mathewhe/aqua_rat huggingface dataset:
Question: There are two cars. One is 160 miles north of the other. Simultaneously, the car to the north is driven westward at 10 miles per hour and the other car is driven eastward at 30 miles per hour. How many miles apart are the cars after 3 hours?
(A) 180
(B) 200
(C) 220
(D) 240
(E) 250
Rationale: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:
The right triangle will have a base of 120 and a height of 160. The hidden pattern here is a 3/4/5 right triangle (the 120 lines up with the '3' and the 160 lines up with the '4'). In this way, you can deduce that each side is '40 times' bigger than it's corresponding side:
3/4/5 becomes
120/160/200
Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...
Final Answer:
B
Answer: (B) 200
Question: In Town X, 64 percent of the population are employed, and 45 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 45%
(C) 32%
(D) 40%
(E) 28%
Rationale: answer b
male-employed - 64%
female-employed-19%
Total employed 64%
means total unemployed = 36%
therefore d and e are not correct because female unemployed has to be less than 36%
female-unemployed = 32% male unemployed = 4%
48% + 4% = 52%
16% + 32% = 48%
plug in a and b in place of 32% and the sum is not 100%
19/64 =28 E
Answer: (E) 28%
Question: Tom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4shots. What is the probability that at least 2 shots hit the target ?
(A) 1/2
(B) 2/5
(C) 2/3
(D) 3/7
(E) 3/11
Rationale: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by
Karan hits tha target and Raja not hit the target.
or
Karan does not hit the target and Raja hits the target.
or.
Karan hits the target and Raja hits the target
= 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6
= 24/36 = 2/3
C
Answer: (C) 2/3
Question: A car manufacturer produces only red and blue models which come out of the final testing area at random. What is the probability that five consecutive cars of same color will come through the test area at any one time?
(A) 1 in 16
(B) 1 in 125
(C) 1 in 32
(D) 1 in 25
(E) 1 in 15
Rationale: 2*(1/2)^5 =1 in 16
AS THERE ARE 5 CARS AND 2 TYPES
ANSWER:A
Answer: (A) 1 in 16
Question: A dice is rolled 3times & sum of 3 no.'sappearing on the uppermost face is 15. The chance that the first roll was four is?
(A) 1/21
(B) 1/31
(C) 1/108
(D) 1/113
(E) 2/213
Rationale: Sol. Total number of favorable outcomes n(S) . e . 216 Combinations of outcomes for getting sum of 15 on uppermost face = (4, 5, 6) (5, 4, 6) (6, 5, 4) (5, 6, 4), (4, 6, 5), (6, 4, 5), (5, 5, 5), (6, 6, 3), (6, 3, 6) (3, 6, 6) Now outcomes on which first roll was a four, n(E) = (4, 5, 6), (4, 6, 5) P(E) n(E) 2 1 Pt') = n(S) = 216 = 1/108
C
Answer: (C) 1/108
Question: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
(A) 50
(B) 55
(C) 100
(D) 25
(E) 52
Rationale: Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
=10 x5/18	m/sec
=25/9m/sec
2 x/36=25/9
2x = 100
x = 50.
Answer A
Answer: (A) 50
Question: Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be?
(A) Rs.16,537.58
(B) Rs.16,537.52
(C) Rs.16,537.50
(D) Rs.16,537.22
(E) Rs.16,537.21
Rationale: P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year = 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20)
= Rs. 16537.50
Answer:C
Answer: (C) Rs.16,537.50
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.50 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
(A) 160
(B) 170
(C) 190
(D) 200
(E) 210
Rationale: Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.50 + X x 3.20 = 432
X = 10.
Hence, total hours of work = (160 + 10) = 170.
answer :B
Answer: (B) 170
Question: Diana is going on a school trip along with her two brothers, Bruce and Clerk. The students are to be randomly assigned into 3 groups, with each group leaving at a different time. What is the probability that DIana leaves at the same time as AT LEAST on her bothers?
