mathewhe/aqua_rat huggingface dataset:
Question: At 6′o a clock ticks 6 times. The time between first and last ticks is 45 seconds. How long does it tick at 12′o clock
(A) 47
(B) 76
(C) 28
(D) 66
(E) 99
Rationale: Explanation:
For ticking 6 times, there are 5 intervals.
Each interval has time duration of 45/5 = 9 secs
At 12 o'clock, there are 11 intervals,
So total time for 11 intervals = 11 × 9 = 99 secs.
Answer: E
Answer: (E) 99
Question: Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 8 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If one minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds does he have to wait?
(A) 12
(B) 24
(C) 36
(D) 60
(E) 72
Rationale: the difference of the speed is 3m per second so in one minute Sacha will be 180 m ahead of Bruno..
Bruno will cover this in 180/5=36 secs..
C
Answer: (C) 36
Question: A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $360 less than the sum lent. What was the sum lent?
(A) 540
(B) 560
(C) 580
(D) 600
(E) 680
Rationale: P - 360 = (P*5*8)/100
P = 600
The answer is D.
Answer: (D) 600
Question: At exactly what time past 6:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 7:00
(B) 20 13/17 minutes past 7:00
(C) 21 3/23 minutes past 7:00
(D) 21 9/11 minutes past 6:00
(E) 22 4/9 minutes past 7:00
Rationale: A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (6*60+M)/12*60 )*360
A2 = M*360/60
Solving all three equation , results in the answer D
Answer: (D) 21 9/11 minutes past 6:00
Question: Ajay spends 45% of his monthly income on household items, 25% of his monthly income on buying cloths, 7.5% of his monthly income on medicines and saves the remaining amount which is Rs. 9000. Find his monthly income.
(A) Rs. 40000
(B) Rs. 36000
(C) Rs. 50000
(D) Rs. 45000
(E) None of these
Rationale: Let the monthly income of Ajay be Rs. x
Savings of Ajay = x - (45 + 25 + 7.5)/100 * x = 22.5/100 x
22.5/100 x = 9000
x = 40000.
ANSWER:A
Answer: (A) Rs. 40000
Question: Of 30 candidates for a job, 14 had at least 4 years of exper, 18 had degrees, and 3 had less than 4 years exper and did not have a degree, how many candidates had at least 4 years exper and a degree?
(A) a)14
(B) b)13
(C) c)9
(D) d)7
(E) e)5
Rationale: Answer is E. Here is how:
The quickest way is to setup a matrix and work through the given values in the question.
For all such problems, set up a matrix with number of columns and rows corresponding to the divisions mentioned in the question stem.
Degrees and Experience
> 4 yrs Exp< 4 yrs ExpTotal
Degree5Required Value1318Given
No Degree9312
Total14Given1630Given answer is E
Answer: (E) e)5
Question: Out of first 30 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
(A) 6/30
(B) 2/30
(C) 4/90
(D) 24/30
(E) 24/60
Rationale: n(S) = 30
n(Even no) = 15 = n(E)
n(Prime no) = 10 = n(P)
P(EᴜP)
= 15/30 + 10/30 - 1/30
= 24/30
Answer:D
Answer: (D) 24/30
Question: In a class, 20% of the students were absent for an exam. 30% failed by 20 marks and 10% just passed. Find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40.
(A) 36
(B) 302
(C) 272
(D) 292
(E) 271
Rationale: Explanation:
Let total students be 100.
Hence, marks of 20 students is 0 as they were absent.
30 students scored 20 marks (as they failed by 20 marks)
10 students scored 40 marks (just passed)
40 students scored 65 marks (average of 65)
Therefore, average score of the class is: (0 + 600 + 400 + 2600)/100 = 3600/100
= 36
ANSWER: A
Answer: (A) 36
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 350 m
Rationale: Explanation:
Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (130 + x)/30 = 25/2 => 2(130 + x) = 750 => x = 245 m.
ANSWER IS C
Answer: (C) 245 m
Question: How many 3 digit numbers can be formed from the digits 2,3,5,6,7 and 9 which are divisible by 5 and none of the digits is repeated?
(A) 16
(B) 12
(C) 20
(D) 25
(E) 30
Rationale: Since each desired number is divisible by 5,
so we much have 5 at the unit place.
The hundreds place
can now be filled by any of the remaining 4 digits .
so, there4 ways of filling it.
