mathewhe/aqua_rat huggingface dataset:
Question: A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?
(A) 33
(B) 77
(C) 72
(D) 55
(E) 88
Rationale: Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer:C
Answer: (C) 72
Question: The time it took car P to travel 300 miles was 2 hours less than the time it took car R to travel the same distance. If car P’s average speed was 10 miles per hour greater than that of car R, what was car R’s average speed, in miles per hour?
(A) 34
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let speed of car R be=x
Then speed of car P= x+10
A/Q,
(300/x)-(300/(x+10))=2
Solving for x=34 miles\hr.
A
Answer: (A) 34
Question: A flagstaff 17.5 m high casts a shadow of length 40.25 m. What will be the height of a building, which casts a shadow of length 28.75 m under similar conditions?  
(A) 12.5 m
(B) 10.5 m
(C) 14
(D) 12
(E) 10
Rationale: Explanation:
Let the required height of the building be x meter
More shadow length, More height(direct proportion)
Hence we can write as
(shadow length) 40.25 : 28.75 :: 17.5 : x
⇒40.25×x=28.75×17.5
⇒x=28.75×17.5/40.25
=2875×175/40250
=2875×7/1610
=2875/230 =575/46 =12.5
Answer: Option A
Answer: (A) 12.5 m
Question: A student can select one of 8 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
(A) 22
(B) 72
(C) 96
(D) 37
(E) 01
Rationale: 8C1×3C1×4C1 = 8x3x4=96 ways
Answer:C
Answer: (C) 96
Question: In how many ways can the letters of the word APPEAR be rearranged such that the vowels always appear together?
(A) 6!/2!
(B) 3!*3!
(C) 4!/2!
(D) 4! *3!/(2!*2!)
(E) 3!*3!/2
Rationale: In the word ABACUS , there are 3 vowels - 2 A's and U
Number of ways the letters of word APPEAR be rearranged such that the vowels always appear together
= (4! * 3! )/2!*2!
We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group AND 2 elements of consonant group are identical we divide by 2! 2! .
The entire vowel group is considered as a single group .
Answer D
Answer: (D) 4! *3!/(2!*2!)
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
(A) 2/5
(B) 3/5
(C) 4
(D) 4/11
(E) 5
Rationale: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
Option is A
Answer: (A) 2/5
Question: How many numbers between 100 and 798 are divisible by 2, 3, and 7 together?
(A) 112
(B) 77
(C) 267
(D) 17
(E) 99
Rationale: Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 798
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 798:
798/42 = 19
Hence, 42*19 = 798 is the last number divisible by 42 within 798
Hence, total numbers divisible by 2, 3, 7 together are (19 â€“ 2) = 17
ANSWER: D
Answer: (D) 17
Question: A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?
(A) 221
(B) 287
(C) 288
(D) 280
(E) 271
Rationale: 80* 7: x* 3 = 1:1 1/2
560: 3x = 2: 3
x = 280
Answer: D
Answer: (D) 280
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/5 and |b| = 2/3, which of the following CANNOT be the result of a + b?
(A) 13/15
(B) -13/15
(C) -7/15
(D) 7/15
(E) 7/5
Rationale: |a| = 1/5
Absolute value of 'a' can have two values = 1/5 and -(1/5)
|b| = 2/3
Absolute value of 'b' can have two values = 2/3 and -(2/3)
Now different combinations of a + b are as follows:
a + b = (1/5) + (2/3) = 13/15
- a - b = -(1/5) - (2/3) = -13/15
a - b = (1/5) - (2/3) = -(7/15)
-a + b = -(1/5) + (2/3) = 7/15
Cross verifying with the given options, left over option is E.
Answer: (E) 7/5
Question: A sum is divided among C, D and E in such a way that for each rupee C gets, D gets 75 paisa and E gets 50 paisa. If the share of E is RS. 80, what is the total amount?
(A) 360
(B) 350
(C) 340
(D) 330
(E) 320
Rationale: c:d:e = 100:75:50
20:15:10
10 --- 80
45 --- ? => 360
Answer:A
Answer: (A) 360
Question: How many times will the hands of a clock coincide in a day?
