RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train 385 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
A.5 sec
B.21 sec
C.7 sec
D.10 sec
Answer: B.21 sec
Explanation: Solution
Speed of train relative to man =(60+6) km/hr= 66km/hr
=(66x5/18) m/sec =(55/3) m/sec
∴ Time taken to pass the man = (385 x 3/55)sec = 21sec
Answer B
Question: In a apartment, 70% of the people speak English, 10% speak Hindi and 30% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
A.1/3
B.2/3
C.2/5
D.1/2
Answer: D.1/2
Explanation: P (E) = 70 / 100 = 3 / 10 , P (H) = 10 / 100 = 1 / 10 and P (E âˆ© H) = 30 / 100 = 3 / 10
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (7 / 10) + (1 / 10) - (3 / 10) = 3 / 10 = 1/2
D
Question: Find the fourth proportional to 2.4, 4.6 and 7.6?
A.14.56
B.15
C.15.23
D.15.34
Answer: A.14.56
Explanation: Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56
A
Question: A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
A.230
B.299
C.267
D.111
Answer: A.230
Explanation: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
Answer: A
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability Y that private Benjamin will be chosen for latrine duty?
A.1/10
B.1/5
C.2/5
D.3/5
Answer: C.2/5
Explanation: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability Y= 1- 3/5 = 2/5. Thus C is the correct answer.
Question: If 1535/1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?
A.165/2
B.175/2
C.178/3
D.187/2
Answer: D.187/2
Explanation: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}
=1+(497/1038) now a=1
=1+{1/(1038/497)}
=1+{1/(2+42/497)}
=1+{1/(2+1/(497/42)} now b= 2 similarly expand
c=11 d= 1 e=34/8
finally a*b*b*c*d*e
1*2*11*1*34/8
187/2
ANSWER:D
Question: A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.
A.10 sec.
B.12 sec.
C.14 sec.
D.16 sec.
Answer: B.12 sec.
Explanation: Solution
Speed of the train	= (30 x 5/18)m/sec
= (25 / 3) m/sec.
Distance moved in passing
the standing man	= 100 m.
Required time taken	= 100 /( 25 / 3)
=(100 x 3 / 25) sec
= 12 sec.
Answer B
Question: Whats the reminder when 58,458,965,231,457,895,684,525,465,985,445 is divided by 16
A.5
B.7.
C.2.
D.3
Answer: A.5
Explanation: A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4. A number ending in 3 zeroes is divisible by 8. A number ending in 4 zeroes in divisible by 16.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.
58,458,965,231,457,895,684,525,465,985,445 = 58,458,965,231,457,895,684,525,465,980,000+5,445
The first number is divisible by 16. You just have to find the remainder when you divide 5445 by 16. That will be the remainder when you divide the original number by 16.
5445/16 gives remainder 5.
Answer (A)
Question: The 3 digits of a number add up to 11. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the 3 digits?
A.38
B.40
C.78
D.88
Answer: B.40
Explanation: xyz is a 3 digit integer divisible by 5. So z can take only 0 or 5. We are also given that x = 2y
This means x+y (2y+y) must be a multiple of 3
xy5 or xy0
CASE 1
x+y+0 = 11
x+y=11
This can't be the case because 11 is not a multiple of 3
CASE 2
x+y+5 = 11
x+y=6
solving we get, x=4y=2
So the 3 digit number is 425
Thus the product of the digits will be = 4 x 2 x 5 = 40
Answer B
Question: Statement: An earthquake measuring 3.7 hit Delhi and its surrounding areas a little before 3 pm today.
Action:
I. Government should immediately provide financial assistance to the families.
II. People should blame the government for not taking appropriate preventive measures.
A.Only I follows
B.Only II follows
C.Either I or II follows
D.Neither I nor II follows
Answer: D.Neither I nor II follows
Explanation: Explanation:
1st option is not a valid option because financial assistance should be provided by the government but not at this stage. First Priority should be to evacuate people from earthquake hit area.
2nd option is also false because earthquake is a natural disaster. So, blaming government will be of no use.
