RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A certain number when divided by 39 leaves a remainder 20, what is the remainder when the same number is divided by 13?
A.7
B.8
C.9
D.6
Answer: A.7
Explanation: Explanation:
39 + 20 = 59/13 = 7 (Remainder)
Answer: A
Question: How many integers k greater than 100 and less than 700 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
A.50
B.60
C.70
D.80
Answer: A.50
Explanation: Not sure if this is the shortest.. But this is how I did this
There are 5 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. ...
5. 506 | 607
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 5 sets with 10 such number in each set will give 5 x 10 = 50 integers.
A
Question: A man can row 3.9 km/hr in still water. It takes him twice as long to row upstream as to row downstream. What is the rate of the current ?
A.1.9
B.1.7
C.1.3
D.1.5
Answer: C.1.3
Explanation: Speed of boat in still water (b) = 3.9 km/hr. Speed of boat with stream (Down Stream), D = b + u Speed of boat against stream (Up stream), U = b – u It is given upstream time is twice to that of down stream. ⇒ Downstream speed is twice to that of upstream. So b + u = 2(b – u) ⇒ u =b/3 = 1.3 km/hr.
Answer: C
Question: In the x- y plane, there are 4 points (0,0), (0,4), (5,4), and (5,0). If these 4 points makes a rectangle, what is the probability that x+y<4?
A.2/3
B.2/5
C.3/4
D.3/7
Answer: B.2/5
Explanation: The line y=-x+4 intersects the rectangle and these three points of intersection (0,0), (0,4) and (4,0) form a triangle.
The points below the line y=-x+4 satisfy x+y<4.
The area of this triangle is (1/2)(4)(4)=8
The area of the rectangle is 20.
P(x+y<4) = 8/20 = 2/5
The answer is B.
Question: In the rectangle below, the line MN cuts the rectangle into two regions. Find x the length of segment NB so that the area of the quadrilateral MNBC is 40% of the total area of the rectangle.
A.1 meter
B.2 meter
C.3 meter
D.4 meter
Answer: A.1 meter
Explanation: Solution
We first note that
MC = 20 - 5 = 15
The quadrilateral MNBC is a trapezoid and its area A is given by
A = (1/2) × 10 × (x + MC) = 5 (x + 15)
40% of the area of the rectangle is equal to
40% × (20 × 10) = (40 / 100) × 200 = 80
Since the area of MNBC is equal to 40% the area of the rectangle, we can write
5(x + 15) = 80
5x + 75 = 80
5x = 5
x = 1 meter
ANSWER IS A
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If t of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
A. y/R
B. y/(R-x)
C. xy/(R-x)
D. ty/(R(R-t))
Answer: D. ty/(R(R-t))
Explanation: y/(R-t)- y/R
if we simplify this we get choice D, which is the correct answer.
Question: The ratio of number of boys to that of girls in a school is 3:2.if 20% of boys and 25 % of girls are scholarship holders,find the percentage of those who are not scholarship holders.
A.75
B.76
C.77
D.78
Answer: D.78
Explanation: since ratio be 3:2 let there is 100 students so there are 60 boys and 40 girls.so 60/40=3:2.now we find 80% of boys who are not scholarship holder so 80% of 60 is 48.now we find out 75% of girls who are not scholarship holder so 75% of 40 is 30.
so total number who are not scholarship holder is 48+30=78
ANSWER:D
Question: Two brands of detergent are to be combined. Detergent X contains 20 percent bleach and 80 percent soap, while Detergent Y contains 45 percent bleach and 55 percent soap. If the combined mixture is to be 35 percent bleach, what percent of the final mixture should be Detergent X?
A.10%
B.32 1/2 %
C.35%
D.40%
Answer: D.40%
Explanation: Let we mix x units of detergent X and y units of detergent Y
Bleach Soap Total
Detergent X 0.20x 0.80x x
Detergent Y 0.45y 0.55y y
Combined 0.20x+0.45y 0.80x+0.55y x+y
Percentage of bleach in combined mixture = (0.20x+0.45y)/(x+y) = 35/100
20x + 45y = 35x + 35y
10y = 15x
x/y = 2/3
So, percentage of detergent x = x*100/(x+y) = (x/y)*100/ ((x/y)+1)
= (2/3)*100/((2/3)+1)
= 200/5 = 40%
So, Answer will be D
Question: If a fair coin is flipped eight times in a row, what is the probability that there will be at least one head and one tail?