(A) 1/27
(B) 4/27
(C) 5/27
(D) 4/9
(E) 5/9
Rationale: 3 This post received
KUDOS 1 This post was
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For "atleast" problems, its easier to do (1 - opposite of what is being asked). Here 1 - different groups
# of ways in which Diana can be assigned a group = 3
# of ways in which Bruce can be assigned a group = 2 (since bruce cannot be assigned the same group as diana)
# of ways in which Clerk can be assigned a group = 2 (since clerk cannot be assigned the same group as diana)
=> 1 - (3/3)(2/3)(2/3)
=> 5/9
ANSWER:E
Answer: (E) 5/9
Question: The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue, in dollars, from the sale of cars priced at $ 13,000?
(A) 1,950,000,000
(B) 750,000
(C) 850,000
(D) 7,500,000
(E) 750,000,000
Rationale: number of cars sold = x=800000-50y
y=13000
x=800000-650000=150000
revenue from 150000 cars=13000*150000=1,950000000 A
Answer: (A) 1,950,000,000
Question: An auto supply store sells steering wheel covers arranged on display such that each of two different colors of steering wheel covers, blue, and purple are consecutive in a repeating pattern. If three consecutively displayed steering wheel covers are purchased, what is the probability that two of the steering wheel covers are purple?
(A) 3/4
(B) 2/5
(C) 1/4
(D) 2/3
(E) 1/2
Rationale: After blue and purple, the next steering wheel cover can be of any given two colours, therefore we have total two possibilites, out of which we need purple i.e. 1 therefore prob is 1/2. Correct answer is E.
Answer: (E) 1/2
Question: There are between 300 and 310 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?
(A)  301
(B)  303
(C)  306
(D)  307
(E)  309
Rationale: Let number of cards = x
If the cards are counted 3 at a time , there are 2 left over-
x= 3p+2
x can take values 306 , 309
If the cards are counted 4 at a time , there is 1 left over
x= 4q+1
x can take values 301 , 309
Therefore , x = 309
Answer E
Answer: (E)  309
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 16%?
(A) 17 per kg
(B) 17.40 per kg
(C) 16.5 per kg
(D) 16 per kg
(E) None of these
Rationale: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 116% of 3000 = (116⁄100 × 3000) = 3480
∴ Rate of S.P. of the mixture = (3480⁄200) per kg
= 17.40 per kg.
Answer B
Answer: (B) 17.40 per kg
Question: When q is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when q + y is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: In my view the answer should be C
q/5 has Remainder=3 -> q = 5 x Q + 3
Y/5 has a Remainder=4 -> Y = 5 x Q + 3
Combining both
((5 x Q1 + 3) + (5 x Q2 + 3))/5 =
5(Q1+Q2)/5 + 7/5 =
Q1+Q2 + 7/5
7/5 = 1+ 2/5 => Remainder 2
Answer C
Answer: (C) 2
Question: Find the cost of fencing around a circular field of diameter 35 m at the rate of Rs.1.50 a meter?
(A) 287
(B) 132
(C) 156
(D) 115.5
(E) 267
Rationale: 2 * 22/7 * 17.5 = 110
110 * 1 1/2 = Rs.115.5
Answer: D
Answer: (D) 115.5
Question: In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is 2/3 of the number of students of 8 years of age which is 24. What is the total number of students in the school?
(A) 50
(B) 80
(C) 120
(D) 150
(E) 100
Rationale: Explanation: Let the number of students be x.
Then, Number of students above 8 years of age = (100 - 20)% of x = 80% of x.
80% of x = 24 + 2/3 of 24
80/100x = 40
x = 50.
Answer: Option A
Answer: (A) 50
Question: .A man has Rs. 312 in the denominations of one-rupee notes, five-rupee notes and twenty-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 36
(B) 24
(C) 28
(D) 32
(E) 30
Rationale: Let number of notes of each denomination =x Then
x+5x+20x=312
⇒26x=312
⇒x=312/26=12
Total number of notes =3x=3×12=36
Answer: A
Answer: (A) 36
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 20 years now, the son's age five years back was:
(A) 2 years
(B) 14 years
(C) 5 years
(D) 38 years
(E) 7 years
Rationale: Let the son's present age be x years.
Then, (20 - x) = x
2x = 20 => x = 10
Son's age 5 years back = (10 - 5) = 5 years.
ANSWER:C
Answer: (C) 5 years
Question: A Sum of Rs.2600, is lent out in 2 parts SI at 10% for 5yrs is equal to SI on 2nd part at 9% rate for 6 yrs. find the ratio of parts.
