RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In right triangle ABC, AC is the hypotenuse. If AC is 35 and AB + BC = 55, what is the area of the triangle ABC?
A.225
B.450
C.25√2
D.200
Answer: B.450
Explanation: Square AB + BC = 55:
(AB)^2 + 2*AB*BC + (BC)^2 = 3025. Since (AC)^2 = (AB)^2 + (BC)^2 = 35^2 = 1225, then (AB)^2 + 2*AB*BC + (BC)^2 = 1225 + 2*AB*BC = 3025.
1225 + 2*AB*BC = 3025.
AB*BC = 900.
The area = 1/2*AB*BC = 450.
Answer: B.
Question: Due to construction, the speed limit along an 6-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A. 4
B. 8
C. 10
D. 15
Answer: A. 4
Explanation: 6/35 - 6/55 = 6/5 * ( 11 - 7)/77
= 6/5 * 4/77 * 60 min
= 6 * 12 * 4/77
= 288/77 ~ 3.7
Answer - A
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Elaine, Gale, and Harold?
A.1,008
B.2016
C.1,512
D.2,018
Answer: B.2016
Explanation: Place D and F first: 8 options for D, 7 options for F
We are left with 6 empty places. A, B and C must take first 3 places and F, G, H must take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for E, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: B
Question: A room is 30 m long and 24 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
A.9.6 m3
B.96 m3
C.960 m3
D.9600 m3
Answer: D.9600 m3
Explanation: Let the height be H
2(30+24) x H – 2(30-24)
H=(2(30x24))/(2(30+24)) = (30x24)/54 = 40/3 m
Volume = 30x24x40/3 = 9600 m3
answer :D
Question: If the cost price of 60 articles is equal to the selling price of 40 articles, then what is the percent profit?
A.30%
B.40%
C.50%
D.60%
Answer: C.50%
Explanation: Let x be the cost price of one article.
Let y be the selling price of one article.
40y = 60x
y = 1.5x
The answer is C.
Question: The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then the average of the remaining numbers is nearly
A.28.32
B.28.78
C.29.27
D.29.68
Answer: D.29.68
Explanation: Solution
Sum of 50 numbers	= 30 x 50
= 1500.
Sum of remaining 48 numbers	= 1500 - (35+40)
= 1425.
∴ Required average	= (1425 / 48)
= 475 / 16.
= 29.68.
Answer D
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.900 is Rs.200 and C's share is Rs.130, what is B's capital?
A.19878
B.14250
C.26908
D.11750
Answer: B.14250
Explanation: 200 + 130 = 330
900 - 330 = 570
200 ---- 5000
570 ---- ? => 14250
Answer: B
Question: The value of 5 in the number 357.21 is
A.5 ones
B.5 twenty
C.5 tens
D.5 hundreds
Answer: C.5 tens
Explanation: Ans is C
The number 357.21 consists of: 3 hundreds, 5 tens, 7 ones, 2 tenths and 1 hundredth =>the value of 5 in 357.21	is 5 tens
Question: Balloons are bought at 8 for Rs.10/- and sold at 10 for Rs.8/-. Find the gain or loss percentage?
A.36% Loss
B.36% Gain
C.18% Loss
D.18% Gain
Answer: A.36% Loss
Explanation: Explanation:
8 Balloons -----> Rs.10/-
10 Balloons ----> Rs.8/-
Note: In every time same in the cost price articles and selling price articles.
10(8 10) ==> 80 100 = Cost price
8(10 8) ==> 80 64 = Selling price
Then, 36/100 × 100 = 36 % Loss
Answer: Option A
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is Q:
A.Q=1
B.Q=2
C.Q=3
D.Q=4
Answer: B.Q=2
Explanation: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Question: The boat moves downside 50km and upside 10km in 2 hours each. Then find the boat speed in still water?
A.10km/hr
B.15km/hr
C.20km/hr
D.25km/hr
Answer: B.15km/hr
Explanation: Down stream = 50/2 = 25km/hr
Up stream = 10/2 = 5km/hr
speed of boat in still water = 30/2 = 15km/hr
Answer is B
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
A.12
B.27
C.26
D.11
Answer: D.11
Explanation: Explanation:
Let the ten's digit be x and unit's digit be y.
Then, number 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y)
which is divisible by 11.
Answer: D
Question: If k, (k+200), (k+350), and 15*K are all multiples of F, then F could equal which of the following ?
A.20
B.F=25
C.75
D.100
Answer: B.F=25
Explanation: {Multiple of F} - {Multiple of F} = {Multiple of F}.
