RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In an election, candidate Smith won 52% of the total vote in Counties A and W. He won 61% of the vote in County A. If the ratio of people who voted in County A to County W is 3:1, what percent of the vote did candidate Smith win in County W ?
A.A.25%
B.B.27%
C.C.34%
D.D.43%
Answer: A.A.25%
Explanation: (61%)*3x + (y%)*x = (52%)*4x
y = 25% of County W
hence answer is A.
Question: In measuring the sides of a rectangle, one side is taken 14% in excess and other 5% in deficit. Find the error percentage in the area calculated from these measurements.
A.3.5%
B.2.4%
C.8.3%
D.5%
Answer: C.8.3%
Explanation: Say both sides of the rectangle are equal to 100 (so consider that we have a square). In this case the area is 100*100=10,000.
Now, the area obtained with wrong measurements would be 114*95=10,830, which is 8.3% greater than the actual area.
Answer: C.
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 4 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.76
D.80
Answer: C.76
Explanation: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 4 = 72
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 â€“ 316 = 4
A = E +4 = 72 + 4 = 76
C
Question: In a certain game, each player scores either 2 points or 5 points. If n players score 2 points and m players score 5 points, and the total number of points scored is 50, what is the least possible positive E difference between n and m?
A.1
B.3
C.5
D.7
Answer: B.3
Explanation: We have equation 2n + 5m = 50
We have factor 2 in first number and we have factor 5 in second number.
LCM(2, 5) = 10
So we can try some numbers and we should start from 5 because it will be less list than for 2
2 * 5 = 10 and n should be equal 20
4 * 5 = 20 and n should be equal 15
6 * 5 = 30 and n should be equal 10
8 * 5 = 40 and n should be equal 5
10 * 5 = 50 and n should be equal 0
third variant give us the mininal difference
n - m = 10 - 6 = 4
And there is some mistake in my way of thinking because we don't have such answer )
If we change the task and will seek for difference between m and n
than minimal result E will be 8 - 5 = 3
And answer B
Question: In a fuel station the service costs $2.05 per car, every liter of fuel costs 0.6$. Assuming that you fill up 3 mini-vans and 2 trucks, how much money will the fuel cost to all the cars owners total, if a mini- van's tank is 65 liters and a truck's tank is 120% bigger and they are all empty-?
A.122.6$
B.128.9$
C.243.7$
D.298.85$
Answer: D.298.85$
Explanation: Mini van cost= 65*0.6+2.05
truck capacity =65(1+120/100)=143 lts.
cost of truck=143+0.6+2.05
Total cost =3* 41.05(car)+2*87.85(truck)=298.85
ANSWER:D
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 9 units?
A.126 sq.units
B.170 sq.units
C.190 sq.units
D.940 sq.units
Answer: A.126 sq.units
Explanation: Explanation:
Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 9 = 126 sq.units
Answer: Option A
Question: A sweet seller sells 3/5th part of sweets at a profit of 10% and remaining at a loss of 5%. If the total profit is Rs 1500, then what is the total cost price of sweets?
A.Rs 36,500
B.Rs 37,000
C.Rs 37,500
D.Rs 38,500
Answer: C.Rs 37,500
Explanation: Assume A be the cost price.
Therefore,
[{(3/5) x A x (10/100)} – {(2/5) x A x 5/100}] = 1500
Or A = Rs 37,500
ANSWER:C
Question: A certain quantity is measured on two different scales, the R scale and the S scale, that are related linearly. Measurements on the R scale of 6 and 24 correspond to the measurements on the S scale of 30 and 60 respectively. What measurement on the R scale corresponds to a measurement of 95 on the S scale?
A.42
B.45
C.48
D.51
Answer: B.45
Explanation: A change of +18 on the R scale is a change of +30 on the S scale.
R = (18/30)*S + K = 3S/5 + K
6 = 3(30)/5 + K
K = -12
R = 3S/5 - 12
R = 3(95)/5 - 12 = 57-12 = 45
The answer is B.
Question: Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of four rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?
A.15
B.20
C.25
D.30
Answer: B.20
Explanation: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.
The relative speed of Sandy and Molly is 4 - 1 = 3 rounds per hour.
The time required to complete one round at this speed is 1/3 hours = 20 minutes.
The answer is B.
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
A.6
B.9
C.8
D.12
Answer: D.12
Explanation: Explanation:
x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer:D
Question: A retailer sold 2 houses at each $15000. On 1st house he got 20% profit and on 2nd house he loss 5% then find his net profit or loss?
A.10%
B.9%
C.14%
D.15%
Answer: C.14%
Explanation: A = 20%
B = -5%
profit% = 20-5 + (-100/100) = 14%
Answer is C
Question: There are six leopards and one sheep.
