RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A class consists of 100 students, 20 of them are girls and 80 boys; 20 of them are rich and remaining poor; 40 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
A.2/125
B.1/59
C.1/56
D.1/54
Answer: A.2/125
Explanation: The probability of selecting girl is: 20/100 = 1/5
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 40/100 = 2/5
Three are independent;probability of rich and fair complexioned girl is:
(1/5) Ã—(1/5) Ã— (2/5) = 2/125
Answer: A
Question: Express 25 mps in kmph?
A.22
B.88
C.90
D.21
Answer: C.90
Explanation: 25 * 18/5 = 90 kmph
Answer: C
Question: A committee of 6 is chosen from 5 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed?
A.150
B.700
C.1404
D.2620
Answer: A.150
Explanation: The only cases possible are :
1. 2 men and 4 women : 5C2 * 5C4 = 50
2. 3 men and 3 women: 5C3*5C3 = 100
Rest of the cases will either have 1 or 0 men (not allowed) or will have 1 or 2 or 0 women (not allowed)
Total possible combinations = 50+100 = 150. Thus A is the correct answer.
Question: How many even multiples of 45 are there between 449 and 901?
A.5
B.6
C.9
D.10
Answer: B.6
Explanation: 450 = 10*45
900 = 20*45
The even multiples are 45 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Question: How many ways are there to split a group of 8 girls into two groups of 4 girls each? (The order of the groups does not matter)
A.30
B.40
C.35
D.45
Answer: C.35
Explanation: the combination is 8C4 /2
= 8!/4!*4! *2 = 35
C
Question: 49 members attended the party. In that 22 are males, 27 are females. The shake hands are done between males, females, male and female. Total 12 people given shake hands. How many such kinds of such shake hands are possible?
A.66
B.291
C.26
D.29
Answer: A.66
Explanation: If only 12 people shaked their hands, then total hand shakes are 12C212C2 = 66
Answer:A
Question: Martin has to secure 80% marks to clear his exam of class 9th.
He got 200 marks and failed by 200 marks.
What is the maximum marks ?
A.500
B.505
C.510
D.515
Answer: A.500
Explanation: A
500
To pass the exam ravish needs 200 + 200 = 400 marks.
=> (400/80) *100 = 500
Question: 96 can be expressed as a product of primes as
A.2 × 2 × 3 × 3 × 3 × 7
B.2 × 3 × 3 × 3 × 7 × 7
C.2 × 2 × 2 × 2 × 2 × 3
D.2 × 3 × 3 × 3 × 3 × 7
Answer: C.2 × 2 × 2 × 2 × 2 × 3
Explanation: Explanation:
It is clear that 96 = 2 × 2 × 2 × 2 × 2 × 3
Answer: Option C
Question: S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the tenth digit of p, counting right to left from the units digit?
A.1
B.2
C.4
D.6
Answer: D.6
Explanation: C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
p7 = (5+48) = 3
p8 = (5+46) = 1
p9 = (5+44) = 9
p10= (4+42) = 6
ANSWER : D
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
A.Rs.282
B.Rs.229
C.Rs.208
D.Rs.285
Answer: D.Rs.285
Explanation: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100]
= Rs.285.
Answer:D
Question: In a throw of dice what is the probability of geÆ«ng number greater than 4
A.1/2
B.1/3
C.1/5
D.1/6
Answer: B.1/3
Explanation: Explanation:
Number greater than 4 is 5 & 6, so only 2 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 2/6 = 1/3
Answer: B
Question: A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?
A.338
B.277
C.229
D.646
Answer: D.646
Explanation: 840 = P [1 + (10*3)/100]
P = 646
Answer:D
Question: The sum of three consecutive multiples of 3 is 72. What is the largest number?
A.21
B.24
C.27
D.36
Answer: C.27
Explanation: Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.
ANSWER:C
Question: 3 boys and 7 girls can complete John work in 10 days . But 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work?
A.10 days
B.20 days
C.40 days
D.56 days
Answer: C.40 days
Explanation: Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
Question: What is the greatest possible (straight line) distance, between any two points on a hemisphere of radius 4?
A.n/8
B.0.8
C.8
D.18
Answer: C.8
Explanation: Maximum distance straight line is diameter
d = 2r = 8..