(K+200) - k = 200 = {Multiple of F}.
(K+350) - k = 350 = {Multiple of F}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Question: A sum of money is to be distributed among P, Q, and R in the ratio 6:19:7. If R gives Rs. 200 from his share to Q, the ratio of P, Q and R becomes 3:10:3, what is the total sum?
A.Rs. 4800
B.Rs. 12800
C.Rs. 3200
D.Rs. 7200
Answer: A.Rs. 4800
Explanation: Explanation:
Let the shares of P, Q and R be 6x, 19x and 7x.
By given condition, R’s new share = 7x – 200
Q’s new share = 19x + 200
New ratio = 6x :19x +200:7x-200=3:10:3
P : R = 6x :7x -200=3 :3
6x=7x-200
x=200
Total sum 6x + 19x + 7x = 32x = Rs. 4800
Answer: A
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
A.288
B.278
C.297
D.176
Answer: D.176
Explanation: 25x + 46 = 26(x – 5)
x = 176
Answer: D
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 people who applied for the army and 1400 were finally selected, what was the value of N?
A.4
B.5
C.6
D.8
Answer: C.6
Explanation: Since 70% is accepted and figure will be 1400 therefore in last stage tested/interviewed no. candidates should be 2000
So from here i will work for those two steps of decrements of 100000 candidates.
fastly i reduce 60% till it gets closer to our required 2000 candidates
step(1) 40000 accepted.
step(2) another 40%of 40000=16000 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 16000=8000
step(4) 50% of 8000=4000
Step(5) 50% of 4000=2000...here we are done with total 5 steps
and last step of accepting 70% of 2000=1400(our target)
total 6 steps required.
Answer: C
Question: If x=-3, which of the following is(are) true? I. x^2=-|x| II |x|=-x III x/-3 = -1
A.II, III only
B.II only
C.I,II only
D.I only
Answer: B.II only
Explanation: I. x^2=-|x| -3^2 = - |-3| Not true
II |x|=-x |-3| =-( -3 ) true
III x/-3 = -1 Not true
Answer : B
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
A.2/81
B.2/91
C.1/81
D.1/91
Answer: B.2/91
Explanation: Total number of balls = 4 + 5 + 6 = 15
n(S) = tot no of ways of drawing 3 balls out of 15 =15c3
let E = event of drawing 3 balls
n(E) = no of ways of drawing 3 balls
= no of ways of drawing 3 balls from the total 5 = 5c3
=>(5*4/2*1)/(15*14*13/3*2*1)=2/91
ANSWER B
Question: A can do a piece of work in 4 days. B can do it in 15 days. With the assistance of C they completed the work in 24 days. Find in how many days can C alone do it?
A.0.391 days
B.0.491 days
C.0.331 days
D.1.391 days
Answer: A.0.391 days
Explanation: C = 1/2 - 1/24 - 1/15 = 0.391 days
ANSWER:A
Question: what is the compound interest on rs:70,000 for 4 months at the rate of 5% per annum
A.1171.98
B.1172.98
C.1173.98
D.1174.98
Answer: C.1173.98
Explanation: it is monthly compound
rate=5/12% per month
70000*(1+5/1200)^4-70000=1173.98
ANSWER:C
Question: A bus trip of 660 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
A.40
B.45
C.50
D.55
Answer: D.55
Explanation: The time is the distance/speed. The time difference is 1 hour.
660/V - 660/(V+5) = 1
660(V+5) - 660V = (V)(V+5)
3300 = (V)(V+5)
55*60 = (V)(V+5)
V = 55 mph
The answer is D.
Question: A worker's daily wage is increased by 50% and the new wage is $51 per day. What was the worker's daily wage before the increase?
A.$28
B.$32
C.$34
D.$35
Answer: C.$34
Explanation: Let x be the daily wage before the increase.
1.5x = $51
x = $34
The answer is C.
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
A.5578
B.5552
C.5550
D.5528
Answer: C.5550
Explanation: Total production of salt by the company in that year
= 5000 + 5100 + 5200 + .... + 6100
= 66600.
Average monthly production of salt for that year
= 66600/12 = 5550.
Answer:C
Question: Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 70 ps per meter is?
A.287
B.369
C.175
D.279
Answer: C.175
Explanation: 3x * 2x = 3750 => x = 25
2(75 + 50) = 250 m
250 * 0.70
= Rs.175
Answer:C
Question: The average of five integers is 56, and none of these integers is greater than 100. If the average of three of the integers is 59, what is the least possible value of one of the other two integers?
