RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 200 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
A.140
B.146
C.152
D.162
Answer: B.146
Explanation: Number of newborns that can die in first month = 1/10 * 200 = 20
Survived = 180
Number of newborns that can die in second month = 1/10 * 180 = 18
Survived = 162
Number of newborns that can die in third month = 1/10 * 162 = 16
Survived = 146
Answer:B
Question: 54671 - 18456 - 33466 = ?
A.2749
B.5449
C.6749
D.6449
Answer: A.2749
Explanation: A
If we calculate we will get 2749
Question: TOM traveled the entire 20 miles trip. If he did the first 10miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour, what is the his average speed, in miles per hour?
A.12.45 mph
B.11.25 mph
C.10.95 mph
D.10.91 mph
Answer: D.10.91 mph
Explanation: avg speed = total distance/ total time = (d1+d2)/(t1+t2) = (10+10) / ((10/12)+(10/10) =120/11 = 10.91 mph D
Question: If x^2 – x = 2, then one possible value of x – 4 =
A.-9
B.-5
C.-3
D.-1
Answer: B.-5
Explanation: x^2 –x = 2
i.e. x^2 – x - 2 = 0
i.e. x^2 +x -2x -2 = 0
i.e. (x-2)(x+1) = 0
i.e. x = 2 or -1
i.e. x-4 = 2-4 or -1-4
i.e. x-4 = -2 or -5
Answer: Option B
Question: Train X and train Y pass one another traveling in opposite directions. Thirty minutes later they are 100 miles apart. If train X’s constant speed is 40 miles per hour greater than train Y’s, how far does train X travel during that time?
A.28
B.40
C.60
D.72
Answer: C.60
Explanation: Let the rate of the Train Y be R
Then the rate of the Train X will be R+40 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+40) [add the rates] i.e. 2R+40
d=100 and t = 30 min i.e 30/60 hr
using RTD table, (2R+40) * 30/60 = 100 ==> R= 80 miles/hr
So the rate of train X is 120 miles/hr (since R+40)
The distance traveled by Train X in 30 min is R*T = 120 * 30/60 = 60 miles (C)
Question: 7 points are marked on a straight line and another 4 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points?
A.91
B.126
C.196
D.21
Answer: B.126
Explanation: getting the answer 126 which is not in the choices, what is the source of the problem?
7C2* 4C1 + 4C2* 7C1 = 126
B
Question: Which of the following is not the square of an integer?
A.275625
B.385641
C.426437
D.532900
Answer: C.426437
Explanation: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is C.
Question: Two marathoners begin their training run on the river bank at the same time. Sally Slow runs due south at 5 miles/hour, while Freddy Fast runs due North at 10 miles/hour. At this pace, how long before they have run 26.2 miles away from each other?
A.1.75 hours
B.1.634 hours
C.1.5 hours
D.3 hours
Answer: A.1.75 hours
Explanation: The runners run a combined pace of 15 miles per hour (10+5).
26.2 miles/ 15 miles/hour= 1.75 hours
Answer is A
Question: A portion of the 95% solution of dye was replaced with an equal amount of 20% solution of dye. As a result, 40% solution of dye resulted. What part of the original dye was replaced?
A.2/5
B.3/7
C.5/17
D.11/15
Answer: D.11/15
Explanation: This is a weighted average question. Say x% of the dye was replaced --> equate the amount of dye in the solution: 0.95(1-x)+0.2*x=0.4 --> x=11/15.
Answer: D.
Question: Danny drove his old car 100 kilometers, from his home to a friend. To prevent the engine from overheating, he stopped his car for 8 minutes every time he completed 40 kilometers of continuous driving. When the car was moving, Danny drove it at an average speed of 60 kilometers per hour. What was Danny's average speed on that trip?
A.37.5 kilometers per hour
B.48 kilometers per hour
C.51.7 kilometers per hour
D.75 kilometers per hour
Answer: C.51.7 kilometers per hour
Explanation: Time taken to reach first 40 km is 40/60 = 2/3 hr
Time taken to reach next 40 km is 40/60 = 2/3 hr
Time taken to reach next 20 km is 20/60 = 1/3 hr
Danny stopped twice on his way at 40 km from starting point and at 80km from the starting point...
