RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What is the value of(a,y) in (13^-20-a*13^y)=168*13^-22?
A.(1,2)
B.(0,1)
C.(-1,22)
D.(1,-22)
Answer: D.(1,-22)
Explanation: (13^-20-a*13^y)=168*13^-22
Divide the LHS and RHS by 13^-22
13^2-a*13^(y+22) =168
168 can be expressed as 13^2 - 1
13^2-a*13^(y+22) =13^2 - 1
a*13^(y+22) =1
Now look at options and substitute .. Its easy for y=-22 . 13^0=1 a also = 1
ANSWER:D
Question: If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have?
A.10
B.16
C.8
D.11
Answer: C.8
Explanation: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1080
180n - 360 = 1080
180n = 1440
n = 1440/180 = 8
ANSWER:C
Question: In an isoscele right angled triangle, the perimeter is 20 metre. Find its area.
A.9,320 m2
B.8,750 m2
C.7,980 m2
D.6,890 m2
Answer: A.9,320 m2
Explanation: In an isoscele right angled triangle,
Area = 23.3 × perimeter2
= 23.3 × 20(2) = 9320 m2
Answer A
Question: HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
A.36
B.66
C.132
D.264
Answer: C.132
Explanation: 12 * 396 = 36 * x
x = 132
ANSWER:C
Question: Find the number of ways in which 4 letters may be selected from the word "Examination"?
A.66
B.70
C.136
D.330
Answer: C.136
Explanation: EXAMINATION has 11 letters, and in which 'A', 'I' and 'N', all occur twice. 11C4, would have been fine if all letters were distinct.
So, we have E, X, M, T, O, (AA), (II), (NN). 8 distinct letters.
1. 4 letters selected, which are all distinct: 8C4 = 70
2. 2 letters alike, and 2 distinct (eg: AAEX) = 3C1 x 7C2 = 63
3. 2 letters alike, and 2 letters alike (eg: AAII) = 3C2 = 3
So answer is, 70 + 63 + 3 = 136.
ANSWER:C
Question: By selling a book for 250, 20% profit was earned. What is the cost price of the book?
A.A)215
B.B)208
C.C)230
D.D)235
Answer: B.B)208
Explanation: SP = 120% of CP; :. CP = 250 × 100/120 = 208
Option 'B'
Question: Calculate the ratio between x and y if 90% of x equal to 60% of y?
A.1 : 2
B.3 : 5
C.3 : 2
D.3 : 4
Answer: C.3 : 2
Explanation: Explanation:
90 x = 60 y
x: y = 90: 60 = 3 : 2
Answer:C
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability R that the number of men is equal to that of women?
A.R=18/35
B.16/35
C.14/35
D.13/35
Answer: A.R=18/35
Explanation: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Question: Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 4000 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
A.15%
B.25%
C.12.5%
D.20.83%
Answer: D.20.83%
Explanation: Only trick n this question is to ignore 60% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (500/4000)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/60) = 20.833% and the answer is not there in the options.
The correct answer is (D).
Question: A train running at the speed of 60 km/hr crosses a pole in 8 seconds. Find the length of the train.
A.133.33
B.882
C.772
D.252
Answer: A.133.33
Explanation: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 8 = 133.33 meter.Answer: A
Question: If an article is sold at 18% profit instead of 9% profit, then the profit would be $54 more. What is the cost price?
A.$500
B.$600
C.$700
D.$800
Answer: B.$600
Explanation: 9% * cost price = $54
1% * cost price = $54 / 9 = $6
The cost price is $600.
The answer is B.
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
A.1000
B.3000
C.2000
D.4000
Answer: C.2000
Explanation: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
Answer is C.
Question: 2, 6, 12, 20, 30, 42, 56, ?
A.63
B.67
C.69
D.72
Answer: D.72
Explanation: The pattern is 1 × 2, 2 × 3, 3 × 4, 4 × 5, 6 × 7, 7 × 8,....
Answer : D.
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {10, 10, 10, 10, 10, 10}, standard deviation = P
Set II = {6, 6, 6, 14, 14, 14}, standard deviation = Q
Set III = {7, 8, 9, 11, 12, 13}, standard deviation = R
Rank these three standard deviations from least to greatest.
A.P, Q, R
B.P, R, Q
C.Q, P, R
D.Q, R, P
Answer: B.P, R, Q
Explanation: SD is minimum when the terms are closer to the mean.
