RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Worker A takes 6 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
A.15/4 days
B.40/9 days
C.39/9 days
D.30/9 days
Answer: A.15/4 days
Explanation: A's one hour work = 1/6.
B's one hour work = 1/10.
(A+B)'s one hour work = 1/6+1/10 = 8/30 = 4/15.
Both A & B can finish the work in 15/4 days
A
Question: Today is Monday. After 50 days, it will be :
A.Thursday
B.Saturday
C.Tuesday
D.Sunday
Answer: C.Tuesday
Explanation: Each day of the week is repeated after 7 days.
So, after 49 days, it will be Monday.
After 50 days, it will be Tuesday
Answer is C
Question: 12 is 4% of a, and 4 is 12% of b. c equals b/a. What is the value of c?
A.1/2
B.1/3
C.1/6
D.1/9
Answer: D.1/9
Explanation: 4a/100 = 12
a = 300
12b/100 = 4
b = 100/3
c = b/a = 100 / (3*300) = 1/9
The answer is D.
Question: By selling a bat for Rs.540/- a man loses 10% what is that bat cost price
A.s.600/-
B.s.630/-
C.s.700/-
D.s.780/-
Answer: A.s.600/-
Explanation: 90 % ------> 540 (90 * 6 = 540)
100 % ------>600 (100 * 6 = 600)
Cost price = Rs.600/-
A)
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 7, the how old is B?
A.	7
B.	8
C.	9
D.	10
Explanation:
A.5
B.7
C.9
D.1
Answer: D.1
Explanation: Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 7
5x = 5
x = 1.
Hence, B's age = 2x = 1 years.
Answer: Option D
Question: Find the probability that the number drawn is a factor of 50.
A.1/25
B.1/50
C.3/25
D.3/50
Answer: D.3/50
Explanation: The factors of 50 are 1, 2, 5, 10, 25, 50
Therefore, required probability = 6/100 = 3/50.
ANSWER:D
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
A.600
B.887
C.256
D.654
Answer: A.600
Explanation: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer: A
Question: A circular road runs around a circular garden. If the sum of the circumferences of the inner and outer circles is 88 metres and the radius of the inner circle is one-third of the outer circle, then the width of the road is :
A.4 metres
B.5 metres
C.7 metres
D.6 metres
Answer: C.7 metres
Explanation: let radius of inner circle=r1
radius of outer circle=r2
Also r1=1/3*r2
3*r1=r2
circumference of inner circle=2*pi*r1
circumference of outer circle=2*pi*r2
=6*pi*r1 (since r2=3*r1)
2*pi*r1 + 6*pi*r1 =88 (as per question)
r1=3.5 m
r2=3*3.5
=10.5 m
width of road =10.5 - 3.5 =7 m Ans.
ANSWER:C
Question: The cost per pound of milk powder and coffee were the same in June. In July, the price of coffee shot up by 300% and that of milk powder dropped by 80%. If in July, a mixture containing equal quantities of milk powder and coffee costs $6.30 for 3lbs, how much did a pound of milk powder cost in July?
A.$4
B.$0.2
C.$1
D.$3
Answer: B.$0.2
Explanation: Lets assume price of Coffee in June =100x
Price of milk powder in June =100x
Price of Coffee in July = 400x (because of 300% increase in price)
Price of milk powder in July = 20x (because of 80% Decrease in price)
Price of 1.5 pound of Coffee 1.5 pound of milk powder in July will be = 600x + 30x = 630x
As per question
630x= 6.30$
x = 0.01S
So the Price of milk powder in July = 20x = 20 x 0.01 = 0.2$/pound
Answer B
Question: Rahul went to a shop and bought things worth Rs. 25, out of which 54 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.19
B.15.7
C.19.9
D.21.7
Answer: B.15.7
Explanation: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 54 Paise is given as tax
=> Total tax incurred = 54 Paise = Rs.54/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 54/100
⇒ 6(25 −0.3 −x) = 54
⇒ (25 − 0.3 − x) = 9
⇒ x = 25 − 0.3 − 9 = 15.7
B)
Question: James celebrated his 23rd Birthday on 2016 but he was strangely born in 1950. How can this be possible?