(A) 21:25
(B) 27:25
(C) 21:23
(D) 31:25
(E) 33:22
Rationale: Solution :
Given SI1 = SI 2
P1 : P2 = 1/R1T1 : 1/R2T2
= 1/(10*5) : 1/(9:6)
27:25
B
Answer: (B) 27:25
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
(A) 339
(B) 349
(C) 369
(D) 359
(E) Data inadequate
Rationale: Explanation:
x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p
17
The least value of p for which q =	2 + 13p	is a whole number is p = 26
17
x = (13 x 26 + 11)
= (338 + 11)
= 349
Answer: B
Answer: (B) 349
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 5 hours while an novice chef would finish the preparations in 9 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Experienced chefs work = 1 wedding/5 hours
Novice chefs work = 1 wedding/9 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equalx
1hr and 36mins = 8/5 an hour
x/5 + x/9 = 1 wedding / (8/5)
x/5 + x/9 = 5/8
x=2
So there are 2 novice chefs and 2 experienced chefs. In total there are 4. The answer is C.
Answer: (C) 4
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 5200 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
(A) 2160
(B) 2350
(C) 2000
(D) 2300
(E) None of these
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+5200 = 20700
Exp in % = 100-10 = 90%, 20700 = 90%
Saving = 10 % = 20700 X 10/90 = Rs. 2300
Answer : D
Answer: (D) 2300
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.8
(B) 12.1
(C) 12.0
(D) 12.2
(E) 12.4
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer:B
Answer: (B) 12.1
Question: A lady bought five books namely A,B,C,D,E to distribute her 7 friends. How many ways she can distribute books?
(A) 7^3
(B) 7^4
(C) 7^5
(D) 7^6
(E) 7^2
Rationale: 7*7*7*7*7
7^5
ANSWER:C
Answer: (C) 7^5
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is five times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 1:1
(B) 2:3
(C) 3:2
(D) 9:4
(E) 45:8
Rationale: Water:soap = 3:2
Soap:Salt=15:2
=> For 15 soap, salt = 2
=> For 2 Soap, salt = (2/15)*2 =4/15
So, water:soap:salt = 3:2:4/15 = 45:30:4
After open container, water:soap:salt = 22.5:30:4
So, water:salt = 22.5:4 = 45:8
E
Answer: (E) 45:8
Question: What is the ratio between perimeters of two squares one having 4 times the diagonal then the other?
(A) 3: 8
(B) 3: 6
(C) 3: 7
(D) 4: 1
(E) 3: 3
Rationale: d = 4d d = d
a√2 = 4d a√2 = d
a = 4d/√2 a = d/√2 => 4: 1
Answer:D
Answer: (D) 4: 1
Question: The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 41 degrees. Find the temperature on Friday?
(A) 65 degrees
(B) 73 degrees
(C) 37 degrees
(D) 34 degrees
(E) 33 degrees
Rationale: M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 41
Tu + W + Th = 192 -41= 151
F = 184 – 151 = 33
Answer:E
Answer: (E) 33 degrees
Question: In how many ways can 5 man draw water from 5 taps if no tap can be used more than once?
(A) None of these
(B) 720
(C) 60
(D) 120
(E) None of these
Rationale: Explanation :
1st man can draw water from any of the 5 taps
2nd man can draw water from any of the remaining 4 taps
3rd man can draw water from any of the remaining 3 taps
4th man can draw water from any of the remaining 2 taps
5th man can draw water from remaining 1 tap
5	4	3	2	1
Hence total number of ways = 5 x 4 x 3 x 2 x 1 = 120. Answer : Option D
Answer: (D) 120
Question: Which number is the odd one out?
(A) 47632
(B) 36119
(C) 84129
(D) 67626
(E) 72927
Rationale: A
47632
All the others are three digit numbers followed by their square root, eg 361 followed by its square root, 19.
Answer: (A) 47632
Question: Find the area of trapezium whose parallel sides are 10 cm and 18 cm long, and the distance between them is 15 cm.
(A) 287 cm2
(B) 785 cm2
(C) 285 cm2
(D) 785 cm2
(E) 210 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (10 + 18) * (15) = 210 cm2
Answer: Option E
Answer: (E) 210 cm2
Question: The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
(A) 23:33:60
(B) 10:11:20
(C) 3:4:5
(D) 10:20:11
(E) 23:30:65
Rationale: Let A = 2k, B = 3k and C = 5k.