Required number of numbers = (1 * 5 * 4)
= 20
Ans: C
Answer: (C) 20
Question: The labeled price of a table is Rs. 6,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
(A) Rs. 5369
(B) Rs. 6195
(C) Rs. 6425
(D) Rs. 7200
(E) None of these
Rationale: Explanation:
Labeled price = Rs. 6,500
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 6500 = Rs. 6175
By earning 15% profit on the selling of price Rs. 6175 the cost price is
= 100 / 115 * 6175 = Rs. 5369
Therefore, approximate cost is 5369
ANSWER A
Answer: (A) Rs. 5369
Question: An investor deposited $5,000 to open a new savings account that earned 4 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
(A) $5050.50
(B) $5100.50
(C) $5200.50
(D) $5300.50
(E) $5400.50
Rationale: The amount in the account after 6 months is 1.01*1.01($5,000) = $5100.50
The answer is B.
Answer: (B) $5100.50
Question: What will be the fraction of 5%
(A) 1/20
(B) 1/50
(C) 1/75
(D) 1/25
(E) None of these
Rationale: Explanation:
5*1/100 = 1/20.
Option A
Answer: (A) 1/20
Question: A committee is to be formed by randomly choosing 4 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
(A) 2/5
(B) 2/7
(C) 3/7
(D) 3/35
(E) 4/35
Rationale: The total number of ways to form a committee is 7C4=35.
The number of committees which include Alice but not Bob is 5C3=10.
The probability that Alice is selected but Bob is not selected is 10/35=2/7.
The answer is B.
Answer: (B) 2/7
Question: Walking at 3/4 of her normal speed, a worker is 8 minutes later than usual in reaching her office. The usual time (in minutes) taken by her to cover the distance between her home and her office is
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: Let V be her normal speed and let T be her normal time.
D = (3/4)V * (T+8)
Since the distance is the same we can equate this to a regular day which is D = V*T
V*T = (3/4)V * (T+8)
T/4 = 6
T=24
The answer is B.
Answer: (B) 24
Question: total 36 matches are conducted in Knockout match type. How many players will be participated in that tournament?
(A) 35
(B) 36
(C) 21
(D) 32
(E) 26
Rationale: 35 players
ANSWER:A
Answer: (A) 35
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 2^a and y = 3^b, which of the following is a possible units digit of xy?
(A) 4, 2, 8, 6
(B) 4 and 2
(C) 2 and 8 only
(D) 6 and 4
(E) 8 and 6
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values of X for positive values of a
When,
a=1; X=2
a=2; X=4
a=3; X=8
a=4; X=16
a=5; x=32........ Units digit repeat in a cycle of 2,4,8,6,2,4......
Similarly, Finding all values of Y for positive values of b
When,
b=1; Y=3
b=2; Y= 9
b=3; Y= 27
b=4; Y=81
b=5; Y=243....... Units digit repeat in cycle of 3,9,7,1,3,9....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=2 and Y=3: Units digit of XY = 6
When X=2 and Y=9: Units digit of XY = 18
When X=2 and Y=7: Units digit of XY = 14
When X=2 and Y=1: Units digit of XY = 2
When X=4 and Y=3: Units digit of XY = 12
When X=4 and Y=9: Units digit of XY = 36
When X=4 and Y=7: Units digit of XY = 28
When X=4 and Y=1: Units digit of XY = 4
When X=8 and Y=3: Units digit of XY = 24
When X=8 and Y=9: Units digit of XY = 72
When X=8 and Y=7: Units digit of XY = 56
When X=8 and Y=1: Units digit of XY = 8
When X=6 and Y=3: Units digit of XY = 18
When X=6 and Y=9: Units digit of XY = 54
When X=6 and Y=7: Units digit of XY = 42
When X=6 and Y=1: Units digit of XY = 6
There are 4 possibilities for Units digit of XY i.e. 4, 2, 8 and 6
Ans: A
Answer: (A) 4, 2, 8, 6
Question: Two stations A and B are 200 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 8
Rationale: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 200
45x = 225
x = 5.
So, they meet at 12 a.m.
Answer: Option D
Answer: (D) 12
Question: Find the no.of ways of arranging the boy and 10 guests at a circular table so that the boy always sits in a particular seat?
(A) 3!
(B) 10!
(C) 7!
(D) 9!
(E) 11!
Rationale: Ans.(B)
Sol. Total number of persons = 11 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 10 places in 10P10 = 10! Ways ... The number of required arrangements = 10! x 1= 10! = 10! ways
Answer: (B) 10!