ANSWER IS D
Question: A can finish a piece of work in 4 days. B can do it in 12 days. They work together for two days and then A goes away. In how many days will B finish the work?
A.4 DAYS
B.5 DAYS
C.6 DAYS
D.7 DAYS
Answer: A.4 DAYS
Explanation: 2/4 + (2 + x)/12 = 1 => x = 4 days
Answer: A
Question: One morning is starts to snow at a constant rate. Later, at 6:00am, a snow plow sets out to clear a straight street. The plow can remove a fixed volume of snow per unit time, in other words its speed it inversely proportional to the depth of the snow. If the plow covered twice as much distance in the first hour as the second hour, what time did it start snowing?
A.4.15 am
B.3.20 am
C.5.22 am
D.6.10 am
Answer: C.5.22 am
Explanation: Let the depth of snow at time t to be t units. The speed of the plow at time t will be 1/t. Define t=0 as the time it started snowing and t=x the time the plow started.
The distance covered in the first hour is the integral from x to x+1 of 1/t dt. The antiderivative of 1/t is ln(t) so the total distance covered in the first hour is ln((x+1)/x).
By the same reasoning the distance covered in the second hour in ln((x+2)/(x+1)).
Using the fact that it the plow traveled twice as far in the first hour as the second: ln((x+1)/x) = ln((x+2)/(x+1))2
Exp both sides and you have (x+1)/x = ((x+2)/(x+1))2.
Solving for x you get x=(51/2-1)/2, which is the number of hours that elapsed between the time it started snowing and the snow plow left.It started snowing at (51/2-1)/2 hours before 6:00am, or 5:22:55am.
Question: If x+y=17z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?
A. 2z+1
B. 3z
C. 6z
D. z/3
Answer: C. 6z
Explanation: Pick any number like X=12, Y=22 and Z= 2 so that X+Y=17Z, now then the arithmetic mean will be (12+22+2)/3=12. Now, just look at the answers and put the value of Z there.
(A) 2.2+1=5, no
(B) 3.2=6, no
(C) 6.2=12, it can be the answer, lets check us the other options
(D) 2/3, no
(E) (3.2)/2=3, no
so the answer will be C..
Question: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 3-letter code words?
A.36
B.38
C.40
D.42
Answer: D.42
Explanation: Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 10! / (10 – 5)! = 10*9*8*7*6
# of 3 letter code words:
nPr = 10! / (10 – 3)! = 10*9*8
# of 5 words / # of 4 words = (10*9*8*7*6)/(10*9*8) = 42
D
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be?
A.7:6
B.7:3
C.7:4
D.7:2
Answer: B.7:3
Explanation: Let the age of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40 => x = 20.
Required ratio = (3x + 10):(x + 10)
= 70:30
= 7:3
Answer: B
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
A.Rs. 122
B.Rs. 121
C.Rs. 129
D.Rs. 111
Answer: B.Rs. 121
Explanation: Explanation:
Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.
C.I. = 3321 - 3200 = Rs. 121.
Answer:B
Question: It takes ten minutes to fry a steak (five minutes for each side). You are frying the steaks in a pan that can accommodate only two steaks at one time. What is the least amount of time by which you can fry all the three steaks you have?
A.15
B.19
C.12
D.17
Answer: A.15
Explanation: A
Fifteen Minutes.
After frying for five minutes, you can take out one steak and put the third one inside while turning the other one inside. After five more minutes, one steak is fried from both sides and you can take it out. Now put in the steak that we removed and turn the other one inside. After five more minutes, they both will also be fried from both sides.
Question: A started a business with an investment of Rs. 70000 and after 6 months B joined him investing Rs. 120000. If the profit at the end of a year is Rs. 13000, then the share of B is?
A.6000
B.12000
C.18000
D.24009
Answer: A.6000
Explanation: Ratio of investments of A and B is (70000 * 12) : (120000 * 6) = 7 : 6
Total profit = Rs. 13000
Share of B = 6/13 (13000) = Rs. 6000
Answer: A
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
A.9
B.8
C.5
D.2
Answer: B.8
Explanation: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Question: A, E, F, and G ran a race. A said "I did not finish 1st /4th E said "I did not finish 4th" F said "I finished 1st" G said "I finished 4th" If there were no ties and exactly 3 children told the truth, when who finishes 4th?