A.1250
B.1850
C.1980
D.1950
Answer: D.1950
Explanation: D
I was born in Hospital whose room number is 1950.
Question: The average expenditure of a man for the first five months is Rs.240 and for the next seven months it is Rs.130. If he saves Rs.290 in that year, his monthly average income is :
A.Rs.140
B.Rs.150
C.Rs.160
D.Rs.200
Answer: D.Rs.200
Explanation: Explanation:
Total income = Rs.(240Ã—5+130Ã—7+290)=Rs.2400
Average monthly income
= Rs. (2400/12)=Rs.200
Correct Option: D
Question: In the board game Yahtzee one way to get a lot of points is to roll a "Yahtzee", which is rolling the same number for all five six-sided dice. What is the probability that you will roll a Yahtzee on your first roll?
A.Less than 0.1%
B.Between 0.1% and 0.5%
C.Between 0.5% and 1%
D.Between 1% and 2%
Answer: A.Less than 0.1%
Explanation: The acceptable rolls we need are any quad-tuple: 11111, 22222, 33333, 44444, 55555, and 66666. This makes 6 possibilities. The dice can fall in a combined 6*6*6*6*6 ways.
Hence the probability is 6/6^5 = 1/6^4 = 0.00077 = 0.077%
< 0.1%.
Answer: A
Question: A sum of Rs.4000 is lent out in two parts, one at 8% simple interest and the other at 10% simple interest. In the annual interest is Rs.352, the sum lent at 8% is
A.2376
B.3678
C.3657
D.2400
Answer: D.2400
Explanation: S.I = PNR/100
Answer with Explanation: Step (i) Given the total sum = Rs. 4000 Let the sum lent at 8% be Rs.x Let the sum lent at 10% be Rs. 4000 – x Ie) P = x , n=1, R = 8% P = 4000-x , n=1, R = 10%
100 81 XxX =
100 8x
100 1014000 XxX =
100 1040000 x 
Given annual interest = Rs. 352
100 8x +
100 1040000 x  = 352 8x – 10x = 35200 – 40000 -2x = -4800
X =
2 4800 = Rs.2400/-
Answer:D
Question: The length of a rectangular garden is three times its width. If the area of the rectangular garden is 588 square meters, then what is the width of the rectangular garden?
A.12
B.13
C.14
D.15
Answer: C.14
Explanation: Let x be the width of the garden.
3x^2 = 588
x^2 = 196
x = 14
The answer is C.
Question: A class consists of 4 boys and 5 girls. Given that one kid can only hold one title, in how many ways can you pick 2 boys to be the class clown and the teacher's pet or 2 girls to be the most beautiful girl in class and the smartest kid on the block?
A.9
B.32
C.36
D.60
Answer: B.32
Explanation: Easiest way is to treat it like an arrangements question in the following manner:
From the boys we need to select 2 to be clown and pet: This can be done in 3*4 ways
Similarly for the girls, we have 4*5 ways.
Thus total = 20+12 = 32 ways. Thus B is the correct answer.
Question: a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12
A.7
B.8
C.9
D.10
Answer: B.8
Explanation: add 44+12=56
now 56divided by 12 so we get 8 as reaminder
ANSWER:B
Question: A,B and C started a business by investing Rs.2000/- , Rs.3000/- and Rs.4000/- respectively. Total profit is Rs.4500/-. Find the A’s share?
A.Rs.1000/-
B.Rs.1500/-
C.Rs.2000/-
D.Rs.3000/-
Answer: A.Rs.1000/-
Explanation: A = Rs.2000/- , that is 2 parts
B = Rs.3000/- , that is 3 parts
C = Rs.4000/- , that is 4 parts
Total 9 parts -------> profit (4500/-)
----->1 part -------->Rs.500/-
then A's share 2 parts -----> Rs.1000/-
A
Question: If x and y are positive integers, and x^3*y^4 = 3456, which of the following is the value of xy?