Question: Some consecutive natural numbers, starting with 1, are written on the board. Now, one of the numbers was erased and the average of the remaining numbers is 800/39. Find the number which was erased.
(A) 20
(B) 87
(C) 266
(D) 288
(E) 11
Rationale: We know that average of n consecutive numbes average = n×(n+1)2n=(n+1)2n×(n+1)2n=(n+1)2
If the given n is sufficiently large, the average does not change much even though we exclude one or two numbers from it. So the approximate number of observations is almost double to the average (Remember: the average of consecutive numbers almost lies in the middle)
The approximate average is 800/39 = Approx 20. So the initial numbers may be nearer to 40.
In this question it is actually 40 as from the denominator of the new average 800/39. The initial numbers are 40.
Sum of 40 consecutive numbers = 40×(40+1)2=82040×(40+1)2=820
Sum of 39 numbers = average x numbenumber of observations = 80039×3980039×39 = 800
So the number excluded = 820 - 800 = 20
Answer:A
Answer: (A) 20
Question: Today Mary’s father is four times as old as Mary. Seven years ago, he was 7 times as old. How old is Mary today?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Dad's age = 4M
7*(M-7) = 4M-7
3M = 42
M = 14
The answer is D.
Answer: (D) 14
Question: What is the perimeter of a square with area 9p^2/25 ?
(A) 3p/4
(B) 3p^2/4
(C) 3p
(D) 3p^2
(E) 12p/5
Rationale: Area of square, (side)^2 = (3p/5)^2
Therefore side of the square = 3p/5
Perimeter of square = 4*side = 4* (3p/5) = 12p/5
Answer is E.
Answer: (E) 12p/5
Question: Find the odd man out
253, 136, 352, 328, 631, 244
(A) 328
(B) 136
(C) 352
(D) 631
(E) 531
Rationale: The sum all three digits comes to 10 except 328
ANSWER:A
Answer: (A) 328
Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 3 years?
(A) 1 : 3
(B) 2 : 1
(C) 1 : 2
(D) 3 : 2
(E) 1 : 4
Rationale: Let the principal be P and rate of interest be R%.
Required ratio =
(P x R x 6)/100 DIVIDED BY	(P x R x 3)/100
=	6PR/3PR	=	6/3	= 2 : 1.
ANSWER : B
Answer: (B) 2 : 1
Question: What is the smallest number which, when increased by 7, is divisible by 8, 11, and 24?
(A) 264
(B) 257
(C) 269
(D) 270
(E) 282
Rationale: LCM(8,11,24)=24x11=264
So the least divisible number is 264, and the number we are looking for is 264-7=257.
The answer is B.
Answer: (B) 257
Question: Which of the following must be non-negative number?
(A) (a-0.9)(a-1)
(B) (a+1)(a-1)
(C) (a+0.9)(a+1)
(D) (a-0.8)(a-0.8)
(E) a(a+1)
Rationale: 5-sec approach:
D. (a-0.8)(a-0.8) = (a-0.8)^2.
The square of a number is always non-negative.
Answer: D.
Answer: (D) (a-0.8)(a-0.8)
Question: A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?
(A) 5/5
(B) 5/9
(C) 5/1
(D) 1/3
(E) 5/2
Rationale: Total number of outcomes possible when a die is rolled, n(S) = 6 (∵ 1 or 2 or 3 or 4 or 5 or 6)
E = Event that the number shown in the dice is divisible by 3 = {3, 6}
The probability = 2/6 = 1/3.
Answer: D
Answer: (D) 1/3
Question: If n = 8^11 – 1, what is the units digit of n?
(A) 3
(B) 1
(C) 0
(D) 6
(E) 4
Rationale: 8 ^ 11 - 8 = 8 (8 ^ 10 - 1)
==> 8 (2 ^ 30 - 1)
Last digit of 2 ^ 30 is 4 based on what explanation LiveStronger is saying. 2 ^ 30 - 1 yields 4 - 1 = 3 as the unit digit. Now on multiply this with 1, we get unit digit as 3.
Answer : A
Answer: (A) 3
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2783 in 3 years. Find the rate percent?
(A) 15
(B) 10
(C) 28
(D) 24
(E) 82
Rationale: Explanation:
2420 --- 363
100 --- ? => 15%
Answer: Option A
Answer: (A) 15
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
(A) 123
(B) 267
(C) 277
(D) 267
(E) 120
Rationale: Let xx be the number he chose, then
2⋅x−138=1022⋅x−138=102
2x=2402x=240
x=120
Answer:E
Answer: (E) 120
Question: Sum of two numbers is 25. Two times of the first exceeds by 5 from the three times of the other. Then the numbers will be?