A.3
B.15
C.20
D.21
Answer: A.3
Explanation: When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 56
So, the sum of ALL 5 integers = (56)(5) =280
The average of three of the integers is 65
So, the sum of the 3 integers = (59)(3) =177
So, the sum of the 2 REMAINING integers =280-177=103
If the sum of the 2 REMAINING integers =103, and we want to minimize one value, we must MAXIMIZE the other value.
100 is the maximum value so let 1 integer = 100, which means the other must equal 3
Answer: A
Question: The average (arithmetic mean) of seven numbers is 7. If 4 is subtracted from each of three of the numbers, what is the new average?
A.4.2
B.6.3
C.5.2
D.7.9
Answer: C.5.2
Explanation: Sum of 7 numbers = 7*7=49
If4 is subtracted from each of three of the numbers , we subtract 4*3=12 from the total sum
Sum of 7 number after subtracting 4 from each of three of the numbers =49-12=37
New average = 37/7=5.2
Answer C
Question: If y = 30p, and p is prime, what is the greatest common factor of y and 14p, in terms of p?
A.p
B.2p
C.5p
D.7p
Answer: B.2p
Explanation: Y=30p
other number is 14p
then GCF(30p,14P)=2P; B is the correct answer
Question: A train 600 m long can cross an electric pole in 20 sec and then find the speed of the train?
A.72
B.67
C.108
D.26
Answer: C.108
Explanation: Length = Speed * time
Speed = L/T
S = 600/20
S = 30 M/Sec
Speed= 30*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 108 Kmph
Answer:C
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 60 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
A.8 km/hr.
B.32 km/hr.
C.34 km/hr.
D.18 km/hr.
Answer: D.18 km/hr.
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (60 + 60)/12
2x = 10
x = 5.
Speed of each train = 5 m/sec = 5 x 18/5 km/hr = 18 km/hr.
answer :D
Question: Find the value for m?
21(m + n) + 21 = 21(-m + n) + 21
A.0
B.-1
C.1
D.2
Answer: C.1
Explanation: 21m + 21n - 21 = -21m + 21n + 21
42m= 42 => m = 1
C
Question: Excluding the stoppages, the speed of a bus is 48 km/hr and including the stoppages the speed of the bus is 12 km/hr. For how many minutes does the bus stop per hour?
A.45 min
B.10 min
C.12 min
D.20 min
Answer: A.45 min
Explanation: Speed of the bus without stoppage=48 km/hr
Speed of the bus with stoppage=12 km/hr
Difference in speed=36 km/hr
so,the time taken in the stoppages = time taken to cover 36 km=(36/48)hr = 3/4 hr =45 min
ANSWER:A
Question: rahul played weel in this season.his current batting averagge is 50.if he score 78 runs in today match.his batting average will become 54.how many matches had he played in this season.
A.8
B.10
C.9
D.6
Answer: D.6
Explanation: 50x+78=54(x+1)
=>4x=24
=>x=6
ANSWER:D
Question: If 4x - y = 32 and −x + 2y = 5, then what is the value of 3x + y?
A.37
B.3
C.15
D.52/7
Answer: A.37
Explanation: 4x - y = 32
−x + 2y = 5
Adding both the equations --> 3x + y = 37
Answer: A
Question: Evaluate 2+22+222+2.22
A.269.72
B.268.22
C.248.21
D.248.22
Answer: D.248.22
Explanation: 2+22+222+2.22=248.22
Option D
Question: In what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
A.7 sec
B.8 sec
C.9 sec
D.6 sec
Answer: D.6 sec
Explanation: T = 60/36 * 18/5
= 6 sec
Answer: D
Question: S = { 1,5,3,7}
T = { 4,5,6,7 }
what is the probability that x chosen from S and y chosen from T will result x*y = even
A.1/3
B.4/5
C.2/3
D.1/2
Answer: D.1/2
Explanation: p: the probability that x*y is even, then p=1-p(x*y is odd)
p(x*y odd)=p(x odd)*p(y odd)=4/4*2/4=2/4
And p=1-2/4=1/2
Option: 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.4
B.8
C.12
D.16
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
Answer is B.
Question: In how many different ways can the letters of the word 'APPLE' be arranged?
A.10 ways
B.20 ways
C.30 ways
D.60 ways
Answer: D.60 ways
Explanation: Totally there are 5 letters on the word APPLE. it contains 1A,2P,1L,1E.
The no of ways is 5!/2!=120/2=60 ways.