In set 1, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 2 and Set 3, Set 3 has terms more closer to mean than set 2. hence, Set 2 Sd is the highest.
So, Answer is B
Question: In a graduating class of 238 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A.144
B.119
C.113
D.88
Answer: B.119
Explanation: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 238 = 25
Greatest - Smallest is 144-25 = 119
So answer must be B. 119
Question: A sum was put a simple interest at a certain rate for 2 years. Had it been put at 4% higher rate, it would have fetched Rs. 60 more. The sum is:
A.Rs.750
B.Rs.700
C.Rs.820
D.Rs.940
Answer: A.Rs.750
Explanation: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x × (R+4) × 2/100−x×R×2/100=60
⇒x × 4×2/100=60
⇒x × 2 /100=15
⇒2x=1500
⇒x=750
Answer : Option A
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
A.9:5
B.9:8
C.9:6
D.9:1
Answer: B.9:8
Explanation: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Question: The regular price per can of a certain brand of soda is $0.15. If the regular price per can is discounted 10 percent when the soda is purchased in 24-can cases, what is the price of 75 cans of this brand of soda purchased in 24-can cases?
A.$16.32
B.$18.00
C.$10.125
D.$24.48
Answer: C.$10.125
Explanation: The discounted price of one can of soda is (0.9)($0.15), or $0.135
Therefore, the price of 75 cans of soda at the discounted price would be (75)($0.135) = 10.125
Answer: C.
Question: Line E has the equation 3x + y = 7. Which of the following lines is perpendicular to Line E?
A. y = 3x + 4
B. y = –3x – 6
C. y = (1/3)x – 1
D. y = (–1/3)x + 2
Answer: C. y = (1/3)x – 1
Explanation: I first rewrote the equation in the standard y=mx+b form. Therefore, Line E as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line E? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
A.Rs.51.25
B.Rs.51.26
C.Rs.51.22
D.Rs.51.98
Answer: A.Rs.51.25
Explanation: Sum = (50 * 100) / (2 * 5)
= Rs. 500
Amount = [500 * (1 + 5/100)2]
= Rs. 551.25
C.I. = (551.25 - 500)
= Rs. 51.25.
Answer: A
Question: A train travels 125 km in 2.5 hours and 270 km in 3 hours.find the average speed of train.
A.80 kmph
B.60 kmph
C.72 kmph
D.90 kmph
Answer: C.72 kmph
Explanation: As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 125 + 270 = 395 km
Thus, Total Speed = 5.5 hrs
or,Average Speed = 5=395/5.5
or, 72kmph.
ANSWER:C
Question: A car travelling with 2/3 km of its actual speed covers 12km in 2hr 14 min 28 sec find the actual speed of the car?
A.8.9kmph
B.2.96kmph
C.1.09kmph
D.45.9kmph
Answer: C.1.09kmph
Explanation: time taken =2hr 14 min 28 sec=823/50hrs
let the actual speed be x kmph
then 2/3 x*823/50=12
x==1.09kmph
Answer (C)
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 19!
A.8
B.10
C.12
D.14
Answer: A.8
Explanation: Solution-
Consider multiples of 25!=> 3,6,9,12,15,18
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
---- count 3's =8 so answer is 8
Answer : A
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
A.1 : 1
B.2 : 3
C.5 : 2
D.4 : 3
Answer: D.4 : 3
Explanation: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 3 and 3 parts, respectively.
This will give us in the final mixture (5 + 3) : (3 + 3), which means 4:3
Answer D.
Question: Ramesh purchased a refrigerator for Rs. 17500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
A.34778
B.26888
C.24475
D.17600
Answer: C.24475
Explanation: Price at which the TV set is bought = Rs. 17,500
Discount offered = 20%
Marked Price = 17500 * 100/80 = Rs. 21875
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 21875 + 375 = Rs. 22250
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 22250 * 110/100
= Rs. 24475
Answer: C
Question: Two dice are rolled. What is the probability the sum will be greater than 9?
A.1/9.
B.1/12.
C.5/36.
D.1/6.
Answer: A.1/9.
Explanation: Combinations possible: (6,6) , (5,6) , (6,5) , (5,5) = 4
Total combinations possible: 6*6=36
Answer = 4/36 = 1/9 Option A.