Each stop was of 8 min , so two 8min break = 2*2/15 => 4/15 hr
Total time taken to reach 100 km is (2/3 + 2/3 + 1/3+4/15)= 29/15 hrs
So, Average speed is 100/(29/15) = 51.7 km/hour
Answer will be (C)
Question: A clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 45 percent of what the collector had paid. The shop then sold the clock again at a profit of 85 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $80, for how much did the shop sell the clock the second time?
A.$168.58
B.$187.54
C.$158.74
D.$120.56
Answer: C.$158.74
Explanation: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 15% profit.
This means the clocks' selling price was C (1.15) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 45% the price at which the collector bought it.
Thus, you get = 1.15*0.45*C = 0.5175 C
Furthermore, the store sells the clock for the second time for 85% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.85 = 1.85 * 0.5175 C
Finally given that C - 0.5175 C = 80 ----> C = 165.80$
Thus, the cost of the clock the second time around = 1.85*0.5175 C = 1.85 * 0.5175 * 165.80 = 158.74$. Hence C is the correct answer.
Question: If we have 17 people in a meeting, in how many ways they can sit around a table?
A.10*9!
B.11*12!
C.12*13!
D.16*15!
Answer: D.16*15!
Explanation: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=17
(n-1)!=16!=16*15!
Ans:D
Question: How many points (x, y) lie on the line segment between (32, 12 2/3) and (7, 17 2/3) such that x and y are both integers?
A.one
B.4
C.5
D.8
Answer: C.5
Explanation: slope = (17 2/3 - 12 2/3) / (7 - 32) = -1/5
y = mx + b => 12 2/3 = -22/3 + b => b = 19
y = -x/5 + 19
Only integer values work, and the only multiples of 5 between 7 and 32 for x values are 10, 15, 20, 25 and 30, thus 5 points.
C
Question: The price of pulses has fallen by 25%. How many quintals can be bought for the same amount which was sufficient to buy 22 quintals at the higher price?
A.20
B.22.5
C.29.3
D.28.5
Answer: C.29.3
Explanation: 80% of original price can buy = 22 quintals.
Therefore, he can buy ( 22 x 100 )/ 75 = 29.3 quintals at the lower price.
ANSWER:C
Question: There are 10 women and 15 men in an office. In how many ways can a person can be selected?
A.23
B.25
C.28
D.10
Answer: B.25
Explanation: The number of ways in which a person can be selected = 10 + 15 = 25
Answer is B
Question: For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 54 units per day, what is the value of n ?
A.30
B.18
C.10
D.9
Answer: D.9
Explanation: (average production for n days) * n = (total production for n days) --> 50n=(total production for n days);
(total production for n days) + 90 = (average production for n+1 days) * (n+1) --> 50n + 90 = 54 * (n+1) --> n=9.
Or as 40 extra units increased the average for n+1 days by 4 units per day then 40/(n+1)=4 --> n=9.
Answer D.
Question: If a/b = 1/2, b/c = 5, c/d = 2/3, d/e = 1/6 and e/f = 2/3, then what is the value of abc/def ?
A. 50/729
B. 20/456
C. 45/752
D. 13/452
Answer: A. 50/729
Explanation: Say a = 2. Then:
a/b = 1/2 --> b = 4;
b/c = 5 --> c = 4/5;
c/d = 2/3 --> d = 6/5;
d/e = 1/6 --> e = 36/5;
e/f = 2/3 --> f = 54/2.
abc/def = (2*4*4/5)/(6/5*36/5*54/5) = 50/729.
Answer: A.
Question: A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 127 in his diary to remember his PIN. He also wrote out the way to calculate 127 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 127".
Once, Prafull saw his diary in which Pinaki wrote this number 127. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
A.670
B.770
C.870
D.970
Answer: C.870
Explanation: Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =127.
Thus, (996 × x)/997=127.
=>x= 870.
Answer : C
Question: In what time will a train 130 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5
B.3.25
C.4.5
D.5.25
Answer: B.3.25
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 130/40 = 3.25 sec.