Leopard can eat sheep but since as the land is magical, the leopards who eats the sheep , turns into sheep and then can be eaten by the remaining leopard(s).
If we leave them for some time then how many sheep and leopard will be there , when we come back ?
A.4 leopard and one sheep
B.5 leopard and one sheep
C.6 leopard and one sheep
D.7 leopard and one sheep
Answer: B.5 leopard and one sheep
Explanation: Solution:
5 leopard and one sheep
since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.
Answer B
Question: The red triangle is equilateral with a side of 23 centimetres. Its perimeter is
A.68 cm
B.69 cm
C.70 cm
D.71 cm
Answer: B.69 cm
Explanation: Solution:
All three sides of an equilateral triangle are equal. Thus, its perimeter will be 23 × 3 = 69 cm
Answer B
Question: The simple form of the ratio 9/8:3/4 is?
A.5:8
B.5:5
C.5:9
D.3:2
Answer: D.3:2
Explanation: 9/8 : 3/4 = 3:2
Answer: D
Question: How many even integers n, where 100 <= n <= 200, are divisible neither by seven nor by nine?
A.37
B.38
C.39
D.40
Answer: C.39
Explanation: total 51 even integers
out of which 7 will be divided by 7 and 6 will be divided by 9
(for 7..find intervals of 14 as we are taking even numbers
112,126...196
(for 9..find intervals of 18 as we are taking even numbers
108,126...198)
126 is common
so 51-7-6+1 = 39 will not be divided by 7 or 9
ANSWER:C
Question: 150 men consume 1050 kg of rice in 30 days. In how many days will 70 men consume 980 kg of rice?
A.98 days
B.60 days
C.56 days
D.76 days
Answer: B.60 days
Explanation: Rate of consumption of each man = 1050/(150 * 30) = 7/30 kg/day
Let us say 70 men take x days to consume 150 kg.
Quantity consumed by each item in x days = (7x/30) kg
Quantity consumed by 70 men in x days = (7/30 x)(70) kg
= (7/30 x) * (70) = 960
x = 60 days.
Answer: B
Question: If e=1 and (e-b)/c = 1 which of the following is NOT a possible value of b?
A.-2
B.-1
C.0
D.1
Answer: D.1
Explanation: Equation is:
(e-b)/c = 1 where e = 1
so plug in 1 for e and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Question: In an examination, there were 2,000 candidates, out of which 900 candidates were girls and rest were Boys. If 34% of the boys and 32% of the girls passed, then the total percentage of failed candidates is?
A.35.67%
B.66.90%
C.68.57%
D.69.57%
Answer: B.66.90%
Explanation: Girls = 900, Boys = 1100
Passed = ( 34% of 1100 ) + ( 32% of 900)
= 374 + 288 = 662
Failed = 2000 - 662 = 1338
Failed % = [(1338/2000) x 100]%
= 66.9%.
ANSWER:B
Question: Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?
A.2
B.6
C.5
D.3
Answer: D.3
Explanation: 9261 = 8000(21/20)N
(21/20)3 = (21/20)N => N = 3
Answer: D
Question: Of the 8 members of flight crew, 7 are trained to serve economic class customer, 5 are trained to serve business class customer, and 4 can serve both. If one member is chosen at random, what is the probability that the member chosen will be someone who can serve either type of customer?
A.a) 1/9
B.b) 0
C.c) 1/6
D.d) 1/4
Answer: B.b) 0
Explanation: You know how to solve for Total number of people who can serve at least one type of customer:
Total = n(A) + n(B) - n(A and B)
Total people who can serve at least one type of customer = 7 + 5 - 4 = 8
So All 8 people know how to serve at least one type of customer. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to serve any type of customer
Answer (B)
Question: In a certain city, 70 percent of the households have cable television, and 50 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:
A.30,000 to 75,000 inclusive
B.30,000 to 90,000 inclusive
C.60,000 to 75,000 inclusive
D.60,000 to 90,000 inclusive
Answer: A.30,000 to 75,000 inclusive
Explanation: The maximum percentage with both is 50% which is 75,000 households.
This means that every household with a recorder also has cable television.
The minimum percentage with both is 20% which is 30,000 households.
This means that 30% of households have only recorders but not cable television.
The other 20% of households with recorders have cable television.
The answer is A.
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
A.12
B.66
C.87
D.88
Answer: A.12
Explanation: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
Answer: A
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
A.18
B.20
C.23
D.24
Answer: D.24
Explanation: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
Option 'D'
Question: In an office, 50 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
A. 8
B. 64
C. 50
D. 144
Answer: A. 8
Explanation: (10/100)Workers = 16 = > number of workers = 160
(50/100)*Workers = x+16 = > x = 8
Answer A
Question: At a florist shop on a certain day, all corsages sold for either $40 or $45. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 20 percent. What was the store's actual revenue from corsages that day?