(A) A)5
(B) B)9
(C) C)11
(D) D)13
(E) E)15
Rationale: Explanation:
x + y = 25
2x – 3y = 5
x = 16 y = 9
B)
Answer: (B) B)9
Question: Kiran had 85 currency notes in all , some of which were of Rs.100 denomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?
(A) 3500
(B) 1500
(C) 2500
(D) 4500
(E) None of them
Rationale: Let the no of fifty rupee notes be x
Then,no of 100 rupee notes =(85-x)
50x+100(85-x)=5000
x+2(85-x)=100
x=70
so, required amount=Rs.(50*70)= Rs.3500
Answer is A.
Answer: (A) 3500
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent of the original cost?
(A) 200
(B) 600
(C) 800
(D) 1600
(E) 50
Rationale: Original Cost C1=t1*b1^4
New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Answer: (D) 1600
Question: The function g(a) is defined for integers a such that if a is even, g(a) = a/2 and if a is odd, g(a) = a + 5. Given that g(g(g(g(g(a))))) = 19, how many possible values for a would satisfy this equation?
(A) 1
(B) 5
(C) 7
(D) 8
(E) 11
Rationale: Let me define terms:
in g(a) = R
a is argument, R is result, g() is function,
in g(g(g(g(g(a))))), g1 is inner most, g5 is outermost for identification.
From definition of function g, we can deduce that:
If Result is even then two possibilities for argument = 1 Even 1 Odd
If Result is odd then one possibility for argument = 1 Even
Since final result = 19 = Odd
Possibilities:
g1:1 Even
g2: 1*(Even,Odd ) =1 Even 1 Odd
g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd
g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd
g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8
Ans D it is!
Answer: (D) 8
Question: Sum of three numbers 275, If the first number be twice then second and third number be one third of the first, then the second number is
(A) A)70
(B) B)71
(C) C)72
(D) D)73
(E) E)75
Rationale: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=275
<=>11x/3=275
=>x=75
Answer: Option E
Answer: (E) E)75
Question: 125^n divides 325^325
(A) 216
(B) 217
(C) 218
(D) 219
(E) 220
Rationale: 325^325=(13*25)^325 = (13^325)*(5^650)
125^n=5^(3n)
power of 5 in numerator should be greater then denominator
so 650>3n and hence
n=216
ANSWER:A
Answer: (A) 216
Question: In 1 hour, a boat goes 6 km along the stream and 12 km against the stream. The speed of the boat in still water (in km/hr) is :
(A) 3 km/hr.
(B) 2 km/hr.
(C) 6 km/hr.
(D) 8 km/hr.
(E) 9 km/hr.
Rationale: Speed in still water = 1/2(6 + 12) km/hr
= 9 km/hr. ANSWER :E
Answer: (E) 9 km/hr.
Question: Machine P and Machine Q are each used to manufacture 110 sprockets. It takes Machine P 10 hours longer to produce 110 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
(A) 5
(B) 15
(C) 55
(D) 95
(E) 1
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
10/x = 110/1.1x + 10
1.1(110) = 110 + 11x
11x = 11
x = 1
The answer is E
Answer: (E) 1
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 36. By how much do the two digits differ?
(A)  3
(B)  4
(C)  5
(D)  6
(E)  7
Rationale: Given that (10a + b) - (10b + a) = 36 --> 9a - 9b =36 --> a - b = 4.
Answer: B.
Answer: (B)  4
Question: If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
(A) 32 kg
(B) 25 kg
(C) 72 kg
(D) 88 kg
(E) 92 kg
Rationale: C
72 kg
(3 * 4)/48 = (9 * 2)/ x
x = 72 kg
Answer: (C) 72 kg
Question: If 0.60: x : : 6 : 4, then x is equal to
(A) 0.1
(B) 0.4
(C) 0.82
(D) 0.8
(E) None
Rationale: Sol.
(x×6) = (0.60×4) ⇒ x = 2.4/6 = 0.40.
Answer B
Answer: (B) 0.4
Question: When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/7 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
(A) 3/10
(B) 2/5
(C) 1/2
(D) 2/3
(E) 6/5
Rationale: Say, the tree grows by x feet every year.