A.6
B.10
C.12
D.14
Answer: C.12
Explanation: 3456 = 2^7*3^3 = 2^4*6^3
xy = 2*6 = 12
The answer is C.
Question: If 20 typists can type 48 letters in 20 minutes, then how many letters will 30 typists working at the same rate complete in 1 hour?
A.63
B.72
C.144
D.216
Answer: D.216
Explanation: 20 typists can type 48 letters, so 30 typists can type = 48*30/20
48*30/20 letters can be typed in 20 mins. In 60 mins typist can type= 48*30*60/20*20= 216
D is the answer
Question: The ratio of number of boys and girls in a school is 3:5. If there are 320 students in the school, find the number of girls in the school?
A.150
B.250
C.300
D.200
Answer: D.200
Explanation: Let the number of boys and girls be 3x and 5x
Total students = 320
Number of girls in the school = 5*320/8 = 200
Answer is D
Question: If 1.5 a = 0.03 b, then the value of (b – a)/ (b + a) is
A.490/51
B.49/51
C.4.9/51
D.4.99/51
Answer: B.49/51
Explanation: Explanation:
a/b = 0.03/1.5 = 3/150 = 1/50
(b – a)/(b + a)
= (1 – a/b)/((1 + a/b)
= (1 – 1/50)/ (1 + 1/50)
= 49/51
ANSWER B
Question: There is enough provisions for 600 men in an army camp for 25 days. If there were 250 men less, how long will the provision last?
A.10days
B.40days
C.50days
D.60days
Answer: D.60days
Explanation: Exp: We have, M1D1 = M2D2
600*25= 250* D2
D2 = 600*25/250 = 60 days.
Answer: D
Question: The sale price sarees listed for Rs.495 after successive discount is 15% and 10% is?
A.288
B.378
C.342
D.662
Answer: B.378
Explanation: 495*(85/100)*(90/100)
= 378
Answer: B
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 28 revolutions, what will be the number of revolutions made by the larger wheel?
A.15
B.12
C.21
D.9
Answer: B.12
Explanation: Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (Indirect proportion)
Hence we can write as
(cogs) 6 : 14 :: x : 28
â‡’6Ã—28=14 Ã— x
â‡’x = 12
Answer: Option B
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much
Look at this series: 1.4, 2.4, 3.4, 4.4, ... What number should come next?
A.5.4
B.3.6
C.4.9
D.5.0
Answer: A.5.4
Explanation: 5.4
In this simple addition series, each number increases by 1.0
Answer : A
Question: 4 dice are thrown simultaneously on the board. Find the probability show the same face?
A.2/121
B.2/227
C.1/216
D.1/219
Answer: C.1/216
Explanation: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let XX be the event that all dice show the same face.
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability,
=n(X)n(S)=664=n(X)n(S)=664
=1/216
C
Question: Pablo plays 3 rounds of a game, in which his chances of winning each round are 1/2, 1/4, and 1/n, respectively. If n ≠ 0, what is the probability that Pablo wins the first two rounds, but loses the third?
A.1/16n
B.(n-1)/8n
C.1/2n
D.(n+2)/2n
Answer: B.(n-1)/8n
Explanation: 1/2 * 1/4 * (1-1/n)
= 1/8 * (n-1)/n
= (n-1)/8n
Answer - B
Question: If 5 men can paint a wall 100 metres long in 10 days of a 8 hours each. In how many days of 6 hours each will 8 men paint a wall 30 metres long?
A.1.5 DAY
B.2 days
C.2.5 days
D.3 days
Answer: C.2.5 days
Explanation: Total hours in 10 days = 10 *8 = 80 hours.
Total man-hours needed for paint 100m wall = 5 *8 = 40 man-hours.
Man-hour needed for 1 meter wall painting = 400/100 = 4 man-hour.
Now,
30*4 = 120 m-h to do 30 meters.
120 m-h/8 men = 15 hours.
