mathewhe/aqua_rat huggingface dataset:
Question: Thurston wrote an important seven-digit phone number on a napkin, but the last three numbers got smudged. Thurston remembers only that the last three digits contained at least one zero and at least one non-zero integer. If Thurston dials 40 phone numbers by using the readable digits followed by 40 different random combinations of three digits, each with at least one zero and at least one non-zero integer, what is the probability that he will dial the original number correctly?
(A) 1/9
(B) 10/243
(C) 4/27
(D) 10/271
(E) 1/1000000
Rationale: If the last three digits have 1 zero (XX0), the total # of numbers possible is 9*9*3 (multiply by 3 since XX0 can be arranged in 3 ways: XX0, X0X, or 0XX).
If the last three digits have 2 zeros (X00), the total # of numbers possible is 9*3 (multiply by 3 since X00 can be arranged in 3 ways: X00, 00X, or X0X).
P = 40/(9*9*3+9*3) = 4/27.
Answer: C.
Answer: (C) 4/27
Question: What is the least integer greater than 0+0.5?
(A) –2
(B) –1
(C) 0
(D) 1
(E) 2
Rationale: This question is just about doing careful Arithmetic and remembering what makes a numberbiggerorsmallercompared to another number.
First, let's take care of the Arithmetic:
(0) + (0.5) = 0.5
On a number line, since we're ADDING +.5 to a number, the total moves to the RIGHT (so we're moving from 0 to 0.5).
Next, the question asks for the LEAST integer that is GREATER than 0.5
Again, we can use a number line. Numbers become greater as you move to the RIGHT. The first INTEGER to the right of 0.5 is 1.
Final Answer:
D
Answer: (D) 1
Question: Mathematics, physics, and chemistry books are stored on a library shelf that can accommodate 25 books. Currently, 20% of the shelf spots remain empty. There are twice as many mathematics books as physics books and the number of physics books is 4 greater than that of the chemistry books. Ricardo selects 1 book at random from the shelf, reads it in the library, and then returns it to the shelf. Then he again chooses 1 book at random from the shelf and checks it out in order to read at home. What is the probability Ricardo reads 1 book on mathematics and 1 on chemistry?
(A) 3%
(B) 6%
(C) 12percent
(D) 20%
(E) 24%
Rationale: Shelf can accomodate 25 books but 20% of it is empty so there are in all 20 books.
If no of Chem books = x, number of Physics book = x+4, number of Math books = 2(x+4)
x + x+4 + 2(x+4) = 4x + 12 = 20
x = 2
Chem books = 2, Phy books = 6, Math books = 12
Probability of picking a Math book = 12/20
Probability of picking a Chem book = 2/20
Total Probability = Pick Math first and then Chem + Pick Chem first and then Math
= (12/20) * (2/20) + (2/20) * (12/20) = 12/100 = 12%
Answer: (C) 12percent
Question: A train covers a certain distance at a speed of 200kmph in 4 hours. To cover the same distance in 1 3/4 hours, it must travel at a speed of
(A) 400km/hr
(B) 457km/hr
(C) 450km/hr
(D) 650km/hr
(E) 750km/hr
Rationale: Explanation:
Distance = 200Ã—4 = 800km
Required speed = (800Ã— 4/7) = 457km/hr
Answer: Option B
Answer: (B) 457km/hr
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 308 but three tickets from city A to B and two tickets from city A to C cost Rs. 292. What are the fares for cities B and C from A ?
(A) s. 4, Rs. 23
(B) s. 8.2, Rs. 97.2
(C) s. 15, Rs. 14
(D) s. 17, Rs. 13
(E) s. 17, Rs. 15
Rationale: If fares for cities B and C from A are x and y respectively, then
2x+3y=308 or 6x+9y= 924
3x+2y =292 or 6x+4y= 438
subtracting
5y =486
y= Rs 97.2
Hence B. Rs. 8.2, Rs. 97.2
ANSWER:B
Answer: (B) s. 8.2, Rs. 97.2
Question: A total of 3000 chocolates were distributed among 120 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates. Find the respective number of boys and girls?
