RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A total of 24 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
A. 32.2
B. 31.5
C. 32
D. 32.5
Answer: A. 32.2
Explanation: Let Aw = average age of women
Average = (Number of men X average age of men + Number of women X average age of women)/total number of people
35 * 50 = 24 * 38 + 26 * Aw
=>1750 = 912 + 26 Aw
=> 26 Aw = 838
=>Aw = 32.2
Answer A
Question: How many different values of positive integer x, for which |x+7|<x, are there?
A.0
B.2
C.3
D.8
Answer: B.2
Explanation: Answer A
I opted to put the random value option.
i used 0 , 7 , -7 and the the extreme of 30 and -30..
i was able to solve it in 1:09
B
Question: The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years Q in which the population would be doubled assuming there is no emigration or immigration is
A.Q=20
B.Q=25
C.Q=30
D.Q=35
Answer: D.Q=35
Explanation: Suppose the population of the country in current year is 1000.
So annual increase is 1000 + 39.4 - 19.4=1020
Hence every year there is an increase of 2%.
2000=1000(1+(2/100))^n
n=35 Answer is D
Question: What is the greatest power that 2 can be raised to so that the resulting number is a factor of 20!?
A.4
B.8
C.10
D.20
Answer: C.10
Explanation: the number of 2s in 20!= 20/2=10..
ans C
Question: Q-1: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 5?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: 6
Two digit numbers divisible by 5 must end in either 0 or 5. Since there is no 0, all correct answers are a combination of the other digits and 5. There are six other numbers plus the 5 so there are 6 correct answers.
Correct answer is D.
Question: 8,13,23,43,83, (...)
A.123
B.223
C.143
D.163
Answer: D.163
Explanation: 8
8Ã— 2 - 3 = 13
13 Ã— 2 - 3= 23
23 Ã— 2 - 3 = 43
43 Ã— 2 - 3 = 83
83 Ã— 2 - 3 = 163
Answer is D
Question: The original price of a suit is $160. The price increased 25%, and after this increase, the store published a 25% off coupon for a one-day sale. Given that the consumers who used the coupon on sale day were getting 25% off the increased price, how much did these consumers pay for the suit?
A.$140
B.$145
C.$150
D.$155
Answer: C.$150
Explanation: 0.75*(1.25*160) = $150
The answer is C.
Question: There are 600 students in a school. The ratio of boys and girls in this school is 3:5. Find the total of girls & boys are there in this school?
A.320
B.345
C.375
D.380
Answer: C.375
Explanation: In order to obtain a ratio of boys to girls equal to 3:5, the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys. The total number of boys and girls is 600. Hence
3x + 5x = 600
Solve for x
8x = 600
x = 75
Number of boys
3x = 3 × 75 = 225
Number of girls
5x = 5 × 75 = 375
C
Question: How many liters of pure alcohol must be added to a 100-liter solution that is 20 percent alcohol in order to produce a solution that is 30 percent alcohol?
A. 100/7
B. 5
C. 20/3
D. 8
Answer: A. 100/7
Explanation: 20% Alcohol solution means; in the 100 liter solution, 20 liters of solution is alcohol and 80 liters other solvents.
If we addxliters of alcohol to the solution, the solution becomes100+xliters and alcohol, which was 20 liters, becomes 20+x liters.
According to the statement;
20+x = 30% of (100+x)
OR
20+x=(100+x)3/10
200+10x=300+3x
7x=100
x=100/7
Ans:A
Question: A, Band C enter into partnership. A invests 3 times as much as B and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 5500. What is the share of B ?
A.1000
B.800
C.1400
D.1200
Answer: A.1000
Explanation: Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x
A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.
Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.
Hence, B's share = Rs. ( 5500 x (2/11))= Rs. 1000.
Answer is A
Question: n is a positive integer and k is the product of all integers from 1 to n inclusive. If k is a multiple of 3360, then what is the smallest possible value of n?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: 3360=2^5*3*5*7
2^5 means that n must be at least 8. That is, We need 2, 4, 6, and 8.
The answer is C.
Question: Indu gave Bindu Rs.1250 on compound interest for 2 years at 8% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
A.1
B.2
C.8
D.4
Answer: C.8
Explanation: 1250 = D(100/4)8
D = 8
Answer: C
Question: Bill bought 100 packets of candy. He was able to sell 1/2 of them at a 20% profit, another 1/4 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Bill after selling those 100 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if possible. Thanks!!