ANS option C.
Question: The pilot of a small aircraft uses 60 gallons of fuel to fly 300 miles. At this rate, how many gallons of fuel are needed for a 700 mile flight?
A.140
B.155
C.160
D.170
Answer: A.140
Explanation: Number of gallons of fuel per mile = 300 /60 = 5 gallons per mile
Number of gallons of fuel for a 700 mile flight = 700/5 = 140
ANSWER:A
Question: If the integer n has exactly four positive divisors, including 1 and n, how many positive divisors does n^3 have?
A.16
B.11
C.10
D.20
Answer: A.16
Explanation: take the example of 6...
it has 4 positive divisors (1,2,3,4)
Now, take the example of 216 ...
it has 16 divisors..
so A is the ans
Question: An escalator moves towards the top level at the rate of 12 ft.sec and its length is 160 feet. If a person walks on the moving escalator at the rate of 8 feet per second towards the top level, how much time does he take to cover the entire length.
A.10sec
B.8sec
C.9sec
D.7sec
Answer: B.8sec
Explanation: Explanation :
Time taken to cover the entire length = tot.dist/resultant speed = 160/ (12+8) = 8sec
Answer : B
Question: The value of 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749 is closest to:
A.0.04
B.0.08
C.0.07
D.0.06
Answer: D.0.06
Explanation: = 489.1375 x 0.0483 x 1.956/0.0873 x 92.581 x 99.749
= 489 x 0.05 x 2/0.09 x 93 x 100
= 489/9 x 93 x 10
= 163/279 x 1/10
= 0.58/10
= 0.058 (or) 0.06.
Answer is D.
Question: The simple form of the ratio 8/5:2/3 is?
A.12:5
B.12:7
C.7:12
D.5:7
Answer: A.12:5
Explanation: 8/5:2/3 = 12:5
Answer: A
Question: The cost of 4 bags and 12 purses is Rs.1600, what is the cost of 10 bags and 30 purses?
A.Rs.3600
B.Rs.4000
C.Rs.3800
D.Rs.3900
Answer: B.Rs.4000
Explanation: Explanation:
Cost of 4 bags + 12 purses = Rs.1600
Multiply each term by 5/2, we get,
Cost of 10 bags + 30 purses = Rs.4000.
Answer: Option B
Question: When positive integer n is divided by 7, the remainder is 1. When n is divided by 11, the remainder is 5. What is the smallest positive integer k such that k+n is a multiple of 77?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: n = 7p + 1 = 11q + 5
n+6 = 7p + 7 = 11q + 11
n+6 is a multiple of 7 and 11, so it is a multiple of 77.
The answer is C.
Question: Starting with 0, a mathematician labels every non-negative integer as one of five types: alpha, beta, gamma, delta, or epsilon, in that repeating order as the integers increase. For instance, the integer 8 is labeled delta. What is the label on an integer that is the sum of an alpha raised to the seventh power and a delta raised to the seventh power?
A.alpha
B.beta
C.gamma
D.delta
Answer: C.gamma
Explanation: Let the alpha be 5k and let the delta be 5j+3.
(5k)^7 + (5j+3)^7 which has the form 5k+2, which is a gamma.
The answer is C.
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
A.11 1/9
B.11 1/4
C.19 1/9
D.11 1/2
Answer: B.11 1/4
Explanation: 3/12 + x/15 = 1
x= 11 1/4
Answer: B
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
A.60 gallons
B.100 gallons
C.120 gallons
D.180 gallons
Answer: C.120 gallons
Explanation: Explanation:
Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER IS C
Question: A and B undertake to do a piece of work for Rs. 1200. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of B.
A.250
B.450
C.750
D.800
Answer: B.450
Explanation: C's 1 day's work = 1/3-(1/6+1/8)=24
A : B : C = Ratio of their 1 day's work = 1/6:1/8:1/24= 4 : 3 : 1.
A’s share = Rs. (1200 *4/8) = Rs.600, B's share = Rs. (1200 *3/8) = Rs. 450
C's share = Rs. [1200 - (300 + 225») = Rs. 150.
Answer is B
Question: Given two fair dice, what is the probability Q that the sum of their numbers is 4 if exactly one die shows a 3?