15 hr/6 hr/day = 2.5 days.
answer : C
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 144km/h, what is the circumference of the tire?
A.2 meters
B.6 meters
C.5 meters
D.3 meters
Answer: B.6 meters
Explanation: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 144,000 m : C is the circumference
C = 6 meters
correct answer B
Question: What is the area of a square field whose diagonal of length 20 m?
A.287
B.269
C.270
D.200
Answer: D.200
Explanation: d2/2 = (20 * 20)/2
= 200
Answer:D
Question: Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-2# = 2, what is the value of #2#?
A.5
B.0
C.-4
D.-3
Answer: C.-4
Explanation: #p# = ap^3 + bp - 1
#-2# = 2
putting p = -2 in above equation
-8a -(2b +1) = 2 or
#-2# = (8a+2b+1) = -2
therefore 8a+2b = -3 .....(1
now putting p =2
#2# = 8 a+2b - 1
using equation 1(8a+2b = -3)
#5# = -3-1 = -4
hence C
Question: Given a spinner with four sections of equal size labeled E, B, C, and D, what is the probability of NOT getting an E after spinning the spinner two times?
A.15/16
B.9/16
C.1/2
D.1/4
Answer: B.9/16
Explanation: The probability of NOT getting an E after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).
Answer: B.
Question: A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
A.400 m
B.450 m
C.560 m
D.600 m
Answer: D.600 m
Explanation: Length of the Ist train=2x m and the length of the other train be x m(1/2)
The relative speed of the train(48+42)=90kmph or 25m/s
Time taken to cross one another=12s
Hence, 12=2x+x/25
Solving, x=100m and 200m
Now to determine the length of the platform
45=100+length of the platform/speed of the Ist train
45=100+L/240/18( 48kmph=240/118m/s)
Solving, we get L=600M
ANSWER:D
Question: On Sunday Mario handled 75 sales. Deshawn handled 20% more sales than Mario, Callie handled 1/5 of the sales that Deshawn handled, and Jane handled 5 less sales than Callie. How much transactions did Jane handle?
A.90
B.13
C.65
D.70
Answer: B.13
Explanation: B
15
Mario handled 75 transactions
Deshawn handled 20% more transactions than Mario
Anthony = 75 + 75 × 20%
= 75+ 75 × 0.20
= 75 + 15
= 90
Callie handled 1/5 of the transactions than Deshawn handled
Callie = 1/5 × 90
= 18
Jane handled 5 less than Callie.
Jane = 18 - 5
= 13
Jane handled 13 transactions.
The correct answer is B.
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the number is 77, find the other?
A.88
B.99
C.76
D.55
Answer: B.99
Explanation: Other number = 11*693/77 = 99
Answer is B
Question: A clock loses a minute every three hours for 4 days and gains 2% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
A.11:54:40 AM
B.01:20:13 PM
C.12:16:40 PM
D.11:54:24 AM
Answer: B.01:20:13 PM
Explanation: Clock loses: 1 minute in 3 hours = 8 minutes in 24 hours = 32 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 2% in 6*24*60 minutes = 172.8 minute in 6 days;
Net gain in 10 days = 172.8 - 32 = 140.8 minutes.
11AM + 140.8 minutes = 01:20 and 13 seconds.
Answer: B.
Question: John weighs twice as much as Susan. Susan's weight is 60% of Sam's weight. Mark weighs 50% of Lynn's weight. Lynn weighs 190% of John's weight. Which of these 5 people weighs the least?
A.John
B.Susan
C.Sam
D.Mark
Answer: B.Susan
Explanation: Let J – John’s weight
S – Susan’s weight
M – Mark’s weight
A – Sam’s weight
L – Lynn’s weight
J = 2S
S = 0.6A
M = 0.5L
L = 1.9J
Let us convert these weights to one variable
S = J/2
A = S/0.6 = J/1.2 = 5J/6
L = 1.9J
M = 0.5 * 1.9J = 0.95J
So Susan has the least weight.