A.0
B.Profit of $87.5
C.Loss of $25
D.Profit of $80
Answer: B.Profit of $87.5
Explanation: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
50 packets was sold at a 20% profit --> gives profit of 10*0.2*50 = $100.
25 packets was sold at a 5% loss --> gives loss of 10*0.05*25 = $12.5.
The overall Profit is $100 - $12.5 = $87.5.
Answer: B.
Question: When E is divided by 9, the remainder is 4. All of the following are possible values of E, except for which of the following?
A.13
B.31
C.49
D.57
Answer: D.57
Explanation: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed E in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
A.10
B.28
C.26
D.11
Answer: A.10
Explanation: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10
= 10 sec.
Answer:A
Question: The sum of the two digits of a number is 10. If the number is subtracted from the number obtained by reversing its digits, the result is 54. Find the number?
A.29
B.84
C.42
D.28
Answer: D.28
Explanation: Any two digit number can be written as (10P + Q), where P is the digit in the tens place and Q is the digit in the units place.
P + Q = 10 ----- (1)
(10Q + P) - (10P + Q) = 54
9(Q - P) = 54
(Q - P) = 6 ----- (2)
Solve (1) and (2) P = 2 and Q = 8
The required number is = 28
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.10
B.11
C.13
D.12
Answer: D.12
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 is D.
Question: A man sells 4000 common shares of a Company x (each of par value Rs. 10), which pays a dividend of 40% at Rs. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Rs. 25) that pays a dividend of 15%. If the market value of Company Y is Rs. 15, find the number of shares of Company Y purchased by the man
A.4000
B.8000
C.3000
D.6000
Answer: B.8000
Explanation: Just too much information is given in the question to confuse. This is a straight and simple question
Market Value of Company X (his selling price) = Rs.30
Total shares sold = 4000
Amount he gets = Rs.(4000 × 30)
He invests this amount in ordinary shares of Company Y
Market Value of Company Y(His purchasing price) = 15
Number of shares of company Y which he purchases = 4000×30/15=8000
Answer is B.
Question: Of all the homes on Gotham Street, 2/3 are termite-ridden, and 3/5 of these are collapsing. What fraction of the homes are termite-ridden, but NOT collapsing?
A.a) 7/15
B.b) 3/15
C.c) 4/15
D.d) 2/5
Answer: C.c) 4/15
Explanation: let total homes be 15
termite ridden= 2/3(15)= 10
termite ridden and collapsing = 3/5(10)=6
thus homes that are termite ridden, but not collapsing = 10-6=4
thus required ratio = 4/15
Answer C
Question: How many positive factors do 120 and 96 have in common?
A.8
B.12
C.16
D.18
Answer: A.8
Explanation: The number of common factors will be same as number of factors of the Highest Common Factor(HCF)
HCF of 120 and 96 is 24
Number of factors of 24 = 8
Answer :A
Question: Kiran received Rs. 6000 as his share out of the total profit of Rs.9000 which he and Arun earned at the end of one year. If Kiran invested Rs. 30,000 for 6 months, whereas Arun invested his amount for the whole year, what was the amount invested by Arun?
A.Rs.5000
B.Rs.6000
C.Rs.7000
D.Rs.7500
Answer: D.Rs.7500
Explanation: Suppose Arun invested Rs.x. Then, Kiran : Arun = (30000 * 6) : (x * 12)
Therefore, 180000/ 12x = 6000/3000
or x = 18000/24
= 7500.
ANSWER:D
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 19 years, 28 years and 30 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
A.33 years
B.44 years
C.35 years
D.36 years
Answer: B.44 years
Explanation: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*19 + 3*28 + 3*30 + x + x + 11 = 11*28.
=> 57+84+90+2x+11=308
so 2x = 66
so x = 33.
Age of the captain = (x+11)
= 44 years.
Answer : B
Question: A highway is to be divided into 3 lanes. For this purpose, two yellow stripes are painted so that stripes divide the highway into 3 lanes. If 2 gallons of paint cover an area of 5P square feet of highway, how many gallons of paint are needed to paint two stripes x inches wide on a stretch of highway m miles long? (1 mile = 5280 feet and 1 feet = 12 inches)
A.880mx/P
B.440P/mx
C.352mx/P
D.1760mx/P
Answer: C.352mx/P
Explanation: 1 square foot needs 2/5P gallons of paint.