A.$200
B.$400
C.$600
D.$800
Answer: A.$200
Explanation: I am doing it elaborately, hope it will help you.
Let, No. of corsages @ $40 = x, no. of corsages @ $45 = y and revenue= r
so, 40 x+45 y=r.........(1)
Now,
Given the situation, 40(x+8) + 45(y-8)= r-.2r
=> 40 x+320+45 y-360 = .8r
=> 40x+45y = .8r+40............(2)
so, r = .8r+40
=> r = 200
The answer is A.
Question: In how many ways 8 different tickets Q can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
A.From 2 to 6 inclusive.
B.From 98 to 102 inclusive.
C.From 122 to 126 inclusive.
D.From 128 to 132 inclusive.
Answer: D.From 128 to 132 inclusive.
Explanation: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
Q=1+28+70+28+1 = 128 Answer is D.
Question: If a is an integer larger than 1, and x=60a, then x must be a multiple of which of the following?
A.8
B.9
C.12
D.18
Answer: C.12
Explanation: X must be divisible by 60 .
a , an integer less than 1 means a could be 0,-1,-2,....... and x = 60a
so if a= 0, x = 0*60=0 is divisible by 12 ( recall 0 is divisible by any integer)
if a= -1, then -60 is divisible by 12 but not 8,9,18 and 120 , if a-2 , then -120 is divisible by 60 and so on
Answer is C
Question: Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?
A.21005
B.10500
C.25200
D.5376
Answer: D.5376
Explanation: Solution
Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)
8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224
Number of group,each having 3 consonants and 1 vowels = 224 .
Each group contains 4 letter.
Number of ways of arranging 5 letters among themselves
= 4 ! = (4 × 3 × 2 × 1) = 24 .
So, Required number of words = (24 × 224) = 5376 .Answer D
Question: The unit digit in the product (784x618x917x463) is
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: Unit digit in the given product = Unit digit in (4x8x7x3)=2
Answer is A
Question: A toy factory stores its toys in either a big box or a small box. The big box can store 35 toys while the small box can store 14 toys. If the factory is to store 86 newly manufactured toys, what is the least number of toys that will be left unboxed?
A.2
B.1
C.3
D.5
Answer: A.2
Explanation: Total toys to be stored 86
The big box can store 35
small box can store 14
storing 85 toys in big box 85/35 =2 r 16
store remainder in small box 16/14=1 r 2
least number of toys that will be left unboxed=2
Answer: A
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
A.25
B.378
C.20
D.27
Answer: A.25
Explanation: M = 15
S = 10
DS = 15 + 10 = 25
Answer: A
Question: An association of mathematics teachers has 1,260 members. Only 640 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
A.30.47%
B.58%
C.42%
D.34%
Answer: A.30.47%
Explanation: Total Number of members = 1260
Number of members that cast votes = 640
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*640 = 384
Percent of total membership that voted for winning candidate = (384/1260)*100 = 30.47%
Answer A
Question: John purchased a fridge and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
A.Rs. 100
B.Rs. 120
C.Rs. 200
D.Rs. 240
Answer: C.Rs. 200
Explanation: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Question: If m is an integer such that (-2)^2m=2^(15-m) then m=?
A.1
B.2
C.3
D.5
Answer: D.5
Explanation: (-2)^(2m) = 4^m
and
2^(15-m) = 4^((15-m)/2)
Therefore,
m = (15-m)/2
2m = 15 - m
m = 5
Answer D
Question: A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
A.8
B.6
C.1
D.5
Answer: B.6
Explanation: The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers.
cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4)
could be correct because the other two sides would be 3 and 4.
cannot be correct because this third side would be greater than the sum of the other two sides.
Answer: B
Question: An athlete runs 100 meters race in 12sec. His speed is?
A.30km/hr
B.15km/hr
C.25km/hr
D.20km/hr
Answer: A.30km/hr
Explanation: speed = 100/12 = 25/3 m/sec
= 25/3 * 18/3 km/hr = 30km/hr
Answer is A
Question: If A : B = 4 : 7 and B : C = 5 : 8 then A : B : C is :
A.20 : 35 : 56
B.35 : 36 : 63
C.30 : 35 : 65
D.25 :34: 68
Answer: A.20 : 35 : 56
Explanation: Expl : A : B = 4 : 7
B : C = 5 :8 = 5*7/5 : 8 *7/5 = 7 : 56/5
A : B : C = 4 : 7 : 56/5 = 20 : 35 : 56
Answer: A
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
A.1/15
B.1/20
C.1/21
D.3/14
Answer: B.1/20
Explanation: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
B
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different E arrangements of plays can be run, if the same play can’t be run more than once?
