RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The sum of three consecutive numbers is 87. The greatest among these three number is:
A.26
B.28
C.29
D.30
Answer: D.30
Explanation: Let the numbers be x, x + 1 and x + 2
Then,
x + (x + 1) + (x + 2) = 87
3x = 84
x = 28
Greatest number, (x + 2) = 30.
ANSWER:D
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 1/5
B.11 1/4
C.11 1/9
D.11 1/2
Answer: B.11 1/4
Explanation: 3/12 + x/15 = 1
x= 11 1/4
Answer:B
Question: A painting at an art gallery is framed such that the area of the square frame is 2/3 the area of the painting itself. If the diagonal line connecting corners of the frame has a length of 10, what is the area of the painting inside the frame?
A.10
B.20
C.30
D.40
Answer: C.30
Explanation: Suppose side of the painting(which is a square) is a and side of the outer square(painting+frame) is b
Area of painting = a^2 and we know that the area of the frame is (2/3) of that of the painting so
Area of frame = (2/3) * a^2
Area of Frame + Painting = a^2 + (2/3)*a^2 = (5/3)*a^2 which is equal to b^2
Line connecting the corners of the frame is the diagonal of the outer square which is equal to b*sqrt2
so, b * sqrt2 = 10
so, b = 5 * sqrt2
b^2 = 50
we know that b^2 = (5/3)*a^2
so, a^2 = (3/5)*b^2 = (3/5)*50 = 30
And area of painting = a^2 = 30
So, answer will be C.
Question: In a room filled with 6 people, all 6 people have exactly 1 sibling in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
A.3/5
B.4/5
C.5/6
D.5/12
Answer: B.4/5
Explanation: The 6 people consist of three sets of 2 siblings.
The number of ways to choose 2 people is 6C2 = 15.
The number of ways to choose 2 from the first group of siblings is 2C2 = 1.
The number of ways to choose 2 from the second group of siblings is 2C2 = 1.
The number of ways to choose 2 from the third group of siblings is 2C2 = 1.
The number of ways to choose 2 people who are siblings is 1+1+1 = 3.
The number of ways to choose 2 people who are not siblings is 15-3=12.
P(the two people are not siblings) = 12/15 = 4/5
The answer is B.
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.3 km long?
A.2 mins 14 sec
B.2 mins 34 sec
C.168 sec
D.344 sec
Answer: C.168 sec
Explanation: D = 25 * 60 + 1300 = 2800 m
T = 2800/60 * 18/5 = 168 sec
ANSWER:C
Question: Find the odd man out
1, 3, 10, 21, 64, 129, 356, 777
A.10
B.21
C.64
D.356
Answer: D.356
Explanation: 1*2+1=3,3*3+1=10,10*2+1=21,21*3+1=64,64*2+1=129,129*3+1=388 but here it placed with 356, so it is wrong. starts with x*2+1,next x*3+1 alternately changes
ANSWER:D
Question: If 2 persons can do 2 times of a particular work in 2 days, then, 7 persons can do 7 times of that work in
?
A.3 days
B.7 days
C.9 days
D.2 days
Answer: D.2 days
Explanation: That is, 1 person can do one time of the work in 2 days.
Therefore, 7 persons can do 7 times work in the same 2 days itself.
Option 'D'
Question: There are 10 periods in each working day of a school. In how many ways can one organize 9 subjects such that each subject is allowed at least one period?
A.16329600
B.16356789
C.16324600
D.15679892
Answer: A.16329600
Explanation: 9 subjects can be arranged in 10 periods in 10P9 ways.
Remaining 1 period can be arranged in 9P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (10p9 x 9P1)/2! = 16329600
ANSWER:A
Question: 19 balls are numbered 1 to 19. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
A.2/9
B.4/19
C.6/29
D.8/39
Answer: B.4/19
Explanation: P(1st ball is even) = 9/19
P(2nd ball is also even) = 8/18
P(both balls are even) = 9/19 * 8/18 = 4/19
The answer is B.
Question: A survey reveals that the average income of a company’s customers is $50,000 per year. If 50 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 40 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
A. $27,500
B. $43,750
C. $37,500
D. $42,500
Answer: B. $43,750
Explanation: let x be the average of 40 customers
40*x + 10* 75000 = 50*50000
solving this we have x= 43750
Answer is B.
Question: The LCM of two numbers is 2310 and HCF is 26. If one of the numbers is 210. Then what is the other number ?