Answer: Option B
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsaleble and there are 15 unsaleable mangoes in the crate then how msny mango are there in the crate?
A.100 mangoes
B.110 mangoes
C.120 mangoes
D.150 mangoes
Answer: D.150 mangoes
Explanation: 150 mangoes
ANSWER:D
Question: One week, a certain truck rental lot had a total of 24 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 12 trucks on the lot that Saturday morning, what is the greatest number of different trucks that could have been rented out during the week?
A.24
B.16
C.12
D.8
Answer: A.24
Explanation: N - Not rented trucks; R - Rented trucks
N + R = 24
N + R/2 = 12
R =24
A
Question: A man saves Rs 350 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
A.Rs 662
B.Rs 2262.01
C.Rs 1158.54
D.Rs 1662.54
Answer: C.Rs 1158.54
Explanation: Explanation:
=[350(21/20×21/20×21/20)+350(21/20×21/20)+350(21/20)]=1158.54
Answer: C
Question: Larry, Michael, and Wilson have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?
A. 21
B. 42
C. 120
D. 504
Answer: A. 21
Explanation: Larry, Michael, and Wilson have five donuts to share to get the answer, see how can we get sum5with 3 numbers.
1) 0,0,5 = 3 combinations or 3! /2!
2) 0,1,4 = 6 combinations or 3!
similarly
3) 0,2,3 = 6 combinations
4) 1,1,3 = 3 combination
5) 2,2,1 = 3 combination
total =21=A
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they take to finish the work, if all the three work together?
A.4
B.9
C.2
D.11
Answer: A.4
Explanation: 1/7 + 1/14 + 1/28 = 7/28 = 1/4
All three can finish the work in 4 days
Answer: A
Question: For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(18)/h(10) ?
A.1.8
B.3
C.6
D.18
Answer: B.3
Explanation: Mean = Median =(First+Last)/2
and Sum = Mean*Number of terms
h(18) = [(2+18)/2]*9 = 90
h(10) = (2+10)/2]*5 = 30
h(18)/h(10) = (90) / (30) = 3
ANSWER:B
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
A.26
B.72
C.25
D.82
Answer: C.25
Explanation: Explanation:
D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer: Option C
Question: Kamal started a business investing Rs 9000. After five months, Sameer joined with a capital of Rs 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit ?
A.Rs 2380
B.Rs 2300
C.Rs 2280
D.Rs 2260
Answer: A.Rs 2380
Explanation: Solution: Now as per question, Kamal invested for 12 months and Sameer invested for 7 months.
So Kamal: Sameer = (9000*12):(8000*7)
= 108 : 56
= 27 : 14
Sameer Ratio in profit will be =(6970*14/41)=Rs 2380.
Answer: Option A
Question: Pipe A can fill a tank in 4 hours, pipe B in 8 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled ?
A.2.5 hours
B.2 hours
C.3.5 hours
D.2.3 hours
Answer: D.2.3 hours
Explanation: Explanation:
Part filled by A in 1 hour = 1/4
Part filled by B in 1 hour = 1/8
Part filled by C in 1 hour = 1/16
Part filled by (A+B+C) in 1 hour =
1/4+1/8+1/16=7/16
So all pipes will fill the tank in 2.3 hours.
Option D
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 100 meters, how long will it take to cross a railway platform 120 meters long
A.6 sec
B.7 ½ sec
C.8 sec
D.8 ½ sec
Answer: A.6 sec
Explanation: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (100 + 120) m = 220 m.
Time taken =220 ×(3/110) sec =6 sec
Answer: Option A
Question: Surekha started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajesh joined him with an amount of Rs. 35,000. In 2001, Surekha invested another additional amount of Rs.10,000 and Jay joined them with an amount of Rs.35,000. What will be Rajesh's share in the profit of Rs.2,70,000 earned at the end of 3 years from the start of the business in 1999?
A.Rs 45000
B.Rs 50000
C.Rs 90000
D.Rs 75000
Answer: C.Rs 90000
Explanation: Surekha:Rajesh:Jay= (25000×12+35000×12+45000×12):(35000×24) : (35000×12) = 1260000 : 840000 : 420000 = 3 : 2 : 1. Rajesh's share =Rs.(270000×2/6) = Rs.90000.