(A) 22,99
(B) 60,60
(C) 40,88
(D) 30,40
(E) 40,30
Rationale: Let the number of boys be x.
Number of girls is 120 - x.
Total number of chocolates received by boys and girls = 2x + 3(120 - x) = 300
=> 360 - x = 300 => x = 60.
So, the number of boys or girls is 60.
Answer:B
Answer: (B) 60,60
Question: What is the next number of the following sequence.
8, 8, 6, 2,.... ?
(A) -4
(B) -5
(C) -6
(D) -7
(E) -8
Rationale: 8-(2*0) = 8
8-(2*1) = 6
6-(2*2) = 2
2-(2*3) = -4
ANSWER:A
Answer: (A) -4
Question: A train 500 m long passes a man, running at 9 km/hr in the same direction in which the train is going, in 20seconds. The speed of the train is:
(A) 105
(B) 95
(C) 90
(D) 99
(E) 100
Rationale: Speed of the train relative to man =500/20 m/sec
=25m/sec.
=25x18/5km/hr
= 90 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 9) km/hr.
x - 9= 90 =99 km/hr.
Answer:D
Answer: (D) 99
Question: How many ways are there for 3 males and 4 females to sit (around a circular table) if no male should sit next to a male (and no female next to female) and Mary wants to sit with her back on the wall?
(A) 6
(B) 36
(C) 72
(D) 100
(E) 720
Rationale: So Mary has her own chair, fixed position. Other 3 females around the table can sit in 3! ways: the first to the left of Mary and the second to the right or vise-versa. Now, if 3 males will sit between them then no two female or two male will sit next to each other (female-male-female-male-female-male). But these males on their spots can also sit in different ways, namely in 3! different ways, so total 3!*3!=36.
Answer B.
Answer: (B) 36
Question: Think of a number, divide it by 6 and add 5 to it. The result is 17. What is the number thought of?
(A) 24
(B) 72
(C) 297
(D) 267
(E) 29
Rationale: Explanation :
17-5 = 12
12 x 6 = 72
Answer : B
Answer: (B) 72
Question: The distance from City A to City B is 180 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob?
(A) 45
(B) 48
(C) 50
(D) 52
(E) 54
Rationale: The time it takes Bob to drive to City B is 180 / 40 = 4.5 hours.
Alice needs to take less than 4 hours for the trip.
Alice needs to exceed a constant speed of 180 / 4 = 45 miles per hour.
The answer is A.
Answer: (A) 45
Question: If the perimeter of a rectangular garden is 1200 m, its length when its breadth is 240 m is?
(A) 338 m
(B) 778 m
(C) 200 m
(D) 276 m
(E) 360 m
Rationale: 2(l + 240)
= 1200 => l
= 360 m
Answer:E
Answer: (E) 360 m
Question: It takes Johnson 10 minutes to walk to the car park and 20 min to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
(A) 8:50 a.m
(B) 5:50 a.m
(C) 7:50 a.m
(D) 6:50 a.m
(E) 8:30 a.m
Rationale: The time it takes Johnson to get to work: time to walk to car park + time to drive
10 + 20 = 30 minutes
Johnson needs to get out of the house 30 minutes before 9:00 am at
9:00 - 0:30 = 8:30 a.m
correct answer E
Answer: (E) 8:30 a.m
Question: What is the least value of integer N such that N! is divisible by 888 ?
(A) 13
(B) 88
(C) 31
(D) 37
(E) D) 888
Rationale: 888 = 8*111 = 3*8*37
Hence 888 is a multiple of 37 and we need at least one 37 in N!
Therefore least value of N! is 37!, which will contain all of 3, 8, and 37.
Correct Option: D
Answer: (D) 37
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
(A) 667 cm2
(B) 886 cm2
(C) 285 cm2
(D) 266 cm2
(E) 226 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2
Answer: C
Answer: (C) 285 cm2
Question: If -1 < x < 0, which of the following must be true?