A.J
B.H
C.K
D.G
Answer: D.G
Explanation: Answer : D
Question: A batsman makes a score of 95 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
A.40
B.50
C.62
D.45
Answer: D.45
Explanation: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+95 = 11x
x = 95-50 = 45
Answer is D
Question: The avg weight of A,B & C is 84 kg. If D joins the group, the avg weight of the group becomes 80 kg.If another man E who weights is 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
A.25
B.35
C.75
D.80
Answer: C.75
Explanation: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 3 = 71
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 71 + 4 = 75
C
Question: A and B start a business jointly. A invests Rs.20000 for 8 months and B remains in the business for 4 months. Out of the total profit B claims 2/7th share. How much money is contributed by B?
A.A)Rs.12829
B.B)Rs.16000
C.C)Rs.12293
D.D)Rs.12804
Answer: B.B)Rs.16000
Explanation: 20*8: x*4 = 5:2
x = 16 =>
Rs.16000
Answer: B
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units X digit of (a+2)^2?
A.1
B.3
C.5
D.6
Answer: A.1
Explanation: I also got A. By punching in numers:
X...7^2=...9
...8^2=...4
...9^2=...1.A
Question: Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 1,80,000 earned at the end of 3 years from the start of the business in 2010?
A.Rs.45000
B.Rs.50000
C.Rs.60000
D.Rs.70000
Answer: C.Rs.60000
Explanation: Explanation :
Aish : Roshan : Atul
= (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1
Roshan's share = Rs. 180000 x 2/6
= Rs. 60000.
Answer : C
Question: The average of 5 numbers is calculated as 15. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
A.12.5
B.26.2
C.6.5
D.7.5
Answer: D.7.5
Explanation: 5 * 15 + 36 – 26
= 75/10
= 7.5
Answer: D
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 5000, the number of valid votes that the other candidate got, was:
A.1800
B.2700
C.2900
D.2200
Answer: A.1800
Explanation: A
Number of valid votes = 80% of 5000 = 4000.
Valid votes polled by other candidate = 45% of 4000
= (45/100 x 4000) = 1800.
Question: Find the product of the local value and absolute value of 2 in 564823
A.40
B.60
C.80
D.100
Answer: A.40
Explanation: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 2 in 564823 is 2 x 10 = 20
The face value of 2 in 564823 is nothing but 2.
=> 20 x 2 = 40
Answer: Option A
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $710,500 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
A. $1,568,000
B. $454,000
C. $406,000
D. $313,600
Answer: B. $454,000
Explanation: My take is B.
(710500*4 + 112000*3)/7 = 454000
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √11 ¤ √11 =
A.44
B.5
C.10
D.15
Answer: A.44
Explanation: X = √11 and Y also =√11
Applying the function (√11+√11)^2 - (√11-√11)^2 = (2√11)^2 - 0 = 4 x 11 = 44.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√11 and y = √11 you get the answer 44.
Answer A
Question: What is the remainder when 43^92 is divided by 5?
A.0
B.1
C.2
D.3
Answer: B.1
Explanation: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
92 has the form 4k so the units digit of 43^92 is 1.
The remainder when dividing by 5 is 1.
The answer is B.
Question: A and B start a business, with A investing the total capital of Rs.500000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.15000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
A.A)590280
B.B)590100
C.C)591900
D.D)590000
Answer: D.D)590000
Explanation: Interest received by A from B = 10% of half of Rs.500000 = 10% * 250000 = 25000.
Amount received by A per annum for being a working partner = 15000 * 12 = Rs.180000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (25000 + 180000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(25000 + 180000 + P) = 2(P)
P = 205000
Total profit = 2P + 180000
= 2*205000 + 180000 = 590000
Answer:D
Question: What is the maximum number R of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
A.36
B.32
C.24
D.21
Answer: C.24
Explanation: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get R=24 cubes.
Ans. C
Question: If x and y are integers such that (x+1)^2 is less than or equal to 49 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?
