multiple of 9 is 18.
19 - 18 = 1.
Answer: D
Answer: (D) 1
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 5%.what is population of after 2 year.
(A) 140
(B) 141
(C) 142
(D) 143
(E) 146
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 5% so total man =150*.95=142.5
women will be= 175-142.5=32.5
so population after two years= [135^2+32.5^2]^.5=146.15=146
so population after two year= 146
ANSWER:E
Answer: (E) 146
Question: On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $2, the second $200, and the third $2000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. What is the probability that a contestant will win more than $2000?
(A) 1/9
(B) 1/8
(C) 1/3
(D) 1/6
(E) 1/2
Rationale: Let's call the boxes that contain $2, $200, and $2000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $2000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $2000, not more than $2000. The only configuration that leads to winning more than $2000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $2000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6,
Answer = D
Answer: (D) 1/6
Question: Given 3^n, for any real integer of n, which of the following is NOT a possible resultant?
(A) 19,683
(B) 17,7147
(C) 6,561
(D) 1,594,332
(E) 59,049
Rationale: Given that the answers have different last digits, there are several ways to solve this, but the most straight forward way is to check the algorithm. 3^n has a cycle of 4.
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
Observe that the last digit of the resultant of 3^1 and 3^5 is 3. If we continue 3^n, the last digit follows the pattern 3, 9, 7, 1, 3, 9, 7, 1, 3, .... So, all we need look for is the last digit in the pattern.
The answer with last digit 2.
Answer: D
Answer: (D) 1,594,332
Question: A person spent Rs. 8,550 from his salary on food and 8,640 on house rent. After that he was left with 40% of his monthly salary. What is his monthly salary ?
(A) 38,650
(B) 28,650
(C) 48,650
(D) 68,650
(E) 18,650
Rationale: Total money spent on food and house rent = 8,550+8,640 = 17,190
Which is 100 - 40 = 60% of his monthly salary
∴ His salary = 17190x100/60 = 28650
Answer : B
Answer: (B) 28,650
Question: In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?
(A) 11
(B) 12
(C) 28
(D) 27
(E) 19
Rationale: Let the number of boys be x. Then, (3/4)x = 18 or x = 18 x(4/3) = 24.
If total number of students is y, then (2/3) y = 24 or y = 24 x (3/2) = 36.
Therefore Number of girls in the class = (36 - 24) = 12.
Answer: B
Answer: (B) 12
Question: In a class of 35 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 10 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
(A) 3
(B) 5
(C) 8
(D) 13
(E) 15
Rationale: Total # of students = 35
Avg # of books per student = 2
Total # of books = 35*2 = 70
# of student borrowed at least 3 books = 35-2-12-10 = 11
# of books borrowed by above 11 students = 70-(12*1)+(10*2) = 38
Considering that 10 out of above 11 students borrowed only 3 books, # of books borrowed = 10*3 = 30
So maximum # of books borrowed by any single student = 38-30 = 8
Option C
Answer: (C) 8