A.3/4
B.11/12
C.31/32
D.127/128
Answer: D.127/128
Explanation: The number of possible outcomes is 2^8 = 256
There is one way to get no heads and one way to get no tails.
Thus there are 254 outcomes with at least one head and one tail.
P(at least one head and one tail) = 254/256 = 127/128
The answer is D.
Question: A trader marks his goods at such a price that he can deduct 15% for cash and yet make 20% profit. Find the marked price of an item which costs him 90 :
A.135 11⁄13
B.105 3⁄21
C.127 1⁄17
D.95 1⁄21
Answer: C.127 1⁄17
Explanation: SP = 90 × 1.2 = 108
Marked price = 108⁄0.85 = 127.05
Answer C
Question: A man has 3 blue shirts, 3 green shirts and 1 red shirt. Everyday of the week we wears a different shirt, how many ways can he choose his shirts to wear them along the week? Consider that he never wears a shirt more than one time a week and he ways wears all his shirts on the week.
A.6!/3!(2)
B.7!/3!(2)
C.6!/3!1!
D.7!/2!(3)
Answer: B.7!/3!(2)
Explanation: n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The man has 7 shirts which there are 3 blue shirts, 3 green shirts and 1 red.
Number of arrangements = 7!/3!(2)
Answer: B
Question: The average of first 9 prime numbers is?
A.10.11
B.11.11
C.12.11
D.13.11
Answer: B.11.11
Explanation: Sum of 10 prime no. = 100
Average = 100/9 = 11.11
ANSWER:B
Question: A dishonest milkman sells a 30 liter mixture of milk and water that contains milk and water in the ratio of 3:2. He takes out 20 liters of the mixture and replaces it with an equal amount of milk. He then takes out 10 liters of this new mixture and replaces it with an equal amount of water to create his final mixture. What is the ratio of milk and water in the final mixture?
A.2:5
B.3:5
C.2:3
D.3:2
Answer: D.3:2
Explanation: D
............................... Milk ............... Water ....................... Total
Initial ...................... 24 .................... 16 .............................. 40
20 Lts mix. taken out 24-12 ............... 16-8 ........................... 40-20
20 Lts milk added..... 12+20 ................ 8 .............................. 40
10 Lts mix. taken out 32-8............... 8-2 ........................... 40-10
10 Lts water added..... 24 ................ 16 .............................. 40
New ratio = 24: 16= 3:2
D
Question: Ram's shop runs a sale on goldfish and platys. If one customer buys 13 goldfish and 12 platys for $5.60, and another buys 14 goldfish and 21 platys for $8.05, what is the ratio of the price of goldfish to platys?
A.0.8
B.0.75
C.c) 8/9
D.5/7
Answer: D.5/7
Explanation: The approach of plugging in the numbers is a fine approach. But, in this case, the answer was the first option and thus, by plugging in a number in the ration given, we arrived at the answer quickly!
However, what if the correct ratio was option D or C?
In any case, the algebraic solution isn't that complex if you realize a key concept:
The number 7 can be factored out of the second equation!
Here's the working:Ram's shop runs a sale on goldfish and platys.
13x + 12y = 5.60 <<<<< Equation 1
14x + 21y = 8.05 <<<<< Equation 2
2x + 3y = 1.15 [Factor Out 7 from equation 2] <<<<< Equation 3
8x + 12y = 4.6 [Multiply Equation 3 with 4]
5x = 1.0 [Equation 1 - Equation 2]
x = 0.2
3y = 1.15 - 0.4 = 0.75 [Substitute for x in Equation 1]
y = 0.25
x/y = 0.2/0.25 = 20/25 = 4/5 = 0.8 [Answer A]
The whole thing must have taken me about 45 s :D
Question: a, b, c, d, and e are five consecutive numbers in increasing order of size. Deleting one of the five
numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of
the following numbers R was deleted?