A. -16
B. -14
C. 0
D. 14
Answer: A. -16
Explanation: (x+1)^2 <= 49
x <= 6
x >= -8
(y-1)^2 < 64
y < 9
y > -7
Max possible value of xy is -8 × -6 = 48
minimum possible value of xy is -8 × 8 = -64
-64 + 48 = -16
Answer : A
Question: A cistern normally takes 6 hours to be filled by a tap but because of a leak, 2 hours more. In how many hours will the leak empty a full cistern ?
A.20 hours
B.24 hours
C.26 hours
D.18 hours
Answer: B.24 hours
Explanation: ∵ cistern fill in 6 hours.
∴ in 1 hour, filled part = 1⁄6th
Now, due to leakage, filled part in 1 hour = 1⁄8th
Part of the cistern emptied, due to leakage in 1 hour
= 1⁄6 - 1⁄8 = 1⁄24th
∴ The leakage will empty the full cistern in 24 hrs.
Answer B
Question: A train passes a station platform in 24 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.123
B.60
C.240
D.157
Answer: B.60
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) / 24 = 15
x + 300 = 360
x = 60 m.
Answer: B
Question: Michael, Steve and Tyler shared a box of cookies. Michael ate 1/8 of the cookies, Steve ate one half and Tyler ate 150 more cookies than Michael. If no cookies remain in the box, how many cookies were in the box?
A.1200.
B.800.
C.600
D.550
Answer: C.600
Explanation: Let no of cookies that Michael, Steve and Tyler ate are M, S, T
M+S+T = Total no of cookies (Let it be C)----------------(1)
Then : M=C/8, S=C\2, T= C/8 +150
Putting the Values in (1)
We get C as 600.. hence the answer : C
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 27 seconds. Find the length of the faster train?
A.270
B.2877
C.187
D.1776
Answer: A.270
Explanation: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 27 * 10 = 270 m.
The length of the faster train = 270 m.
Answer:A
Question: A 20% product produces 50%. The market value of the product is:
A.Rs. 40
B.Rs. 60
C.Rs. 45
D.Rs. 80
Answer: A.Rs. 40
Explanation: Let the face value of the product is Rs.100
It produces Rs.20
Market value of the stock=(20/50)*100=Rs.40
ANSWER:A
Question: Machine R can produce x units in 3/4 of the time it takes machine N to produce x units. Machine N can produce x units in 2/3 the time it takes machine O to produce x units. If all three machines are working simultaneously, what fraction of the total output is produced by machine N?
A. 1/2
B. 1/3
C. 4/13
D. 8/29
Answer: C. 4/13
Explanation: Let the following be true:
R makes x in time t
Then the following follows:
N makes x in 4t/3
O makes x in 3/2(4t/3) = 2t
M:N:O = 1:4/3:2=3:4:6
So N=4/(3+4+6)=4/13=C
Question: If abc < 0 and bc > 0, which of the following must be positive?
A. xy
B. ac
C. (a^2)bc
D. a(b^2)c
Answer: C. (a^2)bc
Explanation: Given that bc is positive and abc is negative, you can say that a MUST be negative. As for b and c either they are both positive or both negative.
Option (C) has a^2 which is positive and bc which is positive. So (C) must be positive.
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.50/10 sq.metre, whose base & perpendicular distance from the other side being 54m & 24m respectively?
A.Rs. 6000
B.Rs. 6250
C.Rs. 6400
D.Rs. 6480
Answer: D.Rs. 6480
Explanation: Area of the parallelogram = Length of the base * Perpendicular height
= 54 * 24 = 1296 m.
Total cost of levelling = Rs. 6480
D
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2970?
A.3000
B.2669
C.2200
D.2766
Answer: A.3000
Explanation: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2970.
=> (90%) of (110%) of x = Rs. 2970.
=> (90/100)(110/100)x = 2970
=> x = (2970 * 100)/(9 * 11)
=> x = Rs. 3000
Answer: A
Question: The public library has exactly 2 floors. It has 1/4 as many shelves on its 2nd floor as it does on its 1st. If the second floor has 5/6 as many books per shelf as the first floor, what fraction of the library's books are on the first floor?