Then, 4 + 6x = (1+1/7)(4+4x)
or, x = 2/5
Answer B
Answer: (B) 2/5
Question: A teacher prepares a test. She gives 9 objective type questions out of which 4 have to be answered. Find the total ways in which they can be answered if the first 6 questions have 3 choices and the last 3 have 4 choices.
(A) 7255
(B) 7632
(C) 7192
(D) 7100
(E) 7144
Rationale: Two cases.
First Case: 2 Questions - 3 Choices, 2 Questions - 4 Choices
6C2 * 3C2 ways to select the questions
3C1 * 3C1 * 4C1 * 4C1 ways to answer the questions
= 15 * 3 * 3 * 3 * 4 * 4
= 6480
Second Case: 1 Question - 3 Choices, 3 Questions - 4 Choices
6C1 * 3C3 ways to select the questions
3C1 * 4C1 * 4C1 * 4C1 ways to answer the questions
= 6 * 1 * 3 * 4 * 4 * 4
= 1152
Total = 6480 + 1152
= 7632
B
Answer: (B) 7632
Question: The population of a bacteria colony doubles every day. If it was started 10 days ago with 2 bacteria and each bacteria lives for 12 days, how large is the colony today?
(A) 512
(B) 768
(C) 1024
(D) 2048
(E) 4096
Rationale: 2^10(2) = 2^11 = 2048
The answer is D.
Answer: (D) 2048
Question: The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
(A) 2
(B) 3
(C) 4
(D) 8
(E) 10
Rationale: Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
Option C
Answer: (C) 4
Question: Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 20 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)
(A) 50 mph
(B) 45 mph
(C) 48 mph
(D) 52 mph
(E) 40 mph
Rationale: Let t be the number of hours he would need to reach office on time.
when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 20
where s is the speed and 20 is the distance.
if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 20
if you solve above equations, you will arrive at t = 2/3 hr and s = 40mph
therefore answer is E
Answer: (E) 40 mph
Question: The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 40 more than the number who did not, and if receipts for registration and lunch totaled $39,480, how many people paid just for registration at the meeting?
(A) 700
(B) 800
(C) 300
(D) 1,500
(E) 1,800
Rationale: Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 40 more than the number who did not. That means, total number of people who registered and paid for lunch = 40 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(40 + x) = 2880 + 72x
Now, total amount received was 39480
Thus, from the above data,
50x + 2880 + 72x = 39480
122x = 39480 - 2880
122x = 36600
x = 300.
Hence the correct Ans is C
Answer: (C) 300
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 240 m
(B) 200 m
(C) 500 m
(D) 360 m
(E) 489 m
Rationale: Explanation:
Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer:A
Answer: (A) 240 m
Question: If the area of a circle is 64pi square feet, find its circumference.
(A) 16 pi feet
(B) 28 pi feet
(C) 38 pi feet
(D) 48 pi feet
(E) 58 pi feet
Rationale: The area is given by pi *r* r. Hence
pi * r *r = 64 pi
r * r = 64; hence r = 64 feet
The circumference is given by
2 * pi * r = 2 * pi * 8 = 16 pi feet
correct answer A
Answer: (A) 16 pi feet
Question: George baked a total of 75 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
(A) 5
(B) 4
(C) 2
(D) 6
(E) 7
Rationale: 3/5 of the 75 pizzas cooked on Saturday = 45 pizzas
3/5 of the remaining pizzas on Sunday = 18 pizzas
We're left with (75-45-18) =12 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.
M T W TH F
5 4 2 1 0 =12
W=2
C
Answer: (C) 2
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The second wheel covers a distance of d feet in 400 revolutions. How many revolutions does the first wheel make in covering d feet?
(A) 400xy
(B) 400y - x
(C) 400x - y
(D) 400y/x
(E) 400x/y
Rationale: second Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
first Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
400 = d/(x*pi)
d = 400 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y
Answer (E)
Answer: (E) 400x/y
Question: One half of the people at the game wore the team colors. Two thirds of those people wore team
hats as well. One fourth of those with team colors and team hats had banners to wave.
Twenty five people had team colors and banners, but no hats. One hundred people had only
banners. If there were 1824 people at the game, how many had banners?
(A) 177
(B) 277
(C) 377
(D) 477
(E) 577
Rationale: 1/2 x 1824 = 912 with team colors
2/3 x 912 = 608 with hats and colors
1/4 x 608 = 152 with hats, colors, and banners
152 + 100 + 25 = 277 with banners
correct answer B
Answer: (B) 277