A. a
B. b
C. c
D. d
Answer: C. c
Explanation: a+b+c+d+e => 1+2+3+4+5=15
20%*15= 3 =>C
Question: A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 30 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
A.	2 hours, 225 miles
B.	5.5 hours, 600 miles
C.	4 hours, 450 miles
D.	5 hours, 550 miles
Answer: B.	5.5 hours, 600 miles
Explanation: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.5) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=120(t-.5)
=> 10t +5 = 12t - 6
=> 2t=11 => t= 5.5 hrs.
Hence x= 100(5.5+.5) =>100 X 6 => 600 miles.
Hence correct answer B
Question: Sandy can do a job in 12 days and Molly can do the same job in 24 days. If they work together, in how many days will they complete the job?
A.6
B.7
C.8
D.9
Answer: C.8
Explanation: Sandy can do 1/12 of the job each day.
Molly can do 1/24 of the job each day.
The combined rate is 1/12 + 1/24 = 1/8 of the job each day.
The job will take 8 days.
The answer is C.
Question: Mark bought a set of 6 flower pots of different sizes at a total cost of $7.80. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?
A.$1.75
B.$1.93
C.$2.00
D.$2.15
Answer: B.$1.93
Explanation: This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS.
We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot.
Since the total price is $7.80(a 25-cent increment) and the the difference in sequential prices of the pots is 25 cents, the largest pot PROBABLY has a price that is a 25-cent increment. From the answer choices, I would then TEST Answer C first (since answers B and D are NOT in 25-cent increments).
IF....
The largest pot = $1.75
The other 5 pots are....
1.75
1.50
1.25
1.00
0.75
Total = $7.80
So this MUST be the answer.
B
Question: A box contains 11 apples, 10 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: P(choosing a red apple 6 times in a row) = 10/11*9/10*8/9*7/8*6/7*5/6 = 5/11 < 0.5
The answer is D.
Question: 1 ltr of water is added with 3 ltr of a solution containing 33%of alcohol in the water. The %of alcohol in the new mixture is?
A.22%
B.23%
C.24.5%
D.24.75%
Answer: D.24.75%
Explanation: We have a 3 litre solution containing 33% of alcohol in the water.
=> Quantity of alcohol in the solution
=3Ã—33/ 100
Now 1 litre of water is added to the solution.
=> Total quantity of the new solution = 3 + 1 = 4
Percentage of alcohol in the new solution
=3Ã—33/100
4
Ã—
100
=3Ã—331004Ã—100
=3Ã—8.25/100
=24.75%
D
Question: Find out the ratio of milk to that of water ,if a mixture is formed after mixing milk and water of 3 different vessels containning the mixture of milk to that of water in the proportion 3:2, 7:3, 9:2 respectively.
A.233:97
B.235:98
C.236:97
D.265:98
Answer: A.233:97
Explanation: 3+2=5,7+3=10,9+2=11
now,
3/5+7/10+9/11 : 2/5+3/10+2/11
=>233/110 : 97/110
=> 233 : 97
ANSWER:A
Question: Which of the following is a parallelogram?
A.110,70,110,70(angle in deg)
B.120,30,130,20(angle in deg)
C.90,90,95,95(angle in deg)
D.a & c
Answer: A.110,70,110,70(angle in deg)
Explanation: sum of adjacent angles is 180 degrees.
ANSWER:A
Question: If n divided by 7 has a remainder of 2, what is the remainder when 4 times n is divided by 7?
A.1
B.2
C.3
D.5
Answer: A.1
Explanation: As per question => N=7P+2 for some integer p
hence 4N => 28Q + 8 => remainder => 6 for some integer Q
Alternatively => N=2 > 3N=> 8 => 8 divided by 7 will leave a remainder 1
hence A
Question: A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:2. The ratio of economy cars to sport utility vehicles is 4:1. What is the ratio of luxury cars to sport utility vehicles?
A.9:8
B.8:3
C.3:2
D.2:3
Answer: B.8:3
Explanation: The ratio of economy to luxury cars is 3:2 --> E:L = 3:2 = 12:8.
The ratio of economy cars to sport utility vehicles is 4:1 --> E:S = 4:1 = 12:3.
Thus, L:S = 8:3.
Answer: B.
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 38, the dividend is:
A.3648
B.3642
C.3636
D.3644
Answer: A.3648
Explanation: Divisor = (5 * 38) = 190
= 10 * Quotient = Divisor
=> Quotient = 190/10 = 19
Dividend = (Divisor * Quotient) + Remainder
Dividend = (190 * 19) + 38 = 3648.
