RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the third smallest sector?
A.1/72
B.1/36
C.1/18
D.1/12
Answer: D.1/12
Explanation: Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=10
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(30/360)( pie r*r)/ (pie r*r) = 30/360= 1/12
D ans ....
Question: A quadratic function f(x) attains its minimum value of -15 at x=3. If f(0)=5, find the value of f(9).
A.65
B.55
C.-25
D.75
Answer: A.65
Explanation: Explanation :
Any quadratic equation can be written as f(x) = α(x-k)2 - β
Given that minimum value of f(x) is -15 at x=3
f(x) is minimum when x=k => k=3
-15=-β => β= 15
Also given that f(0) = 5
=> 5 = α(0-3)2 - 15 => α= 20/9
Hence, f(9)=20/9(9-3)2 - 15 = 65
Answer : A
Question: A circular garden is surrounded by a fence of negligible width along the boundary. If the length of the fence is 1/4 of th area of the garden. What is the radius of the circular garden?
A.1
B.2
C.4
D.8
Answer: D.8
Explanation: as per the question-- width is negligible
now,
let L be the length of the fence =2pir
L=1/4(pir^2)
pir^2=8pir
r=8
Answer : D
Question: If the horse can run 10 miles/hour, how many days would it take for a horse to run from New York City to Washington. D.C.? (240 miles from NYC to D.C.)
A.0.6
B.0.8
C.1
D.1.2
Answer: C.1
Explanation: The horse runs 10 miles/hour, thus it would take the horse 240 miles/10 miles/hour to = 24 hours to run from NYC to D.C. There are 24 hours in a day, so days it take would be 24hours/24hours/day = 1 day. Correct Option: 1
Question: Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together?
A.4 3/8 days
B.7 3/8 days
C.9 3/8 days
D.8 3/8 days
Answer: C.9 3/8 days
Explanation: C
9 3/8 days
1/15 + 1/25 = 8/75
75/8 = 9 3/8 days
Question: 2^2*3^3*2^2*3^6 =
A.3^5*2^5
B.2^9*3^4
C.2^4*3^9
D.5^8
Answer: C.2^4*3^9
Explanation: 2^2*3^3*2^2*3^6 =
A) 3^5*2^5
B) 2^9*3^4
C) 2^4*3^9
D) 5^8
E) 6^10
If the base is same, powers are added so that follows C) 2^4*3^9.
Hence the answer is C
Question: Trapezoid JKLM in the x-y plane has coordinates J = (–2, –4), K = (–2, 1), L = (6, 7), and M = (6, –4). What is its perimeter?
A.34
B.36
C.38
D.40
Answer: A.34
Explanation: This one may look challenging initially, but all kinds of simplifying tricks. First of all, J & K have the same x-coordinate, so that’s a vertical segment, and the length is JK = 1 – (–4) = 5. L & M also have the same x-coordinate, so that’s also a vertical segment, and the length is LM = 7 – (–4) = 11. J & M have the same y-coordinate, so that’s also a horizontal segment, and the length is JM = 6 – (–2) = 8. Right there, we have the lengths of three of the four sides.
The last side to find is KL. From K = (–2, 1), we have to go over 8 and up 6 to get to L = (6, 7), so 6 and 8 the legs of the right triangle, and KL is the hypotenuse. We recognize another common Pythagorean triplet — (6, 8, 10), which is a multiple of the (3, 4, 5) triplet. Thus, without further calculations, we immediately know KL = 10.
Perimeter = JK + KL + LM + JM = 5 + 10 + 11 + 8 = 34
Answer = A
Question: In a garden, carrots are planted in rows. In each row there are as many carrots as the number of rows in the garden. If each plant attracts as many bunnies as the number of carrots in each row and if the total number of bunnies is n, then :
A.n is a perfect square
B.n is an odd number
C.n is an even number
D.n is a perfect cube
Answer: D.n is a perfect cube
Explanation: For example, if there were 4 carrot rows, the garden would have a 4x4 arrangement. If each carrot attracts 4 bunnies, the number of bunnies would be (4*4)*4 = 64 pieces, which is a cube of 4.
Answer: D
Question: The ratio of investments of A and B is 8 : 7 and the ratio of their yearend profits is 20 : 21. If B invested for 12 months, then find the period of investment of A:
A.6 months
B.8 months
C.10 months
D.12 months
Answer: C.10 months
Explanation: Let A invest for x months ; A = 8x months,
B = 7 × 12 = 84 months
8x/84 = 20/21
⇒ x = 10.