A.715
B.825
C.286
D.582
Answer: C.286
Explanation: First number * Second Number = LCM * HCF
Other number = 2310 * 26 / 210 = 11*26 = 286
ANSWER :C
Question: In a country where everyone wants a boy, each family continues having babies till they have a boy. After some time, what is the proportion of boys to girls in the country? (Assuming probability of having a boy or a girl is the same)
A.1:2
B.3:5
C.1:1
D.3:7
Answer: C.1:1
Explanation: C
1:1
This is a very simple probability question in a software interview. This question might be a little old to be ever asked again but it is a good warm up.
Assume there are C number of couples so there would be C boys. The number of girls can be calculated by the following method.
Number of girls = 0*(Probability of 0 girls) + 1*(Probability of 1 girl) + 2*(Probability of 2 girls) + …
Number of girls = 0*(C*1/2) + 1*(C*1/2*1/2) + 2*(C*1/2*1/2*1/2) + …
Number of girls = 0 + C/4 + 2*C/8 + 3*C/16 + …
Number of girls = C
(using mathematical formulas; it becomes apparent if you just sum up the first 4-5 terms)
The proportion of boys to girls is 1 : 1.
Question: The average of 9 observations was 5, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
A.45
B.12
C.15
D.17
Answer: A.45
Explanation: Explanation:
1 to 9 = 9 * 5 = 45
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 45 = 45
Option A
Question: The least number of five digits which is exactly divisible by 12,15 and 18 is :
A.10010
B.10015
C.10020
D.10080
Answer: D.10080
Explanation: Solution
Least number of 5 digits is 10000. L.C.M. of 12, 15 and 18 is 180.
On dividing 1000 by 180, the remainder is 100.
∴ Required number = 10000 + (180 - 100) = 10080. Answer D
Question: If a, b are integers and |a-b|=10, which of the following is the smallest possible value of ab?
A.-16
B.0
C.-25
D.7
Answer: C.-25
Explanation: a=5, b=-5. Hence, the answer is C.
Question: The cost of hiring a bus is shared equally by all passengers. The bus has seats for 40 passengers and the total bill comes to Rs.70.37. How many seats went unoccupied?
A.13
B.11
C.9
D.7
Answer: C.9
Explanation: As the bill of Rs 70.37 is equally divided, it is only possible when 31 passengers shared the bill.
70.37/31= 2.27
Also
70.37 is not fully divisible by 27,29,33.
so 40-31=9 seats went unoccupied.
ANSWER:C
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 80 km apart both 3 and 6 hours after start, then find the distance between the two stations.
A.240 km
B.230 km
C.220km
D.180km
Answer: A.240 km
Explanation: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+80+ 80
2(R+S ) = R+S +160
R+S = 160
Hence distance between XY is R+S+ 80 = 160 +80 =240
Answer : A
Question: Keats Library purchases a number of new books, all in the category of biography, and the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 30% of the total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
A.47%
B.59%
C.71%
D.83%
Answer: C.71%
Explanation: Let x be the number of new biographies added to the library.
Let b be the original number of biographies, so the original number of books was 5b.
0.3(5b+x) = b+x
0.5b = 0.7x
x = 0.71b
The answer is C.
Question: 2 dice are tossed. What is the probability that the total score is a prime no. is?
A.1/13
B.5/12
C.3/11
D.4/13
Answer: B.5/12
Explanation: 5/12
B
Question: The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
A.1/48
B.1/42
C.1/46
D.1/47
Answer: B.1/42
Explanation: 2/3 * 6/7 * 1/3 * 1/8 = 1/42
Answer: B
Question: What two-digit number is less than the sum of the square of its digits by 10 and exceeds their doubled product by 5?
A. 94
B. 99
C. 26
D. 73
Answer: A. 94
Explanation: Let the digits be x and y. The number would be 10x + y.
We are given that 2xy + 5 = 10x +y = x^2 y^2 -10
Thus 2xy +5 = x^2 + y^2 - 10
x^2 + y^2 -2xy = 15
(x-y)^2 = 16
(x-y) = 4 or -4
Substituting the values of (x-y) in the equation 2xy +5 = 10x + y
x comes out to be 1 or 9... thus the two numbers can be 15 or 94
Thus the answer is A
Question: A can run 1.5 km distance in 2 min 20 seconds, while B can run this distance in 2 min 30 sec. By how much distance can A beat B?