(A) 24
(B) 22
(C) 23
(D) 44
(E) 42
Rationale: solution
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). The hands overlap about every 65 minutes, not every 60 minutes. Thus the minute hand and the hour hand coincide 22 times in a day
so Answer is B
Answer: (B) 22
Question: The sector of a circle has radius of 14 cm and central angle 144o. Find its perimeter?
(A) 60cm
(B) 63.2cm
(C) 70cm
(D) 80cm
(E) 90cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (144/360 * 2 * 22/7 * 14) + 2(14)
= 35.2 + 28 = 63.2 cm
Answer:B
Answer: (B) 63.2cm
Question: The area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm. What is the perimeter of the square?
(A) 482
(B) 268
(C) 800
(D) 128
(E) 632
Rationale: Area of the square = s * s = 2(8 * 64)
=> s = 4 * 8 = 32 cm
Perimeter of the square = 4 * 32 = 128 cm.
Answer: D
Answer: (D) 128
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 8 women?
(A) 7C4 8C5
(B) 4C7 5C8
(C) 7C5 8C4
(D) 9C4 7C5
(E) NONE
Rationale: Group consisting of 7 men and 8 women
4 men can be selected from 7 men in 7C4 ways
5 women can be selected from 8 women in 8C5 ways
Therefore, Total number of ways= 7C4 8C5
ANSWER:A
Answer: (A) 7C4 8C5
Question: If p and q are integers and p divided by q is 16.15, then which of the following integers is a possible value for the remainder when p is divided by q?
I. 15
II. 5
III. 3
(A) I only
(B) II only
(C) III only
(D) I,III only
(E) II,III only
Rationale: p=16.15q from which p = 16q + 15q/100 or p = 16q + 3q/20.
Since p and q are integers, 3q/20 must also be an integer. 3 is not divisible by 20, then q must be divisible by 20, and therefore, q/20 is an integer and 3q/20 is an integer which is a multiple of 3. From the given answers, only 15 and 3 are divisible by 3.
Answer D
Answer: (D) I,III only
Question: If, 7 years ago, Jamie was half as old as he is now, how old will he be in x years?
(A) x + 10
(B) x + 14
(C) x + 2
(D) x – 5
(E) 2x
Rationale: let his age be a. a-7=a/2 hence a=14. 14 years hence, a =x+14
Answer B
Answer: (B) x + 14
Question: Suresh and Ramesh started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of total profit of Rs. 20,000, what is Ramesh's share?
(A) s. 8375
(B) s. 9379
(C) s. 10376
(D) s. 11372
(E) s. 12500
Rationale: Explanation:
Ratio of Suresh and Ramesh's share = 24,000 : 40,000 = 3 : 5
Ramesh's share = Rs. (20000 x 5 / 8) = Rs. 12500
ANSWER: E
Answer: (E) s. 12500
Question: The number of even factors of 21600 is
(A) 32
(B) 42
(C) 60
(D) 25
(E) 52
Rationale: Make a prime factorization of the number: 21,600=25∗33∗52
According to the above the number of factors is (5+1)(3+1)(2+1)=72
Now, get rid of powers of 2 as they give even factors --> you'll have 33∗52 which has (3+1)(2+1)=12 factors. All the remaining factors will be odd, therefore 21,600 has 72-12=60 even factors.
Answer: C.
Answer: (C) 60
Question: C and D walk around a circular track. They start at 11 a.m from the same point in the opposite directions. C and D walk at a speed of 7 rounds per hour and 8 rounds per hour respectively. How many times shall they cross each other before 5 p.m
(A) 90
(B) 95
(C) 100
(D) 105
(E) 110
Rationale: Explanation:
Relative speed = (7+8) =15 rounds per hour
So, they cross each other 15 times in an hour hence, they cross 90 times before 5 p.m
Answer: Option A
Answer: (A) 90
Question: Fred and Sam are standing 100 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 5 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
(A) 5
(B) 9
(C) 25
(D) 30
(E) 75
Rationale: relative distance =100 miles
relative speed =5+5 =10 miles per hour
time taken =100/10=15 hours
distance travelled by sam =15*5=75 miles=E
Answer: (E) 75
Question: In how many ways can the letters {U, U, U, R} be arranged?