Answer: C
Question: A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 50 vehicles that are not Speedsters, how many Speedster convertibles are there?
A.30
B.48
C.60
D.80
Answer: D.80
Explanation: Total Vehicle = 2/3 of speedster + 1/3 of others.
Speedster convertibles = 2/3 total vehicle * 4 /5
Given : 1/3 constitutes 50 Vehicles. hence 2/3 constitutes 100
Speedster convertibls = 100 * 4/5 = 80
D
Question: A table is bought for Rs.600/- and sold at a loss of 10% find its selling price
A.Rs.500/-
B.Rs.530/-
C.Rs.540/-
D.Rs.600/-
Answer: C.Rs.540/-
Explanation: 100 % ------> 600 (100 * 6 = 600)
90 % ------> 540 (90 * 6 = 540)
Selling price = Rs.540/-
C
Question: speed of a bus is 54kmph and including stoppages, it is 45kmph. For how many minsdoes the bus stop per hour?
A.10 min
B.15 min
C.20 min
D.25 min
Answer: A.10 min
Explanation: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
A
Question: The no 2.52, when written as a fraction and reduced to lowest terms,the sum of the numeratr n denominator is :
A.7
B.141
C.29
D.349
Answer: D.349
Explanation: the actual question has bar on decimal part. Hence the number is 2.5252525252..... .
So let x=2.525252..
then 100x= 252.525252
100x-x=250
x=250/99
so ans=num+den=349
ANSWER:D
Question: On a certain day, Joey, the ice-cream seller sold his ice creams to four different kids in a manner that each of the kids purchased half of the remaining ice creams and half ice-cream more.
If we tell you that the fourth kid bought just a single ice cream, can you find out how many ice creams were sold by Joey that day?
A.15
B.20
C.22
D.12
Answer: A.15
Explanation: A
Joey sold 15 ice creams that day.
The fourth kid bought a single ice cream. Therefore, we have the following equation:
Total - (Total / 2 + 1/2) = 1
Solving it, we get the total as 3.
Let's work this method till we reach the first kid.
The first kid bought 15 / 2 + 1/2 = 8 (leaving 7)
The second kid bought 7 / 2 + 1/2 = 4 (leaving 3)
The third kid bought 3 / 2 + 1/2 = 2 (leaving 1)
The fourth kid bought 1 / 2 + 1/2 = 1
Adding all of them together, we get
8 + 4 + 2 + 1 = 15.
Question: If f(y)=y^2 and y is a positive integer, which of the following CANNOT be the value of f(f(y))?
A.625
B.1296
C.256
D.350
Answer: D.350
Explanation: f(y)=y^2
f(f(y)) = (y^2)^2 = y^4
Therefore f(f(y)) will be numbers that are 4th power of other numbers.
Checking the options:
625 = 6^4
1296 = 6^4
256 = 4^4
350. This cannot be written as the 4th power of any number
16 = 2^4
Answer: D
Question: A can complete the job in 5 hours and B can complete the same job in 3 hours. A works for 1 hour and then B joins and both complete the job. What fraction of the job did B complete
A.1/8
B.3/10
C.1/2
D.5/6
Answer: A.1/8
Explanation: A=1/8
Question: If x is an integer and (x)(x^2)(x^3)(x^6) is positive, which of the following could be negative?
A.x^4
B.(x)(x^3)
C.(x)(x)
D.x + x^7
Answer: D.x + x^7
Explanation: A) X^4 - always positive (or 0).
B) X(X^3) = X^4 - Again always positive (or 0).
C) (x)(x) = X^2 - Again always positive (or 0).
D) x+x^7 - Could be -ve if x is -ve.
E) 3X^2 - again always positive (or 0)
Answer D.
Question: A six-sided die is rolled once. What is the probability that the number rolled is greater than 4?
A.2 / 3
B.2 / 6
C.3 / 3
D.4 / 5
Answer: B.2 / 6
Explanation: Only 5 & 6 so, 2 / 6
correct answer B
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $4 more than 1/4 of the fine and Peter paid $4 less than 1/3 of the fine, leaving pay $5 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
A.$30
B.$25
C.$35
D.$40
Answer: B.$25
Explanation: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 4] + [(1/3)F – 4] + [(1/2)F – 5]
F = (1/4)F + (1/3)F + (1/2)F – 5
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 60
12F = 13 F – 60
–F = – 60
F = 60
Well, if the fine cost $60, then Sam paid the part not covered by Joe or Peter. Half the fine is $30, and Sam paid $5 less than this: $25.