Answer C
Question: At a loading dock, each worker on the night crew loaded 2/3 as many boxes as each worker on the day crew. If the night crew has 5/6 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
A.6/11
B.7/12
C.8/13
D.9/14
Answer: D.9/14
Explanation: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (5x/6)(2y/3) = 5xy/9
The total number of boxes is xy + 5xy/9 = 14xy/9
The fraction loaded by the day crew is xy / (14xy/9) = 9/14
The answer is D.
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.02, what is value of J?
A.300
B.600
C.500
D.112
Answer: B.600
Explanation: 1) We know that
decimal part of decimal quotient ={remainder/divisor}
So 0.02, the decimal part of the decimal quotient, must equal the remainder, 12, divided by the divisor J.
0.02 = 12/J
0.02*J = 12
J = 12/0.02 = 1200/2 = 600/1 = 600
So J = 600, answer = B.
Question: A train running at the speed of 54 km/hr crosses a pole in 9 sec. What is the length of the train?
A.288
B.279
C.135
D.272
Answer: C.135
Explanation: Speed = 54 * 5/18 = 15 m/sec
Length of the train = speed * time = 15 * 9
= 135 m
Answer: C
Question: Two quarts containing 2⁄3 water and 1⁄3 formula are mixed with three quarts containing 3⁄8 water and 5⁄8 formula. Approximately what percent of the combined five-quart mixture is water?
A.40%
B.45%
C.50%
D.55%
Answer: C.50%
Explanation: Since we are asking of water in the end, lets concentrate on water only..
A solution has 2 quarts with fraction of water =2/3, almost 67%..
B solution has 3 quarts with fraction of water =3/8 almost 37%..
so the ratio A:B=2:3...
the average will therefore be closer to B % and will be 2/(2+3) of {67-37} away from B..
2/(2+3) of {67-37}= 2/5 * 30 =12..
so 37 +12 =49 nearly 50%
ANSWER:C
Question: The letters of the word 'SUBITI' are written in all possible orders and these words are written in alphabetical order. Then what is the rank of the word 'SUBITI'
A.- 246
B.- 245
C.- 237
D.- 315
Answer: C.- 237
Explanation: Total Number of Words = 6!/2! = 360 [(number of characters)/(repeating group )!]
After S, we have T and U.
Number of words starting with T = 5!/2! = 60
Number of words starting with U = 5!/2! = 60
So any word starting with S will have rank < 360 - 60(for Us) - 60(for Ts) = 240
Only option A < 240, so Answer is C.
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 2 days. In how many days can they complete the remaining work?
A.5 days
B.4 days
C.3 days
D.6 days
Answer: B.4 days
Explanation: Explanation:
1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
answer B
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $864 in total compensation, how many total hours did he work that week?
A.36
B.40
C.44
D.48
Answer: D.48
Explanation: For 40 hrs = 40*16=640
Excess = 864-640=224
For extra hours =.75(16)=12+16=28
Number of extra hrs =224/28=56/7=8
Total hrs =40+8=48
Answer D 48
Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
A.1378
B.1800
C.2738
D.2778
Answer: B.1800
Explanation: Explanation:
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
machines & 6:10\\ time(in\; minutes) &1:4 \end{matrix}\right\}::270:x}
6 x 1 x x = 10 x 4 x 270
{10\times 4\times 270}{6}}
=> x= 1800
Answer: B
Question: A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
A.48 min. past 12.
B.20 min. past 12.
C.28 min. past 12.
D.18 min. past 12.
Answer: A.48 min. past 12.
Explanation: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
hrs of this clock = 24 hours of the correct clock.
29 hours of this clock =(24 x 6/145 x 29) hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
Answer A
Question: How many different ways can you select a pilot and a co pilot if you have 70 people to choose from?
A. 199
B. 200
C. 398
D. 4830
Answer: D. 4830
Explanation: You are not just choosing two from 70. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (70C2) x 2 = 4830.
Ans D
Question: During one year, the population of town increased by 5% . If the total population is 9975 at the end of the second year , then what was the population size in the beginning of the first year ?