A.a) 2/11
B.b) 1/18
C.c) 3/11
D.d) 2/39
Answer: A.a) 2/11
Explanation: If exactly one die shows 3, there are 10 such combinations (given that we have 2 fair dice).
1:3, 2:3, 4:3, 5:3, 6:3,
3:1, 3:2, 3:4, 3:5, 3:6
The sum of numbers would be 4 for two events: 1:3, 3:1.the probability Q that the sum of their numbers is 4 if exactly one die shows a 3
2/11 would be the answer if 'at least one of the die shows a 3'.A
Question: 60 + 5 * 12 / (180/3) = ?
A.60
B.120
C.13
D.61
Answer: D.61
Explanation: Explanation:
60 + 5 * 12 / (180/3) = 60 + 5 * 12 / (60)
= 60 + (5 * 12)/60 = 60 + 1 = 61.
ANSWER IS D
Question: A brick measures 20cm*10cm*7.5cm how many bricks will be requiredfor a wall 25m*2m*0.75m ?
A.24000
B.23000
C.22000
D.25000
Answer: D.25000
Explanation: 25*2*0.75=20/100*10/100*0.75/100*X25=1/100*XX=25000Answer :D
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations E of soloists can appear in the liner notes?
A.5!
B.10!/(5!5!)
C.10!/5!
D.10!
Answer: B.10!/(5!5!)
Explanation: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations E of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Question: The largest prime number is?
A.11
B.13
C.5
D.7
Answer: B.13
Explanation: The largest prime number is 13.
B)
Question: A collection of books went on sale, and 2/3 of them were sold for $3 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?
A.$216
B.$135
C.$90
D.$60
Answer: A.$216
Explanation: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($3) or $216. The best answer is therefore A.
Answer: A.
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
A.278
B.166
C.151
D.270
Answer: D.270
Explanation: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer:D
Question: One of the following numbers can be marked out as the odd one out. can you find which one?
1) 680986879
2) 716089780
3) 820670987
4) 932967879
A.The odd number is 680986879
B.The odd number is 820670987
C.The odd number is 716089780
D.The odd number is 932967879
Answer: B.The odd number is 820670987
Explanation: Correct Answer : B
if you add up the first three digits of all the numbers, it adds up to 14 except for second option 820670987
Question: If each term in the sum R=a1+a2+a3+...+an either 2 or 22 and the sum equals 100, which of the following could be equal to n?
A.38
B.39
C.40
D.41
Answer: C.40
Explanation: Min value of 'n' can be 10 i.e 4*22+6*12=R => 22+22+22+22+2+2+2+2+2+2 = 100
Since we don't have 10 in the options proceed further, (10-1)+22/2 => 20 digits, which is again not in the options
(20-1) + 22/2 = 30 digits ( not in options)
(30-1) + 22/2 = 40 digits
Hence C.
Question: The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 32,000 locusts?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: - 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
Answer : C
Question: The price of a book is increased from $300 to $330. What is the % of increase in its price?
A.10%
B.20%
C.30%
D.35%
Answer: A.10%
Explanation: Explanation: Change in the price = Rs 330 – Rs 300
= Rs 30
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 30 / 300
) *100 = 10%
A
Question: The 44 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
A.4
B.6
C.8
D.9
Answer: A.4
Explanation: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=44
solving for x you get 4
Answer A
Question: A and B together can do a piece of work in 2 days. If A alone can do the same work in 22 days, then B alone can do the same work in?
A.0.35 days
B.0.45 days
C.0.55 days
D.0.25 days
Answer: B.0.45 days
Explanation: B = 1/2 – 1/22 =0.45 days
ANSWER:B
Question: A farmer wishes to start a 100 sq. m. rectangular vegetable garden. Since he has only 30 meter barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. Then find the dimension of the garden.
A.20 m * 58 m
B.20 m * 7 m
C.20 m * 5 m
D.80 m * 5 m
Answer: C.20 m * 5 m
Explanation: From the question, 2b+l = 30
=> l = 30-2b
Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0
Area=100m2=>l×b=100=>b(30−2b)=100b2−15b+50=0=>(b−10)(b−5)=0
b = 10 or b = 5
when b = 10 then l = 10
when b = 5 then l = 20
Since the garden is rectangular so we will take value of breadth 5.