Answer = B
Question: The product of the first seven positive multiples of three is closest to which of the following powers of 10?
A.10^9
B.10^8
C.10^7
D.10^6
Answer: C.10^7
Explanation: The product will be 3^7 * 1 * 2 * 3 * 4 * 5 * 6 * 7
=3^7 * 5140
= 9^3 * 15420
= ~135000 * 9 * 9
= ~1220000 * 9
= ~11000000 which is very close to 10^7
The correct answer is therefore (C)
Question: Calculate the number of tanks of 50x50x20m size needed to discharge crude oil from a cargo ship of volume 120000 m3 and is 90% full, if the tanks can only be filled up to 95%.
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Volume of the tank that needed to be filled=50x50x20x0.95=47500
Volume of the crude in ship=120000x0.9=108000
No. of tanks needed to discharge the ship=108000/47500= 2.27
Which is 3 tanks
Answer: C
Question: Average age of boys in a class is 16 years and average age of girls is 15 years, what is the average age of all
A.15.5
B.15
C.16
D.Cant be computed
Answer: D.Cant be computed
Explanation: Explanation:
As number of girls and boys is not given so result cant be computed
Answer: Option D
Question: The C.P of 10 pens is equal to the S.P of 5 pens. Find his gain % or loss%?
A.50%
B.40%
C.30%
D.60%
Answer: A.50%
Explanation: 10 CP = 5 SP
10 --- 5 CP gain
100 --- ? => 50%(gain)
Answer: A
Question: The average age of a group of 10 students is 20 years. If 2 more students join the group, the average age increases by 1 year. The average age of the new students is
A.23
B.21
C.19.5
D.20
Answer: A.23
Explanation: Total age of 10 students = 10 * 20 = 200 and the total age of 16 students = 21*15 = 315.
Let the average age of 2 new students be x.
Therefore total age of the new students = 2x.
So total age of 12 student =200 +5x=315, x=23
Hence, the correct answer is A.
Question: Three candidates contested in an election and received 6136, 7636, 11628 votes respectively. What is the percentage of the total votes did the winning candidate get?
A.46%
B.49%
C.57%
D.51%
Answer: A.46%
Explanation: Total number of votes polled = 6136+7636+11628 = 25400
Required percentage = 11628*100/25400 = 46%
Answer is A
Question: A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?
A.111
B.184
C.122
D.144
Answer: D.144
Explanation: If each of 6 tractors ploughed 120 hectares a day and they finished the work in 4 days, then the whole field is: 120*6*4=720*4=2880hectares. Let's suppose that each of the four tractors ploughed x hectares a day. Therefore in 5 days they ploughed
5*4*x=20*x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=2880
x=2880/20=144. Hence, each of the four tractors would plough 144 hectares a day.
Answer is D.
Question: (1/1*2)+(1/2*3)+(1/3*4)+(1/4*5)+ .............+(1/99*100)=
A.98/100
B.99/100
C.97/100
D.96/100
Answer: B.99/100
Explanation: (1/1*2)+(1/2*3)+(1/3*4)+(1/4*5)+ .............+(1/99*100)= 1-1/100= 99/100
ANSWER:B
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs. 324 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?
A.28
B.37
C.18
D.38
Answer: C.18
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 324/3 = 108 sq m
l b = 108 i.e., l * l/3 = 108
l2 = 324 => l = 18.
Answer:C
Question: How many numbers amongst the numbers 5 to 30 are there which are exactly divisible by 6 but not by 4?
A.Nil
B.1
C.2
D.3
Answer: D.3
Explanation: 6,12,18,24,30 are divisible by 6.
12, 24 are divisible by 4 also.
So there are 3 numbers exactly divisible by 6 but not by 4
ANSWER:D
Question: For any positive integer n, n>1, thelengthof n is the number of positive primes (not necessary distinct) whose product is n. For ex, the length of 50 is 4, since 50=2x5x5. What is the greatest possible length of a positive integer less than 1000.