Question: A man divides $8600 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
A.A)$200
B.B)$1000
C.C)$800
D.D)$1011.76
Answer: D.D)$1011.76
Explanation: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 4*4X+4*4X+2*X=8600
16X+16X+2X=8600
34X=8600, X=252.94.
Daughter receives four times of nephew so 4 * 252.94 = 1011.76.
So Each Daughter receives $800. answer is option D) $1011.76.
Question: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I.	x = y
II.	x > y
III. x = z
A.I and II
B.I only
C.II only
D.III only
Answer: C.II only
Explanation: 3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
II correct.
We can't say much about z though;
x=-5; y=-100; z=-95
I and II incorrect.
Ans:C
Question: The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
A.2&4
B.3&5
C.4&6
D.5&7
Answer: B.3&5
Explanation: Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
correct answer B
Question: 6) A marketing firm determined that , of 180 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
A.a) 15
B.b) 20
C.c) 30
D.d) 10
Answer: D.d) 10
Explanation: 100 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 100
=> 4x = 40
=> x = 10
Answer - D
Question: How many ways are there to split a group of 4 students into two groups of 2 students each? (The order of the groups does not matter)
A.2
B.3
C.4
D.5
Answer: B.3
Explanation: 4C2 = 6
If we consider these groups, each group will be counted twice.
The number of ways to choose 2 groups of 2 is 6/2 = 3
The answer is B.
Question: 40% of the people read newspaper X, 50% read newspaper Y and 10% read both the papers.What percentage of the people read neither newspaper ?
A.18%
B.20%
C.22%
D.16%
Answer: B.20%
Explanation: n(A)=40,n(B)=50,n(AnB)=10.
n(AuB)=n (A)+n (B)-n(AnB)=40+50-10=80.
Hence, percentage passed =(100-80)%=20%.
Answer is B
Question: The speed of a boat in still water is 60kmph and the speed of the current is 25kmph. Find the speed downstream and upstream?
A.80,47 kmph
B.80,80 kmph
C.85,35 kmph
D.80,40 kmph
Answer: C.85,35 kmph
Explanation: Speed downstream = 60 + 25 = 85 kmph
Speed upstream = 60 - 25 = 35 kmph.Answer:C
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 12, what is the sum of the first 15 terms of the progression?
A.90
B.80
C.70
D.60
Answer: A.90
Explanation: 4th term + 12th term = 12
i.e., (a+3d)+(a+11d) = 12
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 12 --------------- From (1)
=90
Answer : A
Question: If r and p are two different prime numbers, which of the following is the smallest possible value of r + p?
A.1
B.3
C.5
D.8
Answer: C.5
Explanation: By definition only positive numbers can be primes.
Two smallest primes are 2 and 3 --> 2 + 3 = 5.
Answer: C
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds W in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
A.25%
B.35%
C.45%
D.70%
Answer: B.35%
Explanation: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out W: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Question: A man rows his boat 70 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
A.1 kmph
B.6 kmph
C.5 kmph
D.8 kmph
Answer: C.5 kmph
Explanation: Speed downstream = d/t = 75/(2 1/2) = 28 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (28 - 18)/2 = 5 kmph
Answer:C
Question: The H.C.F of two numbers is 19 and their L.C.M is 4263. If one of the numbers is 399, then the other is?
A.202
B.203
C.204
D.205
Answer: B.203
Explanation: Other number = (19 * 4263)/399
= 203.
Answer: B
Question: Three years ago the average age of a family of seven members was 20 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
A.A)8
B.B)7
C.C)6
D.D)5
Answer: A.A)8
Explanation: 7 * 23 = 161
7 * 19 = 153
--------------
8
Answer: A
Question: The value of (68.237)2 – (31.763)2 is :
A.3.6474
B.36.474
C.364.74
D.3647.4
Answer: D.3647.4
Explanation: Solution
Given expression = (a2 - b2) = (a + b)(a - b)
= (68.237 + 31.763) (68.237 - 31.763)
= (100 × 36.474)
= 3647.4. Answer D
Question: The price of a mobile was increased by 40 percent. The new price was then decreased by 15 percent. A single increase of what percent is equivalent to these two successive changes?