I. x^4 < x^3
II. x^6 < 1 – x
III. x^5 < x^2
(A) I only
(B) II only
(C) III only
(D) II,III only
(E) I,II,III only
Rationale: Answer : E
Answer: (E) I,II,III only
Question: How many ways are there to arrange the letters in the word freelancer ?
(A) 1
(B) 1260
(C) 3780
(D) 7560
(E) 655200
Rationale: 10 total words, 3E, 2R
= 10! / 3! 2! = 655200 Answer E
Answer: (E) 655200
Question: In a certain game, each player scores either 2 or 5 points. If n players score 2 points and m players score 5 points and the total number of points scored is 60, what is the least possible difference between n and m.
(A) a.1
(B) b.3
(C) c.5
(D) d.7
(E) e.9
Rationale: 2n+5m=60
try with n=5 and m=10 the equation will be satisfied
2(5)+5(10)=60
so difference between M and N is 5,
ANswer C
Answer: (C) c.5
Question: If the average of ten numbers is 20, then which of the following could be the standard deviation of the ten numbers?
I. 0
II. 10
III. 20
(A) all three options
(B) I
(C) II
(D) III
(E) I&II
Rationale: We know that we have 10 numbers (and they could be ANY values - including negatives and non-integers) and we know that the average of those numbers is 10. This is meant to say that there are an INFINITE number of possible sets of 10 numbers that fit this prompt.
IF all ten numbers were the same (meaning that we had ten 10s), then the SD would be 0. The more 'spread out' those ten numbers get, the higher the SD becomes. Since there's no limit to the 'spread', then there's no limit to what the SD could be either. Thus, it could be 10 or 20 or any other number.
A
Answer: (A) all three options
Question: A garrison of 500 men has provisions for 20 days. At the end of 14 days, a reinforcement arrives, and it is now found that the provisions will last only for 3 days more. What is the reinforcement?
(A) 500
(B) 1000
(C) 1500
(D) 3000
(E) 2000
Rationale: 500 ---- 20
500 ---- 6
x ----- 3
x*3 = 500*6
x = 1000
500
-------
500
Answer: A
Answer: (A) 500
Question: To be considered grade AD, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AD eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AD eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
(A) 800
(B) 840
(C) 864
(D) 900
(E) 1,080
Rationale: We're asked for the smallest possible mass, so what could the lowest mass be per egg AD? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Answer: (B) 840
Question: There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a black ball has been drawn, find the chance that it came from second group.
(A) 2/7
(B) 6/35
(C) 8/25
(D) 28/43
(E) 3/5
Rationale: Please go through my solution and suggest any mistake.
Chances of selecting a black ball from group 1: 2/7----------------------Chances of selecting a black ball from group 2: 4/5
Thus combined probability of section of black ball from group 1:
3/5 x 2/7 = 6/35
Thus combined probability of section of black ball from group 2:
2/5 x 4/5 = 8/25
Out of these chances, chance of occurrence of first case : (8/25) / (6/35 + 8/25) = 28/43
D
Answer: (D) 28/43
Question: A work which could be finished in 10 days was finished 3 days earlier after 10 more men joined. The number of men employed was?
(A) 15
(B) 20
(C) 88
(D) 71
(E) 11
Rationale: x ------- 10
(x + 10) ---- 6
x * 10 = (x + 10)6
x = 15
\Answer: A
Answer: (A) 15
Question: With out any halt a train travels a certain distance with an average speed of 55 km ph , and with halts it covers the same distance at an average speed of 30 kmph. When it is traveling with halts, how many minutes/per hour does the train halt on an average ?
(A) 48 min.
(B) 12min.
(C) 15min.
(D) 18min.
(E) 19min.
Rationale: With halt in 1 hour the train travels 60km
With out halt for traveling same distance it take 55/30 = 11/6 = 110 minutes
:. 50 minutes is the halting time per hour
ANSWER:A
Answer: (A) 48 min.
Question: Simplify: 8755 x 95
(A) 831725
(B) 787950
(C) 875500
(D) 43775
(E) 87500
Rationale: 8755 x 95 = 8755 x (100 - 5)
= 875500- 43775
= 831725
Answer is A
Answer: (A) 831725
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
(A) C is younger than A
(B) 6
(C) 12
(D) 24
(E) None of these
Rationale: Sol.