The width of each stripe is x/12 feet.
The length of each stripe is 5280m feet.
The area of each stripe is (5280m)(x/12) = 440mx square feet.
For two stripes, the total area is 880mx square feet.
The number of gallons needed is (880mx)*(2/5P) = 352mx/P gallons.
The answer is C.
Question: If 2^98=256L+N , where Land N are integers and 0≤N≤4 , what is the value of N ?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: If 2^98= 256L + N and 0<=N<=4, what is the value of N?
To solve this, note that 2^8 = 256, so 2^98 = 2^[(8*12)+2]=4*[256*256*......12 times]
As this is a multiple of 256, N can only be 0.
ANSWER:A
Question: If p and r are integers, and p^2 = 36r, then r must be divisible by which of the following?
A.2
B.4
C.9
D.7
Answer: C.9
Explanation: Ans: D
Solution: for p to be an int 36 r must be whole square of a number.
36r= 9*2*2*r
to make it whole square we need 9
so r can must be divisible by 9y where y is itself a whole square.
so C is the ans
Question: 99^n is such a number begin with 8, least value of n?
A.96157627
B.96157601
C.26779287
D.26876297
Answer: B.96157601
Explanation: Answer:
Explanation:
In a more traditional way, this problem can be solved like below.
99(100 - 1) = 9900-99= 9801
9801(100 - 1) = 980100-9801= 971299
971299(100 - 1) = 97129900 - 971299 = 96157601
Answer:B
Question: 44 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be :
A.56 m
B.88 m
C.120 m
D.137 m
Answer: A.56 m
Explanation: Sol.
Let the length of the wire b h.
Radius = 1/2 mm = 1/20 cm. Then,
22/7 * 1/20 * 1/20 * h = 44 ⇔ = [44 * 20 * 20 * 7 / 22] = 5600cm = 56 m.
Answer A
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
A.21 days
B.51 days
C.35 days
D.31 days
Answer: A.21 days
Explanation: A
21 days
WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Question: In how many ways can a cricket eleven be chosen out of a batch
of 15 players
A.1255
B.1355
C.1340
D.1365
Answer: D.1365
Explanation: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
ANSWER D 1365
Question: Two dice are thrown simultaneously. What is the probability of geƫng two numbers whose product is
even ?
A.3/4
B.1/4
C.7/4
D.1/2
Answer: A.3/4
Explanation: Explanation:
Total number of cases = 6*6 = 36
Favourable cases =
[(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
So Probability = 27/36 = 3/4
Answer: A
Question: The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.40, in which year will commodity X cost 40 cents more than the commodity Y?
A.2007
B.2008
C.2009
D.2010
Answer: A.2007
Explanation: The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 20 + 40 = 60 cents on commodity Y, which will take 6 years.
The answer is A.
Question: √0.0081 is equal to :
A.0.09
B.0.9
C.±0.08
D.0.81
Answer: A.0.09
Explanation: √0.0081 = √0.0081/10000 = √81/10000 = 9/100 =0.09
Answer: A
Question: I bought two books; for Rs.490. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
A.337.83
B.285.83
C.284.83
D.266.83
Answer: B.285.83
Explanation: x*(85/100) = (490 - x)119/100
x = 285.83
Answer: B
Question: Oranges are bought at 11 for a rupee and an equal number more at 9 a rupee. If these are sold at 10 for a rupee, find the loss or gain percent?
A.22
B.87
C.65
D.20
Answer: D.20
Explanation: Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
Answer: D
Question: 37.	If the cost price of 15 tables be equal to the selling price of 20 tables, the loss per cent is ?
A.20%
B.30%
C.25%
D.37.5%
Answer: C.25%
Explanation: Let C.P. of each table = Re. 1
C.P. of 20 tables = Rs. 20
S.P. of 20 table = C.P. of 15 tables = Rs. 15
loss = (5/20) x 100 % = 25%
answer :C
Question: (469 + 174)^2 - (469 - 174)^2 /(469 x 174)= ?
A.643
B.2
C.295
D.4
Answer: D.4
Explanation: Given exp. =(a + b)^2 - (a - b)^2/ab
=4ab/ab
= 4 (where a = 469, b = 174.)