A.10
B.9
C.8
D.7
Answer: C.8
Explanation: you are missing something in your post:
For any positive integer n , n > 1, thelengthof n is the number of positive primes (not distinct) whose product is n. For example, the length of 50 is 3 since 50 = (2)(5)(5)
the lenght of 1000 = (2)(5)(2)(5)(2)(5) = 6
but we need n < 1000
using 2 as the base = (2)(2)(2)(2)(2)(2)(2)(2)(2) = 98 the length of 512.
the answer is C
Question: By selling an shirt for $300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
A.2
B.14
C.8
D.12
Answer: C.8
Explanation: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.1 per sq m?
A.675
B.135
C.320
D.430
Answer: A.675
Explanation: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 1 = Rs.675
Answer:A
Question: By investing in 16 2/3% stock at 64, one earns Rs. 1500. The investment made is:
A.Rs. 5640
B.Rs. 5760
C.Rs. 7500
D.Rs. 9600
Answer: B.Rs. 5760
Explanation: To earn Rs.50/3,investment =Rs.64
To earn Rs.1500,investment =(64*1500*3)/50=Rs.5760
ANSWER:B
Question: The balance of a trader weighs 8% less than it should. Still the trader marks up his goods to get an overall profit of 30%. What is the mark up on the cost price?
A.40%
B.19%
C.25%
D.16.66%
Answer: B.19%
Explanation: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 92 gms because it weighs 8% less. Say, the cost price is $92 ($1/gm). Since he gets a profit of 30%, the selling price must be 92+(30/100)*90 = $119
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $119, the mark up is simply 19%
Ans : B.
Question: All the page numbers from a book are added, beginning at page 1. However, one page number was mistakenly added twice. The sum obtained was 1000. Which page number was added twice?
A.44
B.45
C.10
D.12
Answer: C.10
Explanation: Explanation :
sum of n natural numbers = n (n+1)/2
Here, n( n + 1)/2 = 1000 - x (where x is the number that is added twice)
=> n(n+1) < 2000 - 2x
we need to find max value n can take . We know for a product of two numbers to be max the number should be closest. We need to find out the least number whose square is higher than 2000. For example, 452 = 2025.
So our number is somewhere near to 45. it can't be more than 45 as our required product is less than 2000.
44 * 45 = 1980. So, we can have n = 44.
=> n (n+1) = 44 * 45 = 1980 = 2000 - 2 * 10.
=> x = 10.
Hence, we have 44 pages and page number 10 was added twice.
Answer : C
Question: A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:
A.5%
B.10%
C.7%
D.8%
Answer: B.10%
Explanation: Explanation :
Let the rate of interest per annum be R%
Simple Interest for Rs. 5000 for 2 years at rate R% per annum +Simple Interest for Rs. 3000 for 4 years at rate R% per annum = Rs.2200
⇒5000×R×2/100+3000×R×4/100=2200
⇒100R + 120R=2200
⇒220R=2200
⇒R=10
i.e, Rate = 10%.
Answer : Option B
Question: Three cubes of metal whose edges are 5, 10 and 15 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
A.28
B.77
C.66
D.16.5
Answer: D.16.5
Explanation: 53 + 103 + 153 = a3 => a
= 16.5
Answer: D
Question: Fresh grapes contain 85% water by weight and raisins obtained by drying fresh grapes contain 25% water by weight. How many kgs of fresh grapes are needed to get 20kgs of raisins?
A.75 kgs
B.64kgs
C.100 kgs
D.65 kgs
Answer: C.100 kgs
Explanation: The weight of non-water in 20 kg of dried grapes (which is 100-25=75% of whole weight) will be the same as the weight of non-water in x kg of fresh grapes (which is 100-85=15% of whole weight), so 20*0.75 = x*0.15
--> x =100.
Answer: C
Question: Find the probability that the sum of n numbers is divisible by n,assuming n is very large no.
A.1
B.1/2
C.3/4
D.None of these
Answer: B.1/2
Explanation: sum of n numbers is n(n+1)/2
case 1)when n is odd take 3
Sum is 3*4/3 it is divisible by 3
we can conclude that n=odd sum of n numbers is divisible by n
case2) when n is even take 4
Sum is 4*5/2=>10 10/4 rem is 2 so not divisible
we can conclude that n=even sum of n numbers is not divisible by n
Total of total 2 cases 1 case is possible
So probability=possible/total=1/2
ANSWER:B
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
A.30
B.35
C.36
D.37
Answer: C.36
Explanation: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: Option C
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
A.11
B.10
C.8
D.12
Answer: B.10
Explanation: Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 10 a.m.
Answer: B
Question: The number of boys in a class is 2 times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?