A
Question: What is the simplified result of following the steps below in order?
(1)	add 5y to 2q
(2)	multiply the sum by 3
(3)	subtract q + y from the product
A.5q + 14y
B.5x + 16y
C.5x + 5y
D.6x + 4y
Answer: A.5q + 14y
Explanation: 3(5Y+2Q) -Q-Y= 14Y+5Q
'A' is the answer
Question: In how many ways can 5 apples (identical) be distributed among 3 children? (Some children may get no apples.)
A.14
B.18
C.21
D.24
Answer: C.21
Explanation: Generalised form for n = number of identical objects, and r = number of children is n+r-1Cr-1.
n=5 r= 3
7C2 =21
Answer : C
Question: Find the average of all prime numbers between 30 and 50?
A.18.9
B.19.8
C.39.8
D.29.8
Answer: C.39.8
Explanation: there are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 199/5  39.8
ANSWER C 39.8
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.33
B.277
C.40
D.88
Answer: C.40
Explanation: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100 = 40%
Answer: C
Question: Shipment --- No. of Defective Chips/shipment --- Total Chips in shipment
S1 ---------------------- 3 ------------------------------------------ 8,000
S2 ---------------------- 5 ------------------- ---------------------- 12,000
S3 ---------------------- 6 ------------------------------------------ 18,000
S4 ---------------------- 4 ------------------------------------------ 16,000
A computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments S1, S2, S3, and S4 combined, as shown in the table above. What’s the expected number of defective chips in a shipment of 60,000 chips?
A.14
B.22
C.20
D.24
Answer: C.20
Explanation: for a total of 51000 chips (adding S1,S2,S3,S4) total number of defective chips is 17 ((adding defective chips of S1,S2,S3,S4) so ratio is 18/54000 or 1 every 3000 chips.
Keeping this ratio constant for 60000 chips number of defective chips will be (1/3000) * 60000 = 20
C
Question: I. All the offices on the 9th floor have wall-to-wall carpeting.
II. No wall-to-wall carpeting is pink.
III.None of the offices on the 9th floor has pink wall-to-wall carpeting.
If the first two statements are true, the third statement is
A.true
B.false
C.uncertain
D.none
Answer: A.true
Explanation: Explanation:
If no wall-to-wall carpeting is pink and all the offices have wall-to-wall carpeting, none of the offices has pink wall-to-wall carpeting.
Answer: A) true
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
A.Rs.4007
B.Rs.4000
C.Rs.4028
D.Rs.4050
Answer: B.Rs.4000
Explanation: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv)
Subtracting (ii) from (iv), we get, P = 4000.
P's monthly income = Rs. 4000.
Answer:B
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 54kmh, what was the average speed of the car for the entire trip?
A.36 kmh
B.40 kmh
C.41 kmh
D.44 kmh
Answer: C.41 kmh
Explanation: Assume D/3 = 2160 (this number is convenient because it is divisible by 80, 24 and 54)
So:
2160 = 80*T1 = 27 hrs
2160 = 24*T2 = 90 hrs
2160 = 54*T3 = 40 hrs
T = T1 + T2 + T3 = 157 hrs
D = RT
(240*3) = R*157
R = 41.27
ANSWER: C
Question: If p and n are positive integers, with p > n, what is the average of n consecutive multiples of p (starting with p), less the average of p consecutive multiples of n (starting with n)?
A.(p + n)/2
B.(p – n)/2
C.p + n
D.p – n
Answer: B.(p – n)/2
Explanation: Let, n = 2
and p = 3
i.e. Average of 2 (n) consecutive multiples of 3 (p) starting from 3 (p) = (3+6)/2 = 9/2
and Average of 3 (p) consecutive multiples of 2 (n) starting from 2 (n) = (2+4+6)/3 = 12/3 = 4
The average of n consecutive multiples of p (starting with p), less the average of p consecutive multiples of n (starting with n) = (9/2)-4 = (1/2)
A. (p + n)/2 = (3+2)/2 = 7/2 INCORRECT
B. (p – n)/2 = (3-2)/2 = 1/2 CORRECT
C. p + n = (3+2) = 7 INCORRECT
D. p – n = (3-2) = 1 INCORRECT
E. p^2 – n^2 = 3^2 - 2^2 = 5 INCORRECT
Answer: option B
Question: Sripad has scored average of 65 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ?