So its dimensions are 20 m * 5 m
Answer: C
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.27
B.82
C.245
D.288
Answer: C.245
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer:C
Question: A, B and C invest in a partnership in the ratio: 7/2, 4/3, 6/5. After 4 months, A increases his share 50%. If the total profit at the end of one year be Rs. 27,000, then what is B's share in the profit?
A.Rs. 2000
B.Rs. 3000
C.Rs. 4000
D.Rs. 5000
Answer: D.Rs. 5000
Explanation: Explanation :
Ratio of the initial investment = 7/2 : 4/3 : 6/5
= 105 : 40 : 36
From this ratio, we can assume that actual initial investments of A, B and C
are 105x, 40x and 36x respectively
A increases his share 50% after 4 months. Hence the ratio of their investments =
(105x * 4) + (105x * 150/100 * 8) : 40x * 12 : 36x : 12
= 105 + (105 * 3/2 * 2) : 40*3 : 36 * 3
= 105 * 4 : 40 *3 : 36 * 3
= 35 * 4 : 40 : 36
= 35 : 10 : 9
B's share = total profit * (10/54) = 27,000 * 10/54 = 5000. Answer : Option D
Question: In 16 minutes, the minute hand gains over the hour hand by
A.16°
B.80°
C.88°
D.96°
Answer: C.88°
Explanation: In 1 hour, the minute hand gains 330° over the hour hand.
i.e. in 60 minute, the minute hand gains 330° over the hour hand.
∴ In 16 minutes, the minute hand gains over the hour hand by 330°⁄60 × 16° = 88°
Answer C
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
A.11
B.18
C.19
D.12
Answer: B.18
Explanation: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.10 days
B.12 days
C.15 days
D.20 days
Answer: C.15 days
Explanation: A's 2 day's work = 1	x 2 =	1	.
20	10
(A + B + C)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
Option C
Question: What is the greatest positive integer E such that 3^E is a factor of 9^10?
A.E=5
B.E=9
C.E=10
D.E=20
Answer: D.E=20
Explanation: What is the greatest positive integer E such that 3^E is a factor of 9^10?
9^10 = (3^2)^10 = 3^20
D. 20
Question: A parking garage rents parking spaces for $10 per week or $35 per month. How much does a person save in a year by renting by the month rather than by the week?
A. $100
B. $160
C. $220
D. $240
Answer: A. $100
Explanation: 10$ per week!
An year has 52 weeks.
Annual charges per year = 52* 10 = 520$
35$ per month!
An year has 12 months.
Annual charges per year = 12 * 35 = 420$
520 - 420 = 100
Ans A
Question: How many arrangements of the letters of the word CONTINUES can be made, without changing the place of the vowels in the word?
A.130
B.140
C.150
D.120
Answer: D.120
Explanation: O,I,E,U fixed. Consonants can be arrangements in 5P5 = 5! = 120 ways
Option 'D'
Question: A train passes a station platform in 48 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.476 m
B.420 m
C.440 m
D.407 m
Answer: B.420 m
Explanation: Speed = [54 * 5/18] m/sec
= 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 15
x + 300 = 720
x =420 m.
Answer: B
Question: What was the day of the week on 17th June 1998?
A.Monday
B.Sunday
C.Wednesday
D.Friday
Answer: C.Wednesday
Explanation: Explanation:
17 Jun 1998 = (1997 years + period from 1-Jan-1998 to 17-Jun-1998)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 1600 years = 0 (Since 1600 is a perfect multiple of 400)
Number of odd days in the period 1601-1900
= Number of odd days in 300 years
= 5 x 3 = 15 = 1
(As we can reduce perfect multiples of 7 from odd days without affecting anything)
Number of odd days in the period 1901-1997
= 73 normal years + 24 leap year
= 73 x 1 + 24 x 2 = 73 + 48 = 121 = (121 - 7 x 17) = 2 odd days
Number of days from 1-Jan-1998 to 17-Jun-1998
= 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31(may) + 17(Jun)
= 168 = 0 odd day
Total number of odd days = (0 + 1 + 2 + 0) = 3
3 odd days = Wednesday
Hence 17th June 1998 is Wednesday.