(A) 4
(B) 20
(C) 120
(D) 720
(E) 840
Rationale: My answer : A
There is 4! ways to arrange those letters in total, however letter U repeats 3! times and letter R repeats 1! times
=> the way to arrange without repeating = 4!/ [3!x1!] = 4
Answer: (A) 4
Question: Find the value of X, Y by solving the below equations
X + Y = 12
X - Y = 4
(A) 5, 7
(B) 8, 4
(C) 6, 6
(D) 7, 5
(E) 9, 3
Rationale: X + Y = 12 ---(I)
X - Y = 4 -----(II) by adding (I) and (II)
------------
2X = 16 ==> X = 16/2 = 8
By Replacing the value of X in (I) we get 8 + Y = 12 ==> Y = 12-8=4.
So, X = 8, Y = 4
Answer B) 8, 4
Answer: (B) 8, 4
Question: One hour after Adrienne started walking the 60 miles from X to Y, William started walking from X to Y as well. Adrienne walks 3 miles per hour and William walks 1 mile per hour faster than Adrienne. How far from X will William be when he catches up to Adrienne?
(A) 8 miles
(B) 9 miles
(C) 10 miles
(D) 11 miles
(E) 12 miles
Rationale: First, determine how far Adrienne has walked in the one hour. She has walked three miles which means she is three miles ahead of William when he sets off. William walks at four miles/hour which means that every hour, William will get one mile closer to Adrienne. If he gets one mile closer every hour, it will take him three hours to catch up to her which means he travels 3hours * 4 miles/hour = 12 miles and she travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (William ) = r*t (adrienne)
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
D) 12 miles
Answer: (D) 11 miles
Question: If -12 < x < 14, Then which of the following must be true ?
(A) x = -11
(B) x <= 13
(C) x > 12
(D) x > -43
(E) x >= 11
Rationale: SOLUTION:
A. x = -11 --> Not always true. x can be any value between -12 and 14
B. x <= 13 --> Not always true. If x = 13.5 then x > 13.
C. x > 12 --> Not always true. x can be a value less than 12.
D. x > -43 --> Always true. x can take a minimum value of -12 (approx.). Hence x is always greater than -43.
E. x >= 11 -->Not always true. x can be a value less than 11.
Answer: D
Answer: (D) x > -43
Question: The R train leaves station A moving at a constant speed, and passes by stations B and C, in this order. It takes the R train 7 hours to reach station B, and 5 additional hours to reach station C. The distance between stations A and B is m kilometers longer than the distance between stations B and C. What is the distance between stations A and C in terms of m?
(A) 1.8m
(B) 6m
(C) 7m
(D) 9m
(E) 12m
Rationale: The reason it is failing for you is that you chose incorrect numbers. If the question says R it took 7 hrs to reach from A to B and 5 hrs to reach from B to C at a constant speed. It shows that distance AB and BC should be in ratio of 7/5.
If you take such numbers you can solve problem.
AB = 7, BC=5
Therefore
AB-BC = 2
But from question, AB-BC =m
=> m=2
Now total distance = AB+BC= 12
Substitute 12 to get answer in terms of m
Total distance =12 =6m
Ans B
Answer: (B) 6m
Question: A towel, when bleached, lost 20% of its length and 20% of its breadth. What is the percentage decrease in area?
(A) 24%
(B) 36 %
(C) 32%
(D) 54%
(E) 64%
Rationale: percentage change in area
=(−20−20+(20×20)/100)%=−36%
i.e., area is decreased by 36%
ANSWER:B
Answer: (B) 36 %
Question: A class has a ratio of 3:6:7 of children with red hair, blonde hair and black hair respectively. If the class has 9 kids with red hair, how many kids are there with black hair?