(A + B) - (B + C) = 12 ⇔ A - C = 12.
Answer C
Answer: (C) 12
Question: Ten coins are tossed simultaneously. In how many of the outcomes will the second coin turn up a head?
(A) 2^9
(B) 2^10
(C) 3 * 2^8
(D) 3 * 2^9
(E) 3 * 2^10
Rationale: Fix the second coin as H. The remaining 9 coins have 2^9 outcomes.
Ans:A
Answer: (A) 2^9
Question: There are 80 people and 3 clubs M, S, and Z in a company. 20 people joined M, 22 people joined S and 15 people joined Z. If the members of M did not join any other club, at most, how many people of the company did not
join any club?
(A) 30
(B) 32
(C) 34
(D) 36
(E) 38
Rationale: Answer E.
key is 'atmost' here.
so 20 people joined M.
22 people joined S and 15 people joined Z. to get maximum people who did not join any club, 15 people who joined Z are among 22 people who joined S.
so 22+20 = 42
80-42 = 38
Answer: (E) 38
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
(A) 1/2
(B) 1/3
(C) 3/5
(D) 3/7
(E) 3/11
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
B)
Answer: (B) 1/3
Question: The value of (34.5*0.473*1.567)/(0.0673*23.25*7.57) is close to
(A) 2
(B) 1.15
(C) 2.05
(D) 2.16
(E) 2.35
Rationale: (34.5*0.473*1.567)/(0.0673*23.25*7.57) = 25.5710895/11.845
= 2.16
ANSWER:D
Answer: (D) 2.16
Question: Three candidates contested an election and received 3000, 7500 and 6500 votes respectively. What percentage of the total votes did the winning candidate get ?
(A) 50.2%
(B) 45.5%
(C) 44.11%
(D) 85%
(E) 94.2%
Rationale: Explanation :
Total number of votes polled = ( 3000 + 7500 + 6500 )
= 17000
Required percentage = (7500/ 17000) x 100 %
= 44.11%.
Answer : C
Answer: (C) 44.11%
Question: Albert has a box of crayons. Each box contains 20 different colored crayons. How many crayons does Albert have if he buys 2 additional boxes?
(A) 40
(B) 20
(C) 80
(D) 120
(E) 60
Rationale: E. 60
Answer: (E) 60
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 9 months. At this time, the construction was behind schedule by how many projects?
(A) 34
(B) 96
(C) 198
(D) 204
(E) 504
Rationale: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*9 =306
Lag :306-108 = 198
C is the answer
Answer: (C) 198
Question: Its not easy having a mathematics professor as a friend. When she invited you to her house she
says, “All the houses on my side of the street are numbered consecutively in even numbers. There are
Six houses on my Side of my block and sum of their numbers is 9870. You don’t know which block I
live on, and it’s a long street, but I will tell you that I live in the lowest number on my side of the block. What’s the number? Or are you just going to ring the first- numbered doorbell for twenty blocks?
(A) 22388
(B) 2777
(C) 199
(D) 1640
(E) 2912
Rationale: Given all the number are even consecutive numbers. This is AP.
Formula for sum of numbers = Sn=n2[2a+(n−1)d]Sn=n2[2a+(n−1)d]
Sum = 9870, n = 6, d = 2
9870=62[2a+(6−1)2]9870=62[2a+(6−1)2]
⇒ 9870 = 3 (2a + 10)
⇒ 9840 = 6a
⇒ a = 1640
Answer:D
Answer: (D) 1640
Question: capacity of doing work of A is double than B.if both together finish a work in 12 days,then B alone in how many days will finish the work?
(A) 24 days
(B) 27 days
(C) 36 days
(D) 48 days
(E) 30 days
Rationale: let B do work in 1 day=x,then A do work in 1 day=2x
(x+2x)=1/12=3x=1/12,x=1/36
work of B in 1 day=1/36
B alone finish the work in 36 days
answer C
Answer: (C) 36 days
Question: Find the value of 72519 x 9999 = m?