A.90 m
B.100 m
C.120 m
D.180 m
Answer: B.100 m
Explanation: A takes time 2.20 minutes=140sec
B takes time 2.30 minutes=150sec
diffrence= 150-140=10sec
now we are to find distance covered in 10 sec by B
150sec=1500m
1sec=10m
10sec=10x10=100m
ANSWER:B
Question: subash can copy 50 pages in 10 hrs.subash and prakash together can copy 300 pages in 40 hours.in how much time prakash can copy 25 pages.
A.8
B.10
C.12
D.14
Answer: B.10
Explanation: subhas 's 1 hr copy page=50/10=5 page
(subhas+prakash)'s 1 hr copy page=300/40=7.5 page
from above prakash's 1 hr copy page= 2.5 page
so time taken in 30 page's copy =(25/2.5)=10 hrs
ANSWER:B
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
A.24%
B.74%
C.69%
D.64%
Answer: D.64%
Explanation: r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
Answer: D
Question: If b is a positive integer, then 3^b + 3^(b) =
A.3^(b + 1)
B.2^(b + 1)
C.2(3^b)
D.2b^(b + 1)
Answer: C.2(3^b)
Explanation: If b is a positive integer,3^b+3^b=2(3^b)
option C is answer
Question: On a race track a maximum of 5 horses can race together at a time. There are a total of 25 horses. There is no way of timing the races. What is the minimum number Q of races we need to conduct to get the top 3 fastest horses?
A.5
B.7
C.8
D.10
Answer: B.7
Explanation: Q=7 is the correct answer.
Good solution Buneul.B
Question: The sequence a1, a2, a3, a4. a5 is such that an = a n-1 +5 for 2≤ n ≤ 5. If a5 = 33 what is the value of a1 ?
A.1
B.6
C.13
D.16
Answer: C.13
Explanation: Here, each value of an is the previous value plus 5
Since the numbers are less, the fastest way to solve this problem is to successively subtract 5 from a5 till you reach a1
a5 = 33
a4 = 29
a3 = 23
a2 = 18
a1 = 13 <<<< Ans C
Question: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 60 kg. What might be the weight of the new person ?
A.75 kg
B.55 kg
C.80 kg
D.85 kg
Answer: C.80 kg
Explanation: Explanation:
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (60 + 20) kg = 80 kg.
Answer: C
Question: During a car trip, Maria stopped to rest after she traveled 1/2 of the total distance to her destination. she stopped again after she traveled 1/4 of the distance remaining between her first stop and her destination, and then she drove the remaining 135 miles to her detination. What was the total distance, in miles from Maria's starting point to her destination?
A.280
B.320
C.360
D.420
Answer: C.360
Explanation: Easy 360 is the answer.
3/4 ( x/2) = 135
x = 135 * 8 /3 = 360.
Answer C
Question: Among the employees of a certain company, 51 percent of the employees are male and 49 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or she is NOT married?
A. 0.3
B. 0.6
C. 0.5
D. 0.4
Answer: D. 0.4
Explanation: Much faster: draw 4 quadrants
______________Male (51%)_____Female (49%)
Married :__________70%____________50%
Not Married:_______30%____________50%
Therefore: the probability of picking one random person Not Married (he or she) is: 0,51 x 0,30 + 0,50 x 0,50 = 0,15 + 0,25 (approx.)
Solution: approx. 0,4 (answer D)
Question: Set M contains numbers that satisfy the condition that, if integer x is in the set then x+2x will also be in the set M. If -4 is one of the value in the set, which of the following numbers must also be present in the set M.
I. -12
II. -1
III. 2
A.I only
B.II only
C.I and II only
D.II and III only
Answer: A.I only
Explanation: Notice that we are askedwhich of the following numbers MUST also be present in the set MnotCOULD be in the set.
Now, if -4 is in the set, then -4-8=-12mustbe in the set. Could -1 or2 be in the set?sure no.
Answer: A.
Question: A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $70 to incur a loss 20%?
A.45
B.35
C.40
D.50
Answer: B.35
Explanation: Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $70*(100% + 20%) = $84
Number of articles to be sold for $84 to incur a 20% loss: $84 / $2.40 = 35
Thus, solution B is correct.
Question: J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 4 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?
A.a)4y
B.b)5y
C.c)6y
D.d)8y
Answer: B.b)5y
Explanation: J and M were both paid x dollars
If M gave Y dollars from her X to J then at the end
J will have X+Y dollars
M will have X- Y dollars
Now since the hourly wages have to be same then
Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs)
Hourly wage of M = (X-y) /8 (Since M worked 4 hrs less than J)
Equating both
(X+Y)/12=(X-Y)/8
on simplifying X=5y
Answer B
Question: Find the simple interest on Rs. 70,400 at 16 2/3% per annum for 9 months.