A.1/4
B.5/14
C.5/9
D.24/29
Answer: D.24/29
Explanation: Let x be the no of shelves and y be the no of books per shelf on first floor.
Now no of shelves on 2nd floor = (1/4)*x
no of books per shelf on 2nd floor = (5/6) * y
So total no books on first floor = xy and total no of books on 2nd floor = (1/4)*x*(5/6)*y = (5/24)*xy
fraction of library books on first floor = (xy)/(xy + (5/24)*xy)
=1 / (1+(5/24))
=24/29
So D
Question: The population of a town increased from 1,75,000 to 2,80,000 in a decade. The average percent increase of population per year is
A.4.37%
B.5%
C.6%
D.8.75%
Answer: C.6%
Explanation: Solution
Increase in 10 years	= (280000 - 175000)
= 105000.
Increase%	= (105000/175000Ã—100)%
= 60%.
Required average	= (60/10)%
= 6%.
Answer C
Question: At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 41 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?
A.7
B.9
C.12
D.15
Answer: A.7
Explanation: 150=41+90+65-32-2x
x=7
A. 7
Question: If a rectangular room measures 9 meters by 5 meters by 4 meters, what is the volume of the room in cubic centimeters? (1 meter=100 centimeters)
A.24,000
B.240,000
C.18,000,000
D.24,000,000
Answer: C.18,000,000
Explanation: C. 180,000,000
9*100*5*100*4*100 = 180,000,000
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor.
A.8
B.12
C.16
D.18
Answer: B.12
Explanation: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
B)
Question: What is the product of all the prime factors of 26?
A.24
B.25
C.22
D.26
Answer: D.26
Explanation: 26 , factors are 2,13,1. Now again prime Numbers are Only Two i.e 2 and 13 , this time we would have 2*13=26
Answer : D
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 150?
A.15
B.75
C.25
D.18
Answer: B.75
Explanation: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (150 - 75) = 75 points to C.
Answer:B
Question: In the coordinate plane, a circle centered on point (3, -4) passes through point (1, 1). What is the area of the circle?
A.29π
B.18π
C.25π
D.37π
Answer: A.29π
Explanation: r^2=(3-1)^2+(-4-1)^2=4+25=29
Area of circle=πr^2=29π
Answer : A
Question: The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 ½ cm and 2 cm respectively. The diameter of third ball is?
A.2.66 cm
B.2.5 cm
C.3 cm
D.3.5 cm
Answer: B.2.5 cm
Explanation: 4/3 π * 3 * 3 * 3 = 4/3 π[(3/2)3 + 23 + r3]
r = 1.25
d = 2.5
ANSWER:B
Question: Find (7x + 6y ) / (x-2y) if x/2y = 3/2 ?
A.24
B.25
C.26
D.27
Answer: D.27
Explanation: x/2y=3/2
=>x=6y/2=3y
=>(7x+6y)/(x-2y)=((7*(3y))+6y)/(3y-2y)
=>27y/y=27
ANSWER:D
Question: Two varieties of wheat - A and B costing Rs. 9 per kg and Rs. 15 per kg were mixed in the ratio 3 : 7. If 5 kg of the mixture is sold at 25% profit, find the profit made?
A.Rs. 13.50
B.Rs. 16.54
C.Rs. 16.80
D.Rs. 16.50
Answer: D.Rs. 16.50
Explanation: Explanation:
Let the quantities of A and B mixed be 3x kg and 7x kg.
Cost of 3x kg of A = 9(3x) = Rs. 27x
Cost of 7x kg of B = 15(7x) = Rs. 105x
Cost of 10x kg of the mixture = 27x + 105x = Rs. 132x
Cost of 5 kg of the mixture = 132x/10x (5) = Rs. 66
Profit made in selling 5 kg of the mixture = 25/100 (cost of 5 kg of the mixture) = 25/100 * 66 = Rs. 16.50
Answer: Option D
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
A.4.01%
B.4.04%
C.4.16%
D.5.12%
Answer: B.4.04%
Explanation: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B