(A) 346568796
(B) 235467889
(C) 766444332
(D) 725117481
(E) 235656788
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: Look at this series: VI, 10, V, 11, __, 12, III, ... What number should fill the blank?
(A) II
(B) IV
(C) IX
(D) 14
(E) 12
Rationale: There will be two series.
1st : VI, V , ?? , III (decreasing by 1 in roman letters of numbers)i.e,6,5,4
2nd : 10, 11, 12 , 13 (Increasing by 1 number)
Final sequence : VI, 10, V, 11, 1V, 12, III
ANSWER:B
Answer: (B) IV
Question: The angle between the minute hand and the hour hand of a clock when the time is 4.20, is:
(A) 10º
(B) 75º
(C) 90º
(D) 130º
(E) 180º
Rationale: Angle traced by hour hand in 13/3 hrs = (360/12 x 13/3)º = 130º.
Angle traced by min. hand in 20 min. = (360/60 x 20)º = 120º.
Required angle = (130 - 120)º = 10º.
Answer A
Answer: (A) 10º
Question: Which of the following is equal to the value of 2^2 + 2^2 + 3^2 + 3^2 + 3^2 ?
(A) 2^8 + 3^3
(B) 2^4+ 3^5
(C) 2^3 + 3^3
(D) 2^4 + 3^3
(E) 2^3 + 3^5
Rationale: 2^2 + 2^2 + 3^2 + 3^2 + 3^2
= 2 (2^2) + 3 (3^2)
= 2^1 (2^2) + 3^1 (3^2)
= 2^(1+2) + 3^(1+2)
= 2^3 + 3^3
Ans: C
Answer: (C) 2^3 + 3^3
Question: The number N is 5,H48, where H represents the hundred's digit. If N is divisible by 11, what is the value of H
(A) 1
(B) 7
(C) 6
(D) 5
(E) 2
Rationale: If the number is divisible by 11, then the alternate digits' sum must be divisible by 11 or difference is 0. Only 1 yields such a number.
Answer: A
Answer: (A) 1
Question: The digital sum of a number is the sum of its digits. For how many of the positive integers 24-100 inclusive is the digital sum a multiple of 7?
(A) 7
(B) 11
(C) 14
(D) 16
(E) 20
Rationale: is there other way than just listing?
25
34
43
52
59
61
68
70
77
86
95
11 ways..
B
Answer: (B) 11
Question: In a certain game, you pick a card from a standard deck of 52 cards. If the card is a heart, you win. If the card is not a heart, the person replaces the card to the deck, reshuffles, and draws again. The person keeps repeating that process until he picks a heart, and the point is to measure: how many draws did it take before the person picked a heart and won? What is the probability that one will have at least two “heartless” draws on the first two draws, not picking the first heart until at least the third draw?
(A) 1/2
(B) 9/16
(C) 11/16
(D) 13/16
(E) 15/16
Rationale: A full deck of 52 cards contains 13 cards from each of the four suits. The probability of drawing a heart from a full deck is 1/4. Therefore, the probability of “not heart” is 3/4.
P(at least three draws to win) = 1 – P(win in two or fewer draws)
Furthermore,
P(win in two or fewer draws) = P(win in one draw OR win in two draws)
= P(win in one draw) + P(win in two draws)
Winning in one draw means: I select one card from a full deck, and it turns out to be a heart. Above, we already said: the probability of this is 1/4.
P(win in one draw) = 1/4
Winning in two draws means: my first draw is “not heart”, P = 3/4, AND the second draw is a heart, P = 1/4. Because we replace and re-shuffle, the draws are independent, so the AND means multiply.
P(win in two draws) =(3/4)*(1/4) = 3/16
P(win in two or fewer draws) =P(win in one draw) + P(win in two draws)
= 1/4 + 3/16 = 7/16
P(at least three draws to win) = 1 – P(win in two or fewer draws)
= 1 – 7/16 = 9/16
Answer = B
Answer: (B) 9/16
Question: Jim wishes to buy 3 gifts that cost 31 dollars, 9 dollars, and 12 dollars. He has 1/4 of the money
he needs. How much more money must he earn in order to buy the gifts?