Answer is D.
Question: Of the three-digit positive integers whose three digits are all different and nonzero, how many are odd integers greater than 700?
A.84
B.91
C.100
D.105
Answer: B.91
Explanation: Number of combinations for type 1 : 1*7*4 = 28
Number of combinations for type 2: 1*7*5 = 35
Number of combinations for type 3 : 1*7*4 = 28
Thus, total numbers possible = 28+35+28 = 91.
B is thus the correct answer
Question: In what ratio should a variety of rice costing Rs. 6.5 per kg be mixed with another variety of rice costing Rs. 8.75 per kg to obtain a mixture costing Rs. 7.50 per kg?
A.5/6
B.5/9
C.5/4
D.5/3
Answer: C.5/4
Explanation: Let us say the ratio of the quantities of cheaper and dearer varieties
= x : y
By the rule of allegation, x/y
= (8.75 - 7.50) / (7.50 - 6.5) =5/4
Answer: C
Question: Joe drives 360 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?
A.42
B.53
C.50
D.54
Answer: B.53
Explanation: t1= 360/60=6 hours
t2=120/40=3 hours
T=t1+t2=9 hours
Avg speed = Total Distance/T
= 480/9 = 53mph=B
Question: If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
A.2.87
B.2.965
C.3.876
D.3.9
Answer: C.3.876
Explanation: log5 512 = log 512/ log 5
= log 2^9/log(10/2)
=9 log 2 /log 10 - log 2
=(9*0.3010)/1-0.3010
=2.709/0.699 = 2709/699
= 3.876
ANSWER C
Question: John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/2 the number of cans that Karen collected and 1/3 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
A. 1/5
B. 1/3
C. 2/5
D. 1/2
Answer: B. 1/3
Explanation: John = (1/2)Karen --> Karen = 2(John)
John = 1/3(Luke) --> Luke = 3(John)
Total = 6(John)
Karen/Total = 2/6 = 1/3
Answer: B
Question: From January 1, 1991, to January 1, 1993, the number of people enrolled in health maintenance organizations increased by 25 percent. The enrollment on January 1, 1993, was 45 million. How many million people, to the nearest million, were enrolled in health maintenance organizations on January 1, 1991 ?
A. 36
B. 39
C. 40
D. 41
Answer: A. 36
Explanation: 1.25x=45 --> 5/4*x=45 --> x=45*4/5=180/5=36.
Answer: A.
Question: James can finish a job in 20 dasy he worked for 10 days alone and completed the remaining part working with David 2 days how many days would both David and James together take to complete the entire job?
A.4
B.5
C.10
D.12
Answer: A.4
Explanation: Explanation:
James and David complete half work in 2 days
=> they can complete whole work in 4 days
Answer: Option A
Question: The difference between the local value and face value of 7 in the numeral 657903 is:
A.0
B.7896
C.6993
D.903
Answer: C.6993
Explanation: (Local value)-(Face value)= (7000-7)=6993.
Answer: C
Question: A shopkeeper sold 50articles at the cost price of 60 articles. Then find the profit% or lost%
A.20%
B.22%
C.25%
D.30%
Answer: A.20%
Explanation: here 50 articles selling price = 60 articles cost price
so the difference = 60-50 = 10
% of profit = 10*100/50 = 20%
correct option is A
Question: x is a positive integer of S less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
A.21
B.22
C.23
D.24
Answer: D.24
Explanation: Took me more than 2 mins to solve.
That's how I did it.
x is between 1-499 included.
Smallest number that can be written as 7n+1 (7*0+1) is 1
Largest number that can be written as 7n+1 is (7*71 +1) is 498
So there are total 72 numbers that can be written as 7n+1
Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2
7*0+1 can not be written in the form 3m+2
7*1+1 can be written in the form 3m+2
7*2+1 can not be written in the form 3m+2
7*3+1 can not be written in the form 3m+2
7*4+1 can be written in the form 3m+2
Here we see a sequence that one out of every 4 numbers can be written as 3m+1
72/4= 24 numbers can be written as 3m+1
D is the answer
Question: Rs.200 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
A.388
B.266
C.120
D.150
Answer: D.150
Explanation: 4x 5x 6x
100 50 25
400x + 250x + 150x = 20000
x = 25
6x = 150
Answer: D
Question: If m > 0, y > 0, and x is m percent of 2y, then, in terms of y, m is what percent of x?