Answer - B
Question: If n is an odd integer less than 10, which of the following must also be an odd integer?
A.2n + n^2 + 2
B.n^3 + 2n
C.3n + 2^n
D.n^3 + 1
Answer: D.n^3 + 1
Explanation: Answer: D
A: 2n = even
B: 3n = even
C: 3n + n^2 + 2 = even
D: n^2 + 1 = odd
E: 2n + n^2 = even
Answer: D
Question: P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
A.3
B.8
C.12
D.4
Answer: B.8
Explanation: Let work done by P in 1 day = p
work done by Q in 1 day =q
Work done by R in 1 day = r
p + q = 1/8 ---(1)
q + r= 1/12	---(2)
p+ q+ r = 1/6	---(3)
(3) – (2) => p = 1/6 - 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days
Option B
Question: A Student got 78 marks in avg of 4 subjects.the avg odf 5 subjects is 80.what is the amrk he got in 5th subject.
A.87
B.88
C.89
D.90
Answer: B.88
Explanation: avg mrk he got in 5th subject=80*5-78*4
avg mrk he got in 5th subject=400-312=88
ANSWER:B
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent F of her bushes have only yellow roses?
A.20
B.30
C.50
D.70
Answer: B.30
Explanation: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, F=0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
OA B
Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 40%, what is the total capacity of the pool in gallons?
A.1000
B.1312.5
C.1400
D.1600
Answer: B.1312.5
Explanation: 300 gallons of water increases capacity by 40% that means
40% is 300 gallons, so 100% would be = 300*100/40= 750 gallons
Now 750 +300 gallons is 80% capacity of tank.
so 100% capacity would be= 1050 *100/80= 1312.5
B is the answer
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/3 of th area of the garden. What is the radius of the circular garden?
A.6
B.2
C.4
D.8
Answer: A.6
Explanation: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/3(pir^2)
pir^2=6pir
r=6
Answer : A
Question: If 60! is written out as an integer, with how many consecutive 0’s will that integer end?
A.6
B.12
C.14
D.42
Answer: C.14
Explanation: Soln:-
60/5+60/52=12+2=14
Answer: C
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 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.175
C.180
D.195
Answer: B.175
Explanation: Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
160 x 2.40 + x x 3.20 = 432
3.20x = 432 - 384 = 48
x = 15.
Hence, total hours of work = (160 + 15) = 175.
ANSWER IS B
Question: In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 31st in an arithmetic progression if the sum of the 14th and 18th terms of the sequence is 122?
A.46
B.51
C.56
D.61
Answer: D.61
Explanation: Let x be the difference between any two consecutive terms.
The mean of a sequence like this is the middle term, thus the 16th term in the sequence.
Then the mean of the 15th and 17th term is also equal to the overall mean, because the 15th term is (16th term - x) and the 17th term is (16th term + x).
Similarly the mean of the 14th and 18th term is also equal to the mean.
etc...
Thus the mean is 122/2 = 61
The answer is D.
Question: Yogesh started a business investing Rs. 45000. After 3 months, Pranab joined him with a capital of Rs. 60000. After another 6 months, Atul joined them with a capital of Rs. 90000. At the end of the year, they made a profit of Rs. 20000. What would be Atuls share in it?
A.Rs 7000
B.Rs 6000
C.Rs 5000
D.Rs 4000
Answer: D.Rs 4000
Explanation: Explanation:
Just take care of the months of investment, rest all will be simple.
Yogesh:Pranab:Atul = 45000*12:60000*9:90000*3
= 2:2:1
Atul's share = Rs. 20000 * (1/5) = Rs. 4000
Option D
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
A.80%
B.105%
C.120%
D.124.2%
Answer: C.120%
Explanation: Let's TEST:
1998
Revenues= $100
Profits = $10
Next we're told that, in 1999, revenue FELL by 20%, but profits were 15% of revenues. Using the numbers from 1998 (above), we end up with...
1999
Revenues = $80
Profits = $12
We're asked to compare the profits in 1999 to the profits in 1998 (as a percentage):
$12/$10 = 1.2 = 120%
ANSWER:C
Question: If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 25 men in 3 days?