A.79
B.47
C.29
D.27
Answer: A.79
Explanation: Explanation:
Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 65.
i.e (58+58+x)/3 = 65
116 + x = 195
x = 79 marks.
Therefore, the maximum marks he can score in maths is 79.
Answer: A
Question: Awordis defined as a sequence of four dots arranged in a row. Each dot is colored either red or blue. How many distinct words can be formed?
A.16
B.15
C.6
D.18
Answer: A.16
Explanation: Each dot can be either yellow or blue, so 2 options for each dot: 2*2*2*2 = 16.
Answer: A.
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.76
B.5.78
C.5.76
D.5.75
Answer: C.5.76
Explanation: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer: C
Question: A man purchases 2 watches for $ 520. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :
A.$ 208 and $ 312
B.$210 and $ 350
C.$224 and $336
D.$560 and $560
Answer: A.$ 208 and $ 312
Explanation: x + y = 520 --- (1)
1.15x + 0.9y = 520 --- (2)
(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*104)/(3*104) = 208/312
Answer: A
Question: If p and q are positive integers each greater than 1, and 17(p+1)=21(q+1), what is the least possible value of p+q?
A.36
B.42
C.44
D.46
Answer: A.36
Explanation: 17(p+1)=21(q+1) --> (p+1)/(q+1) = 21/17 --> the least positive value of p+1 is 21, so the least value of p is 20 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 20+16=36.
Answer: A.
Question: The roof of an apartment building is rectangular and its length is 3 times longer than its width. If the area of the roof is 675 feet squared, what is the difference between the length and the width of the roof?
A.38.
B.30.
C.42.
D.44.
Answer: B.30.
Explanation: Let the width= x
x*3x=675
x^2= 225
x= 15
Length= 3*15= 45
difference= 45-15= 30
B is the answer
Question: If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 2
III. ab is even
A.I only
B.III only
C.I and II
D.I and III
Answer: B.III only
Explanation: Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
III only.letter B
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an odd number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.
A.2 only
B.3 only
C.1 and 3 only
D.2 and 3 only
Answer: B.3 only
Explanation: Using the properties for even and odd numbers along with positive and negatives,
1. (X + Y) is an odd number : even + odd is always a odd number, so eliminate 1
2. Y^(X + Y) is an integer. : an odd and positive number could be raised to power of either positive or negative, so not conclusive, eliminate 2
3. X^Y is a positive number. : a negative number raised to power of odd number is always negative.
Answer : B
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
A.3
B.4
C.5
D.7
Answer: A.3
Explanation: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3
A)
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 57?
A.3944
B.920
C.7290
D.3876
Answer: D.3876
Explanation: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 57 = Rs. 3876.
Answer: Option D
Question: A can do a piece of work in 10 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
A.10 2/9
B.10 2/6
C.10 2/3
D.10 2/2
Answer: C.10 2/3
Explanation: 2/10 + 4/15 + x/20 = 1
x = 32/3 = 10 2/3
Answer:C
Question: 16! is equal to which of the following?
A.20,922,789,888,321
B.20,922,789,888,000
C.20,922,789,888,525
D.20,922,789,888,416
Answer: B.20,922,789,888,000
Explanation: After 4!, the units digit of every factorial is 0.
5!=120
6!=720
etc...
The answer is B.
Question: If a 3-member subcommittee is to be formed from a certain 7-member committee, how many different such subcommittee are possible?
A.6
B.18
C.35
D.108
Answer: C.35
Explanation: 1st member can be selected in 7 ways
2nd can be selected in 6 ways
3rd can be selected in 5 ways
So total ways : 210
But to avoid the similar scenarios 210/3!=35
ANS:C
Question: For integers x, y, and z, if (3^x) (4^y) (5^z) = 209,715,200,000 and x + y + z = 18, what is the value of xy/z?
A.0
B.3
C.5
D.7
Answer: A.0
Explanation: The number 209,715,200,000 is not divisible by 3. (We can verify this by adding the digits of the number to see that the sum is not a multiple of 3.)
Thus x = 0 and xy/z = 0.
The answer is A.