A.24
B.125
C.243
D.504
Answer: D.504
Explanation: Number of E ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Question: A train passes a station platform in 36 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.283
B.240
C.883
D.379
Answer: B.240
Explanation: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x
= 240 m.
Answer: B
Question: What value will come in place of question mark in the following equation? 0.006 +? = 0.6
A.0.01
B.0.05
C.0.03
D.0.07
Answer: A.0.01
Explanation: Let 0.006 / x = 0.6, Then, x = (0.006 / 0.6) = (0.006*10) / (0.6*10) = 0.06/6 = 0.01
Answer is A.
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
A.22
B.30
C.99
D.77
Answer: B.30
Explanation: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer:B
Question: Find the positive number which when increased by 17 is equal to 60 times the reciprocal of the number
A.4
B.3
C.2
D.9
Answer: B.3
Explanation: Let the number be x
x+17=60/x
x^2+17x-60=0
(x+20)(x-3)=0
x=3
correct answer B
Question: a is an integer greater than 19 but less than 32, b is an integer greater than 29 but less than 42, what is the range of a/b?
A.1/4
B.1/2
C.3/4
D.1
Answer: B.1/2
Explanation: min value of a/b will be when b is highest and a is lowest ---> a=20 and b=40
So, a/b = 1/2
max value of a/b will be when b is lowest and a is highest ---> a=30 and b=30
So, a/b = 1
Range is 1-(1/2) = 1/2.
Answer should be B
Question: If A is 25 kms east of B, which is 12 kms south of C, which is 9 kms west of D. A person starts walking at 3 kms/hr from A towards D. Calculate the distance of the point from A where he is going to meet a person from D walking towards A at 2 kms / hr.
A.20
B.12
C.8
D.20 sqrt (12*8)
Answer: A.20
Explanation: 2,3=common factor
hence 20
ANSWER:A
Question: 10 years ago Neha's mother was 4 times older than Neha. After 10 years Neha's mother will be twice Neha's age. How old is Neha now?
A.10 years
B.15 years
C.17 years
D.20 years
Answer: D.20 years
Explanation: Let us assume m = mother and n = neha
m-10 = 4(n-10) => 4n-m = 30 this is equation 1
m+10 = 2(n+10 => -2n+m = 10 this is equation 2
By equations 1 and 2
n=20
n means Neha age = 20 years
ANSWER:D
Question: Find the compound ratio of (2:3), (6:11) and (11:2) is
A.3:2
B.2:1
C.1:2
D.4:5
Answer: B.2:1
Explanation: Required ratio = 2/3 * 6/11 * 11/2 = 2/1 = 2:1
Answer is B
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 51 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
A.A)11
B.B)18
C.C)24
D.D)25
Answer: D.D)25
Explanation: lets solve by creating equation..
W = 31..
Total = 52..
Not W = 52 -31= 21..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=21 or x=9..
so who won Nobel but not Wolf = x+3 = 12..
But people who won BOTH W and N = 13..
so total who won N = 12+13 = 25..
D
Question: there is one designed bedsheets having length 6m and breadth 4m.in the middle there is square shape design with 3m side.calculate the % of bedsheet which do not have any design.
A.62
B.60
C.75
D.62.5
Answer: D.62.5
Explanation: area of bedsheet=24m2.
area of square shape design=9m2.
undesigned area=24-9=15m2.
%of undesigned area=15/24*100=62.5%
answer D
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 3 carpenters build in 4 hours?
A.2.4.
B.4.8.
C.4.2.
D.5.5.
Answer: B.4.8.
Explanation: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 3 carpenters in 4 hrs = 3 × rate of each carpenter x time = 3× 2/5 × 4 = 4.8 desks
B is the correct answer.
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
A.39
B.35
C.42
D.40.5
Answer: A.39
Explanation: Explanation:
Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
=> 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39
Answer: Option A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12300 after a year?
A.3630
B.3690
C.2887
D.9977
Answer: B.3690
Explanation: 6300:4200:10500
3:2:5
3/10 * 12300 = 3690.Answer: B
Question: If the length of the sides of two cubes are in the ratio 2:1, what is the ratio of their total surface area?
A.2:1
B.3:1
C.4:1
D.6:1
Answer: C.4:1
Explanation: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(2x)^2=24x^2.
The ratio of surface areas is 4:1.
The answer is C.
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
A.6m
B.9m
C.3m
D.2m
Answer: D.2m
Explanation: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Question: If n is a negative integer and p is a positive integer, which of the options below must be positive?
A.(n + p)^2
B.np
C.n/p
D.p/n
Answer: A.(n + p)^2
Explanation: A.(n + p)^2
will be positive irrespective of the absolute values of x and y
will be positive always
B. np
-ve*+ve=-ve
will be negative
C. n/p
-ve*/ve=-ve
D.+ve/-ve=-ve
+ve/-ve=-ve
Answer A