A.A)47
B.B)44
C.C)42
D.D)40
Answer: C.C)42
Explanation: Explanation:
Let number of girls = x and number of boys = 2x.
Then, 2x + x = 3x = total number of students.
Thus, to find exact value of x, the total number of students must be divisible by 3.
Answer: C
Question: On a certain scale of intensity, each increment of 30 in magnitude represents a tenfold increase in intensity. On this scale, an intensity corresponding to a magnitude of 165 is how many times an intensity corresponding to a magnitude of 125?
A.40
B.100
C.400
D.1000
Answer: B.100
Explanation: Increase of 40 in magnitude corresponds to 10^4 increase in intensity:
If intensity for 125 is x then for 135 it'll be 10*x, for 145 it'll be 10*10*x=10^2*x, for 155 it'll be 10*10*10*x=10^3*x and for 165 it'll be 10*10*10*10*x=10^2*x.
Answer: B.
Question: The least number which should be added to 720 so that the sum is exactly divisible by 5,6,4 and 3 is :
A.3
B.13
C.48
D.33
Answer: C.48
Explanation: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 720 by 60, the remainder is 12.
∴ Number to be added = (60-12) = 48. Answer C
Question: In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
A.21/46
B.25/117
C.1/50
D.3/25
Answer: A.21/46
Explanation: Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S)	= Number ways of selecting 3 students out of 25
= 25C3 `
=	(25 x 24 x 23)/(3 x 2 x 1)
= 2300.
n(E)	= (10C1 x 15C2)
= (10 x	(15 x 14)/(2 x 1))
= 1050.
P(E) =	n(E)	/n(S)	=	1050/2300	=	21/46	.
Answer:A
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
A.33377
B.38000
C.27999
D.2776
Answer: B.38000
Explanation: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer:B
Question: A number is decreased by 10% and then increased by 10%. The number so obtained is 10 less than the original number. What was the oiginal number ?
A.1000
B.3899
C.1028
D.1039
Answer: A.1000
Explanation: Explanation:
Let the original number be x.
Final number obtained = 110% of (90% of x)
Answer: A) 1000
Question: Number of ways in which the letters of word GARDEN can be arranged with vowels in alphabetical order, is
A.360
B.240
C.120
D.480
Answer: A.360
Explanation: Solution
Order of vowels of fixed
∴ required number of ways are 6!/2!
Answer A
Question: If the remainder is 16 when the integer n is divided by 30, what is the remainder when 2n is divided by 15?
A.0
B.2
C.4
D.6
Answer: B.2
Explanation: n = 30k+16
2n = 2(30k+16) = 4k*15 + 32 = 4k*15 + 2*15 + 2 = 15j + 2
The answer is B.
Question: Find the one which does not belong to that group ?
A.35
B.77
C.28
D.19
Answer: A.35
Explanation: Explanation:
48, 75, 84 and 57 are divisible by 3 but not 35.
Answer:A
Question: A student has 8 trousers and 12 shirts. In how many different ways can the student select a trouser and a shirt?
A.84
B.96
C.108
D.120
Answer: B.96
Explanation: The student can select one trouser in 8 ways.
The student can select one shirt in 12 ways.
The number of ways to select one trouser and one shirt is 8 * 12 = 96 ways
The answer is B.
Question: The diagonals of a rhombus are 15 cm and 20 cm. Find its area?
A.158
B.129
C.150
D.123
Answer: C.150
Explanation: 1/2 * 15 * 20 = 150
Answer:C
Question: There are 9 people and 7 chairs. In how many different ways people can occupy the chairs?
A.405
B.504
C.404
D.505
Answer: B.504
Explanation: number of ways = 9*8*7 = 504
Answer is B
Question: Canister C is 1/2 full of water and canister D, which has twice the capacity of canister C, is 1/3 full of water. If the water in canister D is poured in canister C until canister C is completely full of water, canister D will still contain what fraction of its capacity of water?
A.0
B.1/36
C.1/12
D.1/6
Answer: C.1/12
Explanation: Say canister C has a capacity of 6 liters. It's half full, thus there can be poured 3 liters of water.
Canister B is 12 liters and there are 4 liters of water. We can pour 3 liters from D to C and 1 liter will still be left in D, which is 1/12 of its total capacity.
Answer: C.
Question: A cistern 10 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
A.45
B.55
C.65
D.75
Answer: D.75
Explanation: Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 10 x 1.25) + 10 x 4]
= 75
The answer is D.