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?
[A].	3 : 3 : 10
[B].	10 : 11 : 20
[C].
23 : 33 : 60	@
[D].	Cannot be determined
Answer: Option C
Explanation:
Let A = 2k, B = 3k and C = 5k.
A sal = 115/100 of 2k = 23k/10
B sal = 110/100 of 3 k=33k/10
c sal= 6k
new ratio (23k/10:33k/10:6k) = 23:33:60
ANSWER A
Answer: (A) 23:33:60
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
(A) 5/5
(B) 5/9
(C) 3/4
(D) 5/7
(E) 5/2
Rationale: In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E	= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}=27
The probability = 27/36 = 3/4.
Answer: C
Answer: (C) 3/4
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 602 to 700 inclusive?
(A) 24,550
(B) 28,550
(C) 32,550
(D) 36,550
(E) 40,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
602 + 604 + ... + 700 = 50(600) + (2+4+...+100) = 30,000 + 2550 = 32,550
The answer is C.
Answer: (C) 32,550
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor G of 2x and 3y?
(A) G=1
(B) G=Cannot be determined
(C) G=2
(D) 5
(E) 6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD (1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: (B) G=Cannot be determined
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 20 are excluded, the average mark of the remaining will be 95. Find the number of students who wrote the exam.
(A) 15
(B) 45
(C) 35
(D) 25
(E) 55
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 95(x - 5)
80x - (5 * 20) = 95(x - 5)
375 = 15x => x = 25
ANSWER:D
Answer: (D) 25
Question: How many of the positive factors of 10 , 16 and how many common factors are there in numbers?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: factors of 12 - 1, 2, 3, 4, 6, and 12
factors of 16 - 1 , 2, 4, 8 and 16
Comparing both, we have three common factors of 45,16-3
Answer C
Answer: (C) 3
Question: Which among the following is the greatest?
(A) 2^3^2
(B) 2^2^3
(C) 3^2^3
(D) 3^3^3
(E) 5^3^3
Rationale: 2^3^2 = 29
2^2^3 = 28
3^2^3 = 38
3^3^3 = 327
As 327 > 38, 29 > 28 and 327 > 29. Hence 327 is the greatest among the four.
ANSWER:D
Answer: (D) 3^3^3
Question: A and B invests Rs.3000 and Rs.6000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 3:4
(B) 9:8
(C) 9:9
(D) 9:5
(E) 9:1
Rationale: (3*6 + 6*6): (6*12)
54:72 => 3:4
Answer: A
Answer: (A) 3:4
Question: The difference between a two digit number and the number obtained by interchanging the digits is 72. What is the difference between the digits of the number?
(A) 7
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: Description :
=> (10x+y)-(10y+x)=72
=> 9(x-y)=72
=> x-y = 8
Answer D
Answer: (D) 8
Question: Two dogsled teams raced across a 600-mile course in Alaska. Team A finished the course in 6 fewer hours than team B. If team A’s average speed was 5 miles per hour greater than that of team B, what was team B’s average speed, in miles per hour?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: Let v be team B's average speed.
Time = Distance/Rate and the time difference was 6 hours.
600/v - 600/(v+5)= 6
600v + 3000 - 600v = 6(v)(v+5)
500 = (v)(v+5)
(20)(25) = (v)(v+5)
v = 20 mph
The answer is D.
Answer: (D) 20
Question: An investor invests in a new fund. The fund averages 10% growth annually for the first three years, but it loses 25% of its value in the fourth year. At the end of four years, the value of the fund is approximately what percent of the original amount?
(A) 99.825%
(B) 97.785%
(C) 95.125%
(D) 93.675%
(E) 91.175%
Rationale: 0.75*1.1^3 = 0.99825
The answer is A.
Answer: (A) 99.825%
Question: How many factors of 60 are odd numbers greater than 1?
(A) 3
(B) 4
(C) 5
(D) 3
(E) 7
Rationale: prime factors of 60 are 2^2,3^1,5^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,) = (1+1)(1+1)=4
since we need odd divisors other than 1 =>4-1 = 3 odd divisors
D is the answer
Answer: (D) 3
Question: In how many ways can three consonants and two vowels be selected from the letters of the word "TRIANGLE"?