A.y/200
B.2y
C.50y
D.50/y
Answer: A.y/200
Explanation: Answer:
A = Y/200,
Done this by taking numbers:
Let 10 (x) be 5% (m) of 2 * 100 (y)
Then m/x*100 = 5/10*100 = 50% or 1/2
50% or 1/2 in terms of Y = 100/200 = Y/200
ANSWER:A
Question: A boat running downstream cover a distance of 16km in 2 hr while covering the same distance upstream it takes 4 hr then the speed of the boat still in the water
A.43km/hr
B.78km/hr
C.9km/hr
D.7km/hr
Answer: C.9km/hr
Explanation: rate down stream=(16/2)= 8 kmph
rate upstream=(16/4)= 4 kmph
speed still water =1/2(8+4)kmph=km/hr
Answer(C)
Question: If the two-digit integers G and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of G and N?
A.181
B.165
C.121
D.99
Answer: A.181
Explanation: Since the question asks for the answer that CANNOT be the sum of G and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that G and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of M and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Question: The ratio of daily wages of two workers is 4 : 3 and one gets daily Rs 9 more than the other, what are their daily wages?
A.Rs 32 and Rs 24
B.Rs 60 and Rs 45
C.Rs 80 and Rs 60
D.Rs 36 and Rs 27
Answer: D.Rs 36 and Rs 27
Explanation: let us take second worker wages= x
so from the given data
first worker wages= x+9
from the qstn we know that wages of first/ wages of second=4/3
so (x+9)/x = 4/3
==> 3x+27=4x
==> x=27
so x+9= 36
so the answer is 36rs and 27rs
ANSWER:D
Question: In an election between two candidates, one got 60% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was:
A.1200
B.750
C.800
D.600
Answer: C.800
Explanation: Number of valid votes = 80% of 2000 = 1600.
Valid votes polled by other candidate = 40% of 2000
=(40/100)X2000 =800
ANSWER = C
Question: If x = y^2, and x and y are positive integers, which of the following numbers could be the value of x?
A.9,827
B.10,816
C.11,433
D.12,908
Answer: B.10,816
Explanation: The square of an integer can have a units digit of 0, 1, 4, 5, 6, or 9.
The answer is B.
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
A.207
B.209
C.300
D.305
Answer: B.209
Explanation: We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number
of ways	= (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + (6C4)
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + (6C2)
= (24 + 90 + 80 + 15)
=209
ANSWER B
Question: How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg?
A.36 kg
B.42 kg
C.54 kg
D.63 kg
Answer: D.63 kg
Explanation: S.P. of 1 kg of mixture = Rs. 9.24, Gain 10%.
C.P. of 1 kg of mixture = Rs.((100/110) x 9.24) = Rs. 8.40
C.P. of 1 kg sugar of 1st kind Rs.9
Cost of 1 kg sugar of 2nd kind Rs.7
Mean Price Rs. 8.40
Ratio of quantities of 1st and 2nd kind = 14 : 6 = 7 : 3.
Let x kg of sugar of 1st be mixed with 27 kg of 2nd kind.
Then, 7 : 3 = x : 27
x =	(7 x 27)/3	= 63 kg.
Answer:D
Question: Find the principle on a certain sum of money at 5% per annum for 2 years if the amount being Rs.1120?
A.1018
B.1067
C.1977
D.1056
Answer: A.1018
Explanation: 1120 = P [1 + (5*2)/100]
P= 1018
Answer: A
Question: Two trains one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 64 hours and 121 hours respectively. The ratio of their speeds is
A.8 : 7
B.11 : 8
C.6 : 7
D.9 : 16
Answer: B.11 : 8
Explanation: Sol.
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a
= √121 : √64
= 11 : 8.
Answer B
Question: The average age of a family of 5 was 32 . It fell to 18 when the grandmother died.How old was she ?
A.86
B.87
C.88
D.89
Answer: C.88
Explanation: Avg of 5 = 32
total/5=32
Total age of 5 = 160
After grandma died, total ll be
total/4=18
Total age of 4 = 72
Age of grandma ll be => 160-72 = 88
ANSWER:C