Answer: Option C
Question: If p is an odd integer and q is an even integer, which of the following must be an even integer?
A.2q-p
B.3p+q
C.2p+3q
D.4(p+q)
Answer: D.4(p+q)
Explanation: p is odd; for this assume p=1
q is even; for this assume q = 2
(2*2)-1 = 3 Odd
(3*1)+2 = 5 Odd
(2*1)+(3*2) = 9 Odd
4(1+2) = 12 Even
1+(2^2) = 5 Odd
Answer:D
Question: Which of the following cannot be the sum of 2 different prime numbers?
A.10
B.13
C.14
D.15
Answer: C.14
Explanation: Option A: 10 = 7 + 3. Sum of 2 different prime numbers.
Option B: 13 = 11 + 2. sum of 2 different prime numbers
Option C: 4 = This is not a sum of 2 different prime numbers.
Option D: 15 = 13 + 2. Sum of 2 different prime numbers
Option E: 19 = 17 + 2. Sum of 2 different prime numbers
Correct Option: C
Question: A man buys $50 shares in a company which pays 10% dividend. If the man gerts 12.5% on his investment, at what price did he buy the shares?
A.37.5
B.40
C.50
D.48
Answer: B.40
Explanation: Dividend on 1 share = $(10/100*50)
=$5
$12.5 is an income on an investment of $100
$5 is an income on an investment of $(100*2/25*5)=40
Thus, cost of 1 share =$40
ANSWER B
Question: There are 418 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
A.152
B.209
C.242
D.171
Answer: C.242
Explanation: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 418 = 242
ANSWER:C
Question: Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?
A.9
B.12
C.14
D.16
Answer: B.12
Explanation: Explanation:
We have, 2/3 * 2/5 * 3/4 * X = 36
X = 180
Now, 4/5 * X = 4/5 * 180 = 144
√144 = 12
ANSWER: B
Question: A grocer has a sale of Rs. 5921, Rs. 5468, Rs. 5568, Rs. 6088 and Rs. 6433 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5900?
A.4902
B.4922
C.5922
D.5924
Answer: C.5922
Explanation: Total sale for 5 months = Rs. (5921 + 5468 + 5568 + 6088 + 6433) = Rs. 29478.
Required sale = Rs. [ (5900 x 6) - 29478 ]
= Rs. (35400 - 29478)
= Rs. 5922.
ANSWER:C
Question: Four packages have an average weight of 14.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 12 pounds?
A.25
B.24
C.23
D.22
Answer: B.24
Explanation: Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 12 pounds. Therefore (b + c) / 2 = 12.
b + c = 24
The average is 14.5 pounds. Therefore (a + b + c + d) / 4 = 14.5.
a + (b + c) + d = 58
a + 24 + d = 58
a + d = 34
The weight a must be no greater than 12, since 12 is the median. Therefore the minimum possible weight of the heaviest package is 34 – 12 = 24 pounds (all the other packages would weigh 12 pounds in this case).
Answer: B
Question: The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?
A.Rs. 5, Rs.7.50
B.Rs. 8, Rs. 12
C.Rs. 16, Rs. 10
D.Rs. 12, Rs. 14
Answer: C.Rs. 16, Rs. 10
Explanation: Solution:
Total cost of 10 books = Rs. 120
Total cost of 8 books = Rs. 94
=> The cost of 2 books = Rs. 26
Let the price of each book be x and y.
=> x + y = 26 ---------------- (1)
(160/100)y+y =26
On Solving for y, we get
y = 10.
Now, Substituting y = 10 in (1) we get,
x + 10 = 26
x = 16.
So the price of each book is Rs. 16 and Rs. 10 respectively.
Answer: Option C
Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-4) ∆ (4 ∆ −4) ?
A.2
B.4
C.6
D.8
Answer: B.4
Explanation: (-4) ∆ (4 ∆ −4) =
(-4) ∆ (8^2/4^2) =
(-4) ∆ (4) =
(-8^2) / (-4)^2 = 4
The answer is B.
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
A.18/35
B.18/35
C.18/39
D.18/31
Answer: A.18/35
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer: A