(A) 7
(B) 6
(C) 9
(D) 21
(E) 63
Rationale: Since there is a 3:7 ratio between red haired children and black-haired children, if there are 9 children with red hair, then there must be 3 times the amount of black-haired children. Therefore, are 21 children with black hair.
Answer: D)
Answer: (D) 21
Question: What is the probability that out of the combinations that can be made using all the letters of the word EXCESS, Jerome will randomly pick a combination in which the first letter is a vowel and the last letter is a consonant?
(A) 96/320
(B) 24/180
(C) 33/100
(D) 48/180
(E) 96/180
Rationale: lets see the possiblilties with the given restrictions..
lets put the starting letter as vowel E..
then remaining 5 places can be filled in 5!/2!= 60..
but this consists of second E as the last letter and we will have to subtract these ways from 60..
so when first and last places are occupied by E, the remaining 4 places can be filled by 4!/2!=12 ways..
so ways with the restrictions= 60-12= 48..
so prob= 48/180
ANSWER :D
Answer: (D) 48/180
Question: A, B and C are inner angles in a triangle. If A= B+ C, what can't be the size of B?
(A) 90 DEGREES
(B) 70 DEGREES
(C) 760 DEGREES
(D) 940 DEGREES
(E) 940 DEGREES
Rationale: Given A= B+ C, and A, Band Care inner angles in a triangle. Thus A+ B+ C= 180
B+ C+ B+ C= 180 => 2(B+ C) = 180 => B+ C= 90. Thus beta will be less than 90.
Hence the answer is A.
Answer: (A) 90 DEGREES
Question: Length of a rectangular plot is 24 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 52 m
(B) 62 m
(C) 72 m
(D) 82 m
(E) 92 m
Rationale: Let breadth = x metres.
Then, length = (x + 24) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 24) + x] = 200
2x + 24 = 100
2x = 76
x = 38.
Hence, length = x + 24 = 62 m
B
Answer: (B) 62 m
Question: 8 machines can do a work in 10days. How many machines are needed to complete the work in 40days?
(A) 2
(B) 6
(C) 4
(D) 7
(E) 5
Rationale: Required number of machines = 8*10/40 = 2
Answer is A
Answer: (A) 2
Question: Calculate the average marks of a student who obtained 56, 60, 72, 85 and 80 marks (out of 100) in Geography, History and Government, Art, Computer Science and Modern Literature ?
(A) 71.6
(B) 70.6
(C) 80.6
(D) 60.6
(E) 50.6
Rationale: Explanation:
Average = (56+60+72+85+80 )/ 5 = 70.6.
Answer: B) 70.6
Answer: (B) 70.6
Question: If 20,371 + x is a multiple of 4, which of the following could be the value of x?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 6
Rationale: Sum of the digits of 20,371 is 2+0+3+7+1 = 13
Now 13 is not a multiple of 4, the next multiple of 4 close to 13 is 16, which is 3 added to 13.
So the least number to be added to 20,371 is 3.
C
Answer: (C) 3
Question: The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
(A) 2377
(B) 1683
(C) 2677
(D) 9972
(E) 1611
Rationale: Explanation:
L.C.M. of 5, 6, 7, 8 = 840.
{\color{Blue} \therefore } Required number is of the form 840k + 3
Least value of k for which (840k + 3) is divisible by 9 is k = 2.
{\color{Blue} \therefore } Required number = (840 x 2 + 3) = 1683.
Answer: B) 1683
Answer: (B) 1683
Question: Plane leaves from Chelsea every 50 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?
(A) 6:35 pm
(B) 4:35 pm
(C) 4:35 pm
(D) 7:35 pm
(E) 8:35 pm
Rationale: A
6:35 pm
Time of Frank Lampard last missed plane = 7:00 p.m - 50 min = 6:10 p.m
As this information has been given to Frank Lampard 15 minutes after the plane has already left, the air hostess gave the information at 6:10 p.m + 25 min = 6:35 p.m
Answer: (A) 6:35 pm
Question: A number a is squared and then multiplied by negative 3. The result of this operation is equal to three times the sum of three times a and two. What is one possible value of a ?