(A) 14 ways
(B) 61 ways
(C) 71 ways
(D) 31 ways
(E) 30 ways
Rationale: The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways.
3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 =30 ways.
Answer: E
Answer: (E) 30 ways
Question: The length of a rectangular plot is 10 meters more than its width. If the cost of fencing the plot at $15.50 per meter is $868, what is the length of the plot in meters?
(A) 17
(B) 19
(C) 21
(D) 23
(E) 25
Rationale: perimeter = 2L + 2W = 2L + 2(L-10) = 4L - 20
cost of fencing = (4L - 20) * 15.50 = 62L - 310 = 868
62L = 1178
L = 19 meters
The answer is B.
Answer: (B) 19
Question: In a class of 38 children,19 play tennis, 21 play squash and 10 play neither sport. (1)how many children play both sports?
(A) 11
(B) 12
(C) 14
(D) 15
(E) 19
Rationale: 28 play some sport
19+21-both=28
both = 12
Answer is B
Answer: (B) 12
Question: Sharron bakes 6 cookies for 6 friends. 2 of the friend arrive early and eat 3 cookies each. How many cookies are left over if the other friends all have the same number of cookies?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Sharron made 6*6 cookies = 36 cookies. 2 friends eat 3 cookies, leaving 30 remaining for 4 friends.
30=2*3*5. 30 is not divisible by 4. The 4 friends ate a cumulative number of cookies less than 30 that must be divisible by 4, because the number is the same.
A 30 -1=29. 29=1*29, cannot be divided by four
B 30-2=28. 28=2*2*7, can be divided by four
C 30-3 = 27. 27=3*3*3, cannot be divided by four
D. Because there are 4 people, 4 cannot be a remainder (remainder = 0)
E. Because there are 4, people, 5 cannot be a remainder (remainder = 1)
B is the correct answer
Answer: (B) 2
Question: A trader sells 30 meters of cloth for Rs. 4500 at the profit of Rs. 10 per metre of cloth. What is the cost price of one metre of cloth?
(A) Rs. 80
(B) Rs. 185
(C) Rs. 140
(D) Rs. 295
(E) None of these
Rationale: SP of 1m of cloth = 4500/30 = Rs. 150
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 150 - Rs. 10 = Rs. 140.
ANSWER:C
Answer: (C) Rs. 140
Question: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold?
(A) 480
(B) 992
(C) 772
(D) 662
(E) 188
Rationale: 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer:A
Answer: (A) 480
Question: What is the average (arithmetic mean) of all multiples of 10 from 10 to 600 inclusive?
(A) 190
(B) 195
(C) 305
(D) 205
(E) 210
Rationale: This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 600, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
60(10) = 600
So we know that there are 60 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 600 = 610
20 + 590 = 610
30 + 580 = 610
Etc.
Since there are 60 total terms, this pattern will create 30 'pairs' of 610.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(30)(610)/(60) =305
Final Answer: C
Answer: (C) 305
Question: A man bought a computer at 30% discount on its original price. He sold it at a 520% increase on the price he bought it. What percent of profit did he make on the original price?
(A) 1%
(B) 2%
(C) 3%
(D) 4%
(E) 5%
Rationale: Original price = 100
CP = 70
S = 70*(150/100) = 105
105 - 100 = 5%
Answer: E
Answer: (E) 5%
Question: Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?
(A) 2528
(B) 2526
(C) 2522
(D) 2722
(E) 2426
Rationale: A = 1600(21/20)3 = 2522
Answer: C
Answer: (C) 2522
Question: The speed of a boat in still water in 26 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 20 minutes is:
(A) 10.4 km
(B) 10.66 km
(C) 11.4 km
(D) 11.22 km
(E) 12 km
Rationale: Explanation:
Speed downstream = (26 + 6) = 32 kmph
Time = 20 minutes = 20/60 hour = 1/3 hour
Distance travelled = Time × speed = (1/3)×32 = 10.66 km
Answer: Option B
Answer: (B) 10.66 km
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
(A) 4/5
(B) 4/9
(C) 4/6
(D) 4/2
(E) 4/1
Rationale: x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
Answer: (A) 4/5
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 729
(C) 365
(D) 735
(E) 345
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄
= 6 * 5 * 4 * 3 = 360.
Answer:A
Answer: (A) 360