A.s.8500
B.s.8000
C.s.7500
D.s.8800
Answer: D.s.8800
Explanation: P = Rs.70400,R = 50/3% p.a and T = 9/12 years = 3/4years.
S.I. = (P*R*T)/100 = Rs.(70,400*(50/3)*(3/4)*(1/100))
= Rs.8800
Answer is D.
Question: The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%?
A.16 2/3% loss
B.66 2/3% loss
C.56 2/3% loss
D.26 2/3% loss
Answer: A.16 2/3% loss
Explanation: Explanation:
15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
Answer: A
Question: City A to city B, David drove for 1 hour at 60 mph and for 3 hours at 90 mph. What was the average speed for the whole trip?
A.82.5
B.57.5
C.58.2
D.59
Answer: A.82.5
Explanation: The total distance is 1×60+3×90=330
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)=330/4=82.5
Answer : A
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
A.3 months
B.4 months
C.5 months
D.6 months
Answer: B.4 months
Explanation: S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = (100x80)/(1600x15)= 1/3 year = 4 months
answer : B
Question: The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M?
A.8
B.12
C.60
D.72
Answer: C.60
Explanation: Solution
H.C.F of two numbers divides their L.C.M exactly.
Clearly, 8 is not a factor of 60.
Answer C
Question: A 1200 m long train crosses a tree in 80 sec, how much time will I take to pass a platform 1000 m long?
A.288
B.146.66
C.188
D.180
Answer: B.146.66
Explanation: L = S*T
S= 1200/80
S= 15 m/Sec.
Total length (D)= 2200 m
T = D/S
T = 2200/15
T = 146.66Sec
Answer:B
Question: 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?
A.15 bukets
B.17 bukets
C.18 bukets
D.19 bukets
Answer: C.18 bukets
Explanation: Explanation:
Capacity of the tank = (12*13.5) litres
= 162 litres
Capacity of each bucket	= 9 litres.
So we can get answer by dividing total capacity of tank by total capacity of bucket.
Number of buckets needed = (162/9) = 18 buckets
Option C
Question: There are two inlets and one outlet to a cistern. One of the inlets takes 7/2 hours to fill up the cistern and the other inlet takes twice as much time to fill up the same cistern. Both of the inlets are turned on at 8:30 AM with the cistern completely empty, and at 10:30AM, the outlet is turned on and it takes 1 more hour to fill the cistern completely. How much time does the outlet working alone takes to empty the cistern when the cistern is full?
A.2 hours
B.2.5 hours
C.3 hours
D.3.5 hours
Answer: D.3.5 hours
Explanation: The combined inflow rate of the two inlets is 2/7 + 1/7 = 3/7 cistern/hour. Thus, working together, it takes 7/3 hours (time is reciprocal of rate) to fill the cistern.
From 8:30 AM to 10:30 AM, so in 2 hours, the inlet pipes will fill (time)*(rate) = 2*3/7 = 6/7 th of the cistern .
Then the outlet is turned on and the remaining 1/7 th of the cistern is filled in 1 hour.
Letting x to be the rate of the outlet, we would have: 3/7 - x = 1/7 --> x = 2/7 cistern/hour, which means that it takes 7/2 hours the outlet working alone to empty the cistern.
Answer: D.
Question: There are a lot of houses such that the numbers of their doorplates are odd numbers and the first number of the doorplates is 545, the last number of the doorplates is 715. How many houses are there?
A.86
B.71
C.81
D.91
Answer: A.86
Explanation: So it starts from 545 and goes like 547, 549,...... 715. and both first and last number are inclusive. Since every other number is odd, it's just 1/2 of the numbers and since it starts with an odd and ends with an odd inclusive add one to the result.
i.e., ([715-545][/2]+1 = 86
Ans A
Question: Set S is the prime integers between 0 and 50. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
A.15/56
B.3/8
C.15/28
D.4/5
Answer: D.4/5
Explanation: Total number of combinations=15C3=455................(1)
Total number of combinations including 2 and two other numbers=14C2=91......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(455-91)=364
So, probability=364/455=4/5
D
Question: A working mom wakes up every day at 7 am and goes to sleep at 11 pm. She works 8 hours a day. Spends 2 hours working out at the gym. She spends 1.5 hours cooking dinner and doing dishes. She spends .5 of an hour giving her daughter a bath. She spends 1 hour helping with homework and getting her daughter ready for bed. She spends another. 5 of an hour packing lunches for the family for the next day. She spends .5 of an hour cleaning the house and 2 hours taking a shower and reading or watching t.v. before she goes to sleep. What percent of her day does she spend at work?