(A) -3
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: -3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
ANSWER:D
Answer: (D) 2
Question: The value of a machine depreciates at the rate of 10% per annum. If its present value is Rs. 81000, what will be its worth after 2 ears? What was the value of the machine 2 years ago?
(A) Rs 65610,Rs 100000
(B) Rs 64320,Rs 120000
(C) Rs 60000,Rs 90000
(D) Rs 72690,Rs 95700
(E) None of thsee
Rationale: Explanation :
Solution: Value of the machine after 2 years = Rs.[81000(1 - 10/100)^2]
= Rs. 81000*9/10 * 9/10 = Rs. 65610.
Value of the machine 2 years ago = Rs. 81000/(1 - 10/100)^2
= Rs. 81000 * 10/9 * 10/9 = Rs. 100000
Answer : A
Answer: (A) Rs 65610,Rs 100000
Question: The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?
(A) 40%
(B) 8%
(C) 25%
(D) 16.66%
(E) 9%
Rationale: Original cost before weight adjustment: X
Cost after 90% weight adjustment: 9/10 X
20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100
Mark up on original cost of X: (108X/100)/X-1 = 8/100
ANSWER:B
Answer: (B) 8%
Question: What is the probability of getting a number less than 4 when a die is rolled?
(A) 5/5
(B) 1/2
(C) 5/1
(D) 5/7
(E) 5/2
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
i.e., n(S) = 6
E = Getting a number less than 4 = {1, 2, 3}
Hence, n(E) = 3
The probability = 3/6 = 1/2.
Answer: B
Answer: (B) 1/2
Question: There are a total of 17 students in Mr. David's gym class. Over the course of a badminton unit, each of the 17 students will compete exactly once against every other student in the class. How many total games of badminton will be played?
(A) 138
(B) 136
(C) 190
(D) 210
(E) 153
Rationale: there are 17 students , if each play with all other members .
then total games can be calculated as 16+15....+1 = 136.
alternate approach is to choose 2 distinct out of 17 = 17c2 = 136
Answer is B.
Answer: (B) 136
Question: A company organzied a help desk.there have been done 24 hrs work on software,17 hrs on help user nd 40% on other services.find the total no. of hrs have been worked on that day?
(A) 68
(B) 69
(C) 70
(D) 67
(E) 76
Rationale: let total no of hrs = x
they have done 24+17=41
40% of x is 40/100=2/5
x=41+2x/5
x=68.3
ANSWER:A
Answer: (A) 68
Question: Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?
(A) 100%
(B) 1%
(C) 10%
(D) 0.1%
(E) 0.01%
Rationale: Let the rate of interest during the second year be R%. Given,
450 * {(100 + 12)/100} * {(100 + R)/100} = 5544
R = 1%
ANSWER:B
Answer: (B) 1%
Question: In a kilometer race, A beats B by 200 meters or 10 seconds. What time does A take to complete the race?
(A) 180 sec
(B) 190 sec
(C) 290 sec
(D) 490 sec
(E) 40 sec
Rationale: Time taken by B run 1000 meters = (1000 * 10)/200
= 50 sec.
Time taken by A = 50 - 10
= 40 sec.
Answer:E
Answer: (E) 40 sec
Question: At what angle the hands of a clock are inclined at 15 minutes past 5?
(A) 58 1/2 º
(B) 64º
(C) 67 1/2 º
(D) 72º
(E) 77º
Rationale: Angle traced by hour hand in 21 hrs ={(360/12)x(21/4)}º =157 1/2 º Angle traced by min. hand in 15 min. ={(360/60)x 15}º = 90º. Required angle = 157 1/2	º - 90º = 67 1/2ºAnswer : C
Answer: (C) 67 1/2 º
Question: A, B and C enter into a partnership. They invest Rs. 50,000, 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) 16 : 14 : 8
(B) 15 : 16 : 28
(C) 15 : 4 : 28
(D) 3 : 4 : 1
(E) 3 : 4 : 5
Rationale: A : B : C = (50000 x 36) : (80000 x 12 + 40000 x 24) : (120000 x 24 + 40000 x 12)
= 180 : 192 : 336
= 15 : 16 : 28.