A.65mtr.
B.52mtr
C.70mtr.
D.78mtr.
Answer: C.70mtr.
Explanation: 20 men is 6 days can build 112 metres
25 men in 3 days can build = 112*(25/20)x(3/6)
= 70 meters
Answer: C.
Question: A cyclist rides a bicycle 9 km at an average speed of 11 km/hr and again travels 11 km at an average speed of 9 km/hr. What is the average speed for the entire trip?
A.9.3
B.9.6
C.9.8
D.10.1
Answer: C.9.8
Explanation: distance = 20 km
time = 9/11 + 11/9 = (81 + 121) / 99 = 202 / 99 hours
average speed = (20 * 99) / 202 = 9.8 km/h
The answer is C.
Question: If M and N are positive integers that have remainders of 2 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
A.89
B.53
C.34
D.29
Answer: C.34
Explanation: M=6p+2
N=6q+3
We need M+N=6p+3+6q+3=6(p+q)+5
Pick numbers for pq
Since it is an addition of pq and the answer to this expression should be an integer (because all the numbers being added are integers),
we just need to choose values so that we get integer multiples of 6 so
p+q=0 ; M+n = 5
p+q=1 ; M+N = 11
P+q=2 ; M+N = 17
and so on, so basically you get something like - 5,11,17,23,29,35,41,..... all the other options were turning up.
Then I directly tried p+q=5 because it was closer to 34 , i got 35,
So Answer C.
Question: If the sum of two positive integers is 18 and the difference of their squares is 36, what is the product of the two integers?
A.108
B.80
C.128
D.135
Answer: B.80
Explanation: Let the 2 positive numbers x and y
x+ y = 18 -- 1
x^2 - y^2 = 36
=> (x+y)(x-y)=36 -- 2
Using equation 1 in 2 , we get
=> x-y = 2 -- 3
Solving equation 1 and 3 , we get
x= 10
y= 8
Product = 10*8 = 80
Answer B
Question: A, B and C, each working alone can complete a job in 6, 8 and 12 days respectively. If all three of them work together to complete a job and earn $ 2340, what will be C's share of the earnings?
A.$1100
B.$520
C.$1080
D.$1170
Answer: B.$520
Explanation: Explanatory Answer
A, B and C will share the amount of $2340 in the ratio of the amounts of work done by them.
As A takes 6 days to complete the job, if A works alone, A will be able to complete 1/6 th of the work in a day.
Similarly, B will complete 1/8th and C will complete 1/12th of the work.
So, the ratio of the work done by A : B : C when they work together will be equal to 1/6 : 1/8 : 1/12
Multiplying the numerator of all 3 fractions by 24, the LCM of 6, 8 and 12 will not change the relative values of the three values.
We get 24/6 : 24/8 : 24/12 = 4 : 3 : 2.
i.e., the ratio in which A : B : C will share $2340 will be 4 : 3 : 2.
Hence, C's share will be 2*2340/9 = 520.
correct choice is (B)
Question: A man can row three-quarters of a kilometre against the stream in 11 1/4 minutes. The speed (in km/hr) of the man in still water is:
A.4 1/4 km/hr
B.5 km/hr
C.6 km/hr
D.7 km/hr
Answer: B.5 km/hr
Explanation: Sol.
Rate upstream = [750 / 675] m/sec = 10/9 m/sec.
Rate downstream = [750 / 450] m/sec = 5/3 m/sec.
∴ Rate in still water = 1/2 [10/9 + 5/3] m/sec = 25/18 m/sec = [25/18 * 18/5] km/hr
= 5 km/hr
Answer B
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 14 such machines produce in 4 minutes ?
A.2520
B.1800
C.2700
D.10800
Answer: A.2520
Explanation: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
âˆ´ 6 Ã— 1 Ã— x = 14 Ã— 4 Ã— 270 â‡” x = 14x4x270/6= 2520 . Answer A