A.60
B.50
C.70
D.55
Answer: B.50
Explanation: 8+2+1.5+.5+1+.5+.5+2=16= total number of hours
8/16=.05=50 percemt
The Answer is B
Question: How many integer values W are there for x such that 1 < 3x + 5 < 17?
A.Two
B.Three
C.Four
D.Five
Answer: D.Five
Explanation: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values W -1,0 , 1 , 2 , 3
Answer D
Question: P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
A.12
B.16
C.20
D.24
Answer: A.12
Explanation: Explanation :
Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days
Answer : Option A
Question: If n ≠ 0, which of the following must be greater than n?
I. 2n
II. n^2
III. 2 - n
A.I only
B.II only
C.I and II only
D.II and III only
Answer: B.II only
Explanation: n ≠ 0 => n = negative or n = positive
if n = negative:
2n < n (n = -1 then 2n = -2 => -2 < -1)
n^2 > n (n =-1 then n^2 = 1 => n^2 > n)
2 - n > n (n = -1 then 2--1 = 2+1=3 => 2-n > n)
but if n = positive:
n^2 > n (n = 2 then n^2 = 4 => n^2 > n) => II
2 - n < n(n =2 then 2-2 = 0)
=> only II
=>answer is B
Question: How many boxes do you need if you have to pack 240 pairs ornamental bangles into boxes that each hold 2 dozens of bangles?
A.40
B.35
C.20
D.25
Answer: C.20
Explanation: C
20
240 pairs of bangles = 480 bangles =40 dozens.
40 ÷ 2 = 20 boxes.
Question: Find the sum of first 26 natural numbers
A.470
B.468
C.465
D.351
Answer: D.351
Explanation: Explanation:
Sum of n natural numbers
=n(n+1)/2
=26(26+1)/2=26(27)/2=351
Answer: Option D
Question: What is the place value of 6 in the numeral 4634?
A.450
B.500
C.600
D.800
Answer: C.600
Explanation: Option 'C'
6 * 100 =600
Question: A man swims downstream 48 km and upstream 32 km taking 8 hours each time; what is the speed of the current?
A.1
B.2
C.3
D.4
Answer: A.1
Explanation: 48 --- 8 DS = 6
? ---- 1
32 ---- 8 US = 4
? ---- 1 S = ?
S = (6- 4)/2 = 1
Answer: A
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed, what is the minimum number of questionnaires that should be mailed?
A.400
B.420
C.480
D.500
Answer: D.500
Explanation: Minimum no of mail to be sent for getting 300 responses at 60%
= 300/0.6 = 500
Option D
Question: In a 1000 m race, A beats B by 50 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
A.145
B.772
C.552
D.288
Answer: A.145
Explanation: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/900 = 1000/855 So, by the time A covers 1000 m, C covers 855 m.
So in 1000 m race A beats C by 1000 - 855 = 145 m.
AnswerA
Question: Sum of two numbers prime to each other is 20 and their L.C.M. is 99. What are the numbers?
A.8 and 12
B.14 and 6
C.19 and 1
D.11 and 9
Answer: D.11 and 9
Explanation: As two numbers are prime, only two options satisfy ie option C and D.
but option C will not make the product of numbers i.e 99
ANSWER:D
Question: Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents C watch all of the shows?
A. 150
B. 108
C. 42
D. 21
Answer: D. 21
Explanation: OA is D.
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is 3.5% of 600,C is 21. D is the correct answer
Question: n a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
A.289
B.528
C.273
D.279
Answer: B.528
Explanation: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x = 528.
Answer: B
Question: A chemical supply company has 60 liters of a 35% HNO3 solution. How many liters of pure undiluted HNO3 must the chemists add so that the resultant solution is a 50% solution?
A.18
B.15
C.20
D.24
Answer: A.18
Explanation: 60 liters of a 35% HNO3 solution means HNO3 = 21 liters in 60 liters of the solution.
Now, let x be the pure HNO3 added.
As per question,
21 + x = 50% of (60 + x)
or x =18 Hence, A