Answer: B
Answer: (B) 15 : 16 : 28
Question: The average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor. The weight of the new sailor is?
(A) 57 kg
(B) 60 kg
(C) 64 kg
(D) 62 kg
(E) 66 kg
Rationale: The sailor weighing 56 kg is replaced and the average is increased by 1 kg.
Hence, the weight of the new sailor is (56 + increase in total weight)
= 56 +1 x 8
= 56 + 8 = 64 kg.
ANSWER:C
Answer: (C) 64 kg
Question: A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be:
(A) 553681
(B) 555181
(C) 555681
(D) 556581
(E) 556881
Rationale: 987 = 3 x 7 x 47
So, the required number must be divisible by each one of 3, 7, 47
553681->(Sum of digits = 28, not divisible by 3)
555181->(Sum of digits = 25, not divisible by 3)
555681 is divisible by 3, 7, 47
ANSWER C
Answer: (C) 555681
Question: Express of the following as a fraction:
45%
(A) 14/25
(B) 9/20
(C) 9/40
(D) 9/19
(E) None of them
Rationale: 45% = 45/100= 9/20.
Answer is B.
Answer: (B) 9/20
Question: 39 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?
(A) 24
(B) 77
(C) 26
(D) 25
(E) 13
Rationale: Explanation:
Less Men, means more Days {Indirect Proportion}
Let the number of days be x
then,
27 : 39 :: 18 : x
[Please pay attention, we have written 27 : 39 rather than 39 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]
{\color{Blue} x=\frac{39\times 18}{27}}
x = 26
So 26 days will be required to get work done by 27 men.
Answer: C
Answer: (C) 26
Question: a light flashes every 30 seconds, how many times will it flash in ? of an hour?
(A) 550
(B) 600
(C) 650
(D) 700
(E) 120
Rationale: 1flash=30sec
for 1 min=2flashes
so for 1 hour=2*60=120 flashes.
ANSWER:E
Answer: (E) 120
Question: A store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought.
(A) 2/7
(B) 3/11
(C) 4/15
(D) 5/21
(E) 6/25
Rationale: The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 4 bottles of apple juice is 5C4*5C2 = 5*10 = 50
P(selling 4 bottles of apple juice) = 50/210 = 5/21
The answer is D.
Answer: (D) 5/21
Question: Last year a worker saved 6% of her annual salary. This year, she made 20% more money than last year and she saved 5% of her salary. The amount she saved this year was what percent of the amount she saved last year?
(A) 90%
(B) 100%
(C) 110%
(D) 120%
(E) 130%
Rationale: Let x be the worker's salary last year.
Last year, she saved 0.06x.
This year, she saved 0.05(1.2x)=0.06x
0.06x/0.06x=100%
The answer is B.
Answer: (B) 100%
Question: A call center has two teams. Each member of Team A was able to process 6/5 calls as compared to each member of Team B. If Team A has 5/8 as many number of call center agents as Team B, what fraction of the total calls was processed by Team B?
(A) 3/2
(B) 3/4
(C) 4/7
(D) 1/2
(E) 1/5
Rationale: Let team B has 8 agents, so team A has 5 agents
Let each agent of team B picked up 5 calls, so total calls by team B = 40
So, each agent in Team A picked up 6 calls, so total calls for team A = 30
Fraction for team B = 40/(40+30) = 4/7 = Answer = C
Answer: (C) 4/7
Question: A train 520 meters long is running with a speed of 34 kmph. The time taken by it to cross a tunnel 280 meters long is?
(A) 287 sec
(B) 89 sec
(C) 48 sec
(D) 16 sec
(E) 17 sec
Rationale: D = 580 + 280 = 800
S = 34 * 5/18 = 9 mps
T = 800/9 = 89 sec
Answer: B
Answer: (B) 89 sec