A.25%
B.19%
C.30%
D.22.5%
Answer: B.19%
Explanation: consider base price - $100
25% increase = 1.40*100 = $140
Then a 15% decrease on new price = 0.85* 140 = $119
so final price of radio - $119
therefore a 19% increase
correct option - B
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
A.A)Rs.200
B.B)Rs.220
C.C)Rs.250
D.D)Rs.300
Answer: C.C)Rs.250
Explanation: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
A.2882
B.2880
C.7276
D.2786
Answer: B.2880
Explanation: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 4! * 5! = 24 * 120
= 2880.
Answer: B
Question: Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is?
A.388
B.3769
C.8782
D.828
Answer: D.828
Explanation: Let the parts be x, y and [2379 - (x + y)]
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 2379
10k/11 + 20k/23 + 5k/6 = 2379
k = (2379 * 11 * 23 * 6)/3965 = (3 * 11 * 23 * 6)/5
x = [10/11 * (3 * 11 * 23 * 6)/5] = 828
Hence, the first part is Rs. 828.
Answer: D
Question: If A,B is 20%,30% smaller than C then how much percentage is B greater than A?
A.10%
B.11%
C.12 3/4%
D.12 1/2 %
Answer: D.12 1/2 %
Explanation: A = 80 %
B = 70 %
C = 100 %
A-B/A × 100 = 10/80 × 100 = 12 1/2 % greater than A
D)
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.3
B.5
C.9
D.11
Answer: D.11
Explanation: Solution
Let the ten's digit be x and units 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: What is the 149th digit to the right of the decimal point in the decimal form of 30/33?
A.5
B.6
C.9
D.0
Answer: C.9
Explanation: To solve ,we first have to use some long division.Long division allows us to get 30/33 in decimal form, which is 0.909090… where “90” is repeating.
We see that the 1st, 3rd, 5th digit to the right of the decimal point is a 9 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 0. In other words, each odd-positioned digit is a 9, and each even-positioned digit is a 0.
Then the 149th digit to the right of the decimal point and we see that 149 is odd, then 149th digit is a 9.
Answer C.
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
A.33
B.18
C.99
D.787
Answer: B.18
Explanation: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Question: The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many Q grams?
A.Q= 16
B.Q=32
C.64
D.128
Answer: B.Q=32
Explanation: Weight directly proportional to 4 pi r^2
Now, 4pi is constant, so, weight is directly proportional to r^2.
When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;
(0.15)^2 * 4 proportional to 8*4, solving further
(0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B)
Question: 6^9 - 6^2 is approximation of which of the following?
A.9^7
B.9^8
C.6^9
D.9^11
Answer: C.6^9
Explanation: => Since 9^2 is a small number compared to 9^9, it can be disregarded. Thus, 6^9-6^2=6^9 is derived and the answer is C.
Question: A sum is divided among B, C and D in such a way that for each rupee B gets, C gets 150 paisa and D gets 50 paisa. If the share of C is RS. 40, what is the total amount?
A.70
B.75
C.80
D.85
Answer: C.80
Explanation: b:c:d = 100:150:100
20:30:10
30 --- 40
60 --- ? => 80
Answer:C
Question: How many integers from 100 to 800, inclusive, remains the value unchanged when the digits were reversed?
A. 50
B. 60
C. 80
D.70
Answer: D.70
Explanation: question is asking for palindrome
first digit possibilities - 1 through 7 = 7
8 is not possible here because it would result in a number greater than 8 (i.e 808 , 818..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 7 *10 = 70
Answer is D.
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
A.380
B.395
C.400
D.425
Answer: C.400
Explanation: Let the numbers be x and y.
Then, xy = 9375 and	x	= 15.
y
xy	=	9375
(x/y)	15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
ANSWER : C
Question: Set A = {1, 2, 3, 4, 5, 6, y}
Which of the following possible values for y would cause Set A to have the smallest standard deviation?
A.1
B.2.5
C.3
D.3.5
Answer: D.3.5
Explanation: SD is minimum or least when the number is closest to the mean of the existing numbers
Calculating mean of the rest of the numbers gives mean = (approx)3.6
So the new number should be near to the mean and only number closest to the mean is 3.5
Answer: Option D
Question: A builder decided to build a farm house in 40days. He employed 100men in the beginning and 100 more after 35 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
A.5
B.7
C.10
D.15
Answer: A.5
Explanation: 200 men do the rest of the work in 40-35 = 5days
100 men can do the rest of the work in 5*200/100 = 10days
Required number of days = 10-5 = 5 days
Answer is A