(A) $39
(B) $47
(C) $7
(D) $17
(E) $27
Rationale: $31 + $9 + $12 = $52 needed
1/4 x $52 = $13 on hand
$52 - $13 = $39 to earn
correct answer A
Answer: (A) $39
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 21
(C) 24
(D) 26
(E) 27
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: A truck carrying cans of soup contains P stacks. Each stack contains Q cases, and each case contains 3Q cans. How many cans of soup are contained in 6 trucks?
(A) 18PQ^2
(B) 6P
(C) 18P/Q^2
(D) 6Q^2/P
(E) 3PQ^2
Rationale: There are 3Q cans in each case.
There are 3Q^2 cans in each stack.
There are 3PQ^2 cans in each truck.
There are 18PQ^2 cans in 6 trucks.
The answer is A.
Answer: (A) 18PQ^2
Question: A necklace is made by stringing N individual beads together in the repeating pattern red bead, green bead, white bead, blue bead and yellow bead. If the necklace begins with a red bead and ends with a white bead, then N could be:
(A) 16
(B) 32
(C) 54
(D) 68
(E) 86
Rationale: R G W B Y is the bead pattern and it repeats.
Bead want to end with White.
So, the 3rd, 8th, 13th, 18th... beads will be W.
So, number of beads - 3 has to be divisible by 5 for it to be a White bead.
For those conditions, option D(68) only satisfy.
i.e., 68 - 3 = 65 and that also divisible by 5.
S0, 68
ANSWER:D
Answer: (D) 68
Question: The probability that a man will be alive for 10more yrs is 3/4 & the probability that his wife will alive for 10 more yrs is 3/7. The probability that none of them will be alive for 10 more yrs, is
(A) 1/2
(B) 1
(C) 1/7
(D) 3/4
(E) 2
Rationale: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/7
Ans.(C)
Answer: (C) 1/7
Question: How many hours in one year?
(A) 365
(B) 52
(C) 1024
(D) 8760
(E) No one knows
Rationale: The day has 24 hours, and the year contains 365 days.
So the hours exist in one year is the multiplication of 24 by 365.
So the answer = 365*24=8760 hours
So the correct answer is D
Answer: (D) 8760
Question: If f(c)=c^2 and c is a positive integer, which of the following CANNOT be the value of f(f(c))?
(A) 81
(B) 16
(C) 300
(D) 256
(E) 625
Rationale: f(c)=c^2
f(f(c)) = (c^2)^2 = c^4
Therefore f(f(c)) will be numbers that are 4th power of other numbers.
Checking the options:
81 = 3^4
16 = 2^4
300. This cannot be written as the 4th power of any number
256 = 4^4
625 = 5^4
Answer: C
Answer: (C) 300
Question: Half of 6 percent written as decimal is
(A) 5
(B) 0.5
(C) 0.05
(D) 0.005
(E) 0.03
Rationale: Explanation:
It will be 1/2(6%) = 1/2(6/100) = 1/200 = 0.03
Option E
Answer: (E) 0.03
Question: Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 5
(B) 2
(C) 9
(D) 4
(E) 1
Rationale: 2500
= D(100/4)2
D = 4
Answer: D
Answer: (D) 4
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
(A) 3
(B) 9
(C) 3^5
(D) 25
(E) 215
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 3^5
ANSWER C 3^15
Answer: (C) 3^5
Question: A goods train runs at the speed of 72 km/hr and crosses a 210 m long platform in 26 sec. What is the length of the goods train?
(A) 382
(B) 782
(C) 278
(D) 310
(E) 881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 210)/26 = 20
x = 310 m.
Answer: D
Answer: (D) 310
Question: In a race with 9 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?
(A) 35
(B) 120
(C) 504
(D) 840
(E) 604,800
Rationale: Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 9 choices ,for silver 8 remain (one who got gold cannot be given silver) and for bronze 7 choices remain.
So total possibilities=9*8*7
Correct answer C=504
Answer: (C) 504