ANSWER:D
Question: A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?
A.16 km
B.14 km
C.12 km
D.10 km
Answer: A.16 km
Explanation: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 61 km
So,
4x + 9(9-x) = 61
=> 5x = 20
=> x = 4
So distance traveled on foot = 4(4) = 16 km
Answer: Option A
Question: Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.?
A.9
B.12
C.15
D.17
Answer: B.12
Explanation: Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
Question: What is the area of a square field whose diagonal of length 24 m?
A.240 sq m
B.250 sq m
C.200 sq m
D.400 sq m
Answer: A.240 sq m
Explanation: d2/2 = (24 * 24)/2 = 240
ANSWER:A
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.14, 2
B.16, 4
C.14, 8
D.14, 4
Answer: D.14, 4
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14,y = 4.
Answer: D
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.756 find the share of A.
A.240
B.388
C.288
D.277
Answer: C.288
Explanation: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 756 = 288
Answer: C
Question: If |5x-10| = 100, then find the sum of the values of x?
A.1
B.-2
C.3
D.-3
Answer: C.3
Explanation: |5x-10| = 100
5x-10 = 100 or 5x-10 = -100
5x = 110 or 5x = -90
x = 22 or x = -18
sum = 21-18 = 3
Answer is C
Question: What is the are of an equilateral triangle of side 16 cm?
A.64√6
B.64√9
C.64√4
D.64√3
Answer: D.64√3
Explanation: Area of an equilateral triangle = √3/4 S2
If S = 16, Area of triangle = √3/4 * 16 * 16 = 64√3 cm2;
Answer: D
Question: If log(2a - 3b) = log a - log b, then a =
A.3b2/2b -1
B.3b/2b -1
C.b2/2b + 1
D.3b2/2b + 1
Answer: A.3b2/2b -1
Explanation: 2a- 3b = a/b
=>2ab - 3b2 = a
=>3b2 = a(2b - 1)
Therefore, a = 3b2/2b -1.
ANSWER:A
Question: A and B start a business with Rs.5000 and Rs.7000 respectively. Hoe should they share their profits at the end of one year?
A.3:5
B.5:7
C.3:9
D.5:3
Answer: B.5:7
Explanation: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B =
5000 : 7000 => 5:7,Answer: B
Question: How many different three-digit multiples of 5 can be composed of digits 2, 3, 4, and 5 if none of the digits is repeated?
A.3
B.6
C.10
D.12
Answer: B.6
Explanation: Available: 2, 3, 4, 5
You need to make 3 digit numbers which are multiples of 5.
___ ___ ___
For the number to be a multiple of 5, it must end with either 0 or 5. We only have 5 available so the number must end with 5.
___ ___ 5
Now you select 2 numbers out of the leftover 3 numbers (2, 3 and 4) in 3C2 ways and arrange them in the 2 places in 2! ways which gives you 3C2*2! = 6
or you can say that you can select a number for the hundreds place in 3 ways and select a number for the tens place in 2 ways (since numbers cannot be repeated). So you can make the number in 3*2 = 6 ways
ANS:B
Question: Which of the following is the lowest positive integer that is divisible by 7, 8, 9, 10, and 11?
A.27,720
B.29,940
C.31,960
D.33,970
Answer: A.27,720
Explanation: The number needs to be divisible by 7, 2^3, 3^2, 2*5, and 11.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 * 11 = 27,720
The answer is A.
Question: 5/9 of the part of the population in a villagae are males.if 30 % of the males are married.the percentage of unmarried females in the total population is..
A.250/9%
B.150/9%
C.350/9%
D.450/9%
Answer: A.250/9%
Explanation: Let total population = p
no. of males =5p/9
no. of females =(p-5p/9)=4p/9
married males = 30% of 5p/9=30*5p/100*9 =p/6
married females = p/6
unmarried females =(4p/9-p/6)=5p/18
%age of unmarried females in the total population = {(5p/18)/p}*100= 250/9%
ANSWER:A
Question: Find the value of (50+ 20/90) × 90
A.2520
B.3520
C.4520
D.1520
Answer: C.4520
Explanation: (4500+20)/90*90 = 4520
Answer : C
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
A.338
B.378
C.200
D.298
Answer: C.200
Explanation: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50 = 200 km away from Mumbai.
Answer: C
Question: A can complete a project in 30 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 10 days before completion of project, then in how many days the project will be completed?
A.18
B.19
C.20
D.21
Answer: C.20
Explanation: A's 1day work=1/30;
B's 1day work=1/30;
(A+B) 1day work=(1/30+1/30)=1/15;
It is given that A leaves the work 10 days before completion of the project..