A.50000
B.10000
C.90000
D.70000
Answer: B.10000
Explanation: Population in the beginning of the first year
= 9975/[1+(5/100)]*[1-(5/100)]
= [9975*(20/21)*(20/19)]
=10000.
Answer is B.
Question: A train passes a station platform in 48 sec and a man standing on the platform in 40 sec. If the speed of the train is 36 km/hr. What is the length of the platform?
A.80
B.120
C.60
D.90
Answer: A.80
Explanation: Speed = 36 * 5/18 = 10 m/sec.
Length of the train = 10 * 40 = 400 m.
Let the length of the platform be x m . Then,
(x + 400)/48 = 10 => x = 80 m.
Answer: A
Question: How many odd, positive divisors does 520 have?
A.6
B.8
C.12
D.15
Answer: A.6
Explanation: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=6 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: A
Question: When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 41, what is the remainder when k is divided by 7?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Cant think of a straight approach but here is how I solved it:
K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer)
so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 41)
Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5
so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 41)
17 is the only common number in both the sets. Hence k = 17
Answer : A
Question: The speed of a car is 90kmph. What is the speed in metres per second.
A.25 m/s
B.40 m/s
C.35 m/s
D.28 m/s
Answer: A.25 m/s
Explanation: Explanation:
km/hr to m/sec conversion:
x km/hr = (x × 5/18) m/sec
90 × 5/18 = 25.
Answer: Option A
Question: If a man walks 24 Km at 8 Kmph, he will be late by 25min. if he walks 12 Kmph, how early the fixed time Will he reach?
A.30 minutes
B.25 minutes
C.40 minutes
D.35 minutes
Answer: D.35 minutes
Explanation: Time taken to cover 24 Km at the speed of 8 Kmph = 24/8 = 3 hours
Thus, right time was 2 hours 35 mintes
Now, time taken to cover 20 Km at the speed as 12 Kmph = 2 hours
Required time = 2 hours 35 minutes - 2 hours
= 35 minutes
ANSWER IS D
Question: In how many different ways can the letters of the word 'DETAIL' be arranged such that the vowels must occupy only the odd positions?
A.12
B.36
C.45
D.96
Answer: B.36
Explanation: The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions. Let's mark the positions as (1) (2) (3) (4) (5) (6). Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to arrange these vowels
= 3P3 =3!=3×2×1=6
Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order. Hence, number of ways to arrange these consonants
= 3P3=3!=3×2×1=6
Total number of ways
= number of ways to arrange the vowels × number of ways to arrange the consonants
=6×6=36
Answer: B
Question: 10 meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
A.5/2
B.2√5
C.5
D.4√2
Answer: A.5/2
Explanation: Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 10
=> x/360*2*pi*r +2r= 20
=> 2A/r+2r=10 OR 2A +2r^2=10r
=> A= r5-r^2
= r5-r^2
We will now max using derivations
i.e 5-2r=0
r=5/2
A
Question: The radius of the two circular fields is in the ratio 3: 5 the area of the first field is what percent less than the area of the second?
A.50%
B.60%
C.40%
D.64%
Answer: D.64%
Explanation: Explanation:
r = 3 πr2 = 9
r = 5 πr2 = 25
25 π – 16 π
100 ---- ? => 64%
ANSWER IS D
Question: 4, 6, 12, 14, 28, 30, .. ?
A.20
B.40
C.no=60
D.80
Answer: C.no=60
Explanation: C
60
The given sequence is a combination of two series 4, 12, 28, .... and 6, 14, 30, .... The pattern is +8, +16, +32. So, the missing number = (28 + 32) = 60
Question: A bag contains 11 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
A.8/19
B.10/33
C.12/55
D.15/67
Answer: C.12/55
Explanation: Total possible ways to choose three scarves is 11C3 = 165
We need to choose the red scarf and two of 9 other scarves (not the green scarf).
The number of successful possibilities is 9C2 = 36
P(red scarf but not green scarf) = 36/165 = 12/55
The answer is C.
Question: Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is?
A.15
B.17
C.19
D.21
Answer: A.15
Explanation: Let the three integers be x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3 x = 11.
Third integer = x + 4 = 15.
Option A