Thus,B alone does the remaining job in 10 days.
So,In 10 days ,B can do 1/3 w ..
Thus,(A+B) have worked (1-1/3)=2/3 w..
(A+B)can do 1/15 work in 1 day...
They did 2/3 w in 10 days.
Total days=(10+10) = 20
ANSWER:C
Question: If a sum of money doubles itself in 5 years at simple interest, the ratepercent per annum is
A.12
B.12.5
C.20
D.13.5
Answer: C.20
Explanation: Explanation:
Let sum = x then Simple Interest = x
Rate = (100 * x) / (x * 5) = 20
Option C
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 8:30 a.m. and drives north on the same highway at an average speed of 55 km per hour. Mr. Dinkle will
A.overtake Mr. Smitherly at 10:30 a.m.
B.overtake Mr. Smitherly at 11:30 a.m.
C.overtake Mr. Smitherly at 1:30 p.m.
D.be 30 miles behind at 9:35 a.m.
Answer: C.overtake Mr. Smitherly at 1:30 p.m.
Explanation: After thirty minutes, Mr. Smitherly is ahead by 25 km.
Mr. Dinkle gains on Mr. Smitherly 5 km each hour.
5 hours after 8:30 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Question: A and B can do a piece of work in 12 days. With the help of C they finish the work in 3 days. C alone can do that piece of work in?
A.40 days
B.2 days
C.4 days
D.8 days
Answer: C.4 days
Explanation: C
30 days
C = 1/3 – 1/12 = 1/4 => 4 days
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
A.2C7 * 10C6
B.2C7 * 17C5
C.2C7 * 10C5
D.2C9 * 10C5
Answer: C.2C7 * 10C5
Explanation: Here, five seniors out of 12 seniors can be selected in ¹²C₅ ways. Also, five juniors out of ten juniors can be selected 10C5 ways. Hence the total number of different ways of selection = ¹²C₅ * ¹⁰C₅ = ¹²C₇ * ¹⁰C₅
= 12C5 = 12C7
Answer:C
Question: In a bag, there are 6 brown, 4 blue and 10 orange pens. One pen is picked up randomly. What is the probability that it is neither brown nor blue?
A.1/4
B.1/5
C.1/3
D.1/2
Answer: D.1/2
Explanation: Explanation :
Neither brown nor blue means the pen drawn is orange.
Total number of outcomes = (6+4+10) = 20.
Number of Favourable outcomes = 10 = Number of orange pens.
Hence, Probability of the event = 10/20 = 1/2.
Answer : D
Question: A and B are walking with 25 kmph and 30 kmph. A is walking towards east and B is towards south. They both started at 7:00 A.M at what time they are 130 metres apart.
A.130m
B.140m
C.150m
D.160m
Answer: A.130m
Explanation: let after t sec they are 130m apart then
(25* 5/18 *t)^2 + (30* 5/18 *t)^2 = 130^2
=> t * (5/18) * 5 * √ 61 = 130
=> t = 12.98425 sec ~ 13 sec
so, at 7:00:13 AM they are 130m apart.
ANSWER:A
Question: Thefactor countof an integer n greater than 1 is the number of distinct prime factors of n. For example, the factor count of 36 is 2, since 2 and 3 are the distinct prime factors of 36 = 2 x 2 x 3 x 3. For which of the following integers is the factor count greatest E?
A. 60
B. 61
C. 62
D. 63
Answer: A. 60
Explanation: 60 = 2*2*3*5 factor count =3
61= prime number
62 = 2*31 factor count=2
63=3*3*7 factor count=2
64=2*2*2*2*2*2 factor count=1=E
answer is A.
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.82. How much was lent at 5%?
A.899
B.866
C.878
D.800
Answer: D.800
Explanation: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 82
5x/100 + 90 – 6x/100 = 82
x/100 = 8
=> x = 800
Answer:D
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 30 m long and 16 1/2 m board?
A.41
B.23
C.56
D.99
Answer: D.99
Explanation: Explanation:
30 * 33/2 = 5/2 * 2 * x => x = 99
Answer: D
Question: The sum of all the integers g such that -26 < g < 24 is
A.0
B.-2
C.-25
D.-49
Answer: D.-49
Explanation: Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 g= -49.
D is the answer.
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
A.18
B.99
C.77
D.62
Answer: A.18
Explanation: 8/12 + 6/x = 1
X = 18 days
Answer:A