divelab/Sys2Bench huggingface dataset:
Question: A bookseller has two display windows. She plans to display 5 new fiction books in the left window, and 6 new non-fiction books in the right window. Assuming she can put the six fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
Options:
A)86400
B)65777
C)89000
D)34560
E)12420
Rationale: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,
5!*6! =120*720=86400
Answer is A
Answer: A
Question: Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 20 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)
Options:
A)40 mph
B)45 mph
C)48 mph
D)52 mph
E)60 mph
Rationale: Let t be the number of hours he would need to reach office on time.
when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 30
where s is the speed and 30 is the distance.
if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 30
if you solve above equations, you will arrive at t = 2/3 hr and s = 40mph
therefore answer is A
Answer: A
Question: The average of the marks of 12 students in a class is 36. If the marks of each student are doubled, find the new average?
Options:
A)72
B)55
C)44
D)66
E)98
Rationale: Sum of the marks for the 12 students = 12 * 36 = 432. The marks of each student are doubled, the sum also will be doubled.
The new sum = 432 * 2 = 864. So, the new average = 864/12 = 72.
Answer: A
Answer: A
Question: A bicyclist travels uphill from town A to town B for 2 hours at an average speed of 6 miles per hour and returns along the same road at an average speed of 6 miles per hour. What is the bicyclist’s average speed for the round trip, in miles per hour?
Options:
A)(a) 24/5
B)(b) 6
C)(c) 26/5
D)(d) 27/5
E)(e) 28/5
Rationale: from the uphill we can find out the distance = 6*2 = 12
average speed = total distance/total time
= 24/ (2+ (12/6)) = 6
Answer is B.
Answer: B
Question: A student got 72% in math and 84% in history. To get an overall average of 75%, how much should the student get in the third subject?
Options:
A)65%
B)67%
C)69%
D)71%
E)73%
Rationale: 72 + 84 + x = 3*75
x = 69
The answer is C.
Answer: C
Question: A sum amount to Rs.1344 in two years at simple interest. What will be the compound interest on the same sum at the same rate of interest for the same period?
Options:
A)10.28%
B)10.95%
C)10.25%
D)12.25%
E)10.55%
Rationale: 100
5 ---- I
5
0.25 --- II
-----------
10.25%.Answer:C
Answer: C
Question: 180 students appeared for a test, of which 162 passed. The pass percentage is
Options:
A)80%
B)85%x1/2%
C)90%
D)93x1/3%
E)None of these
Rationale: Explanation :
Pass percentage = (162/180 100)%
= 90%
Answer : C
Answer: C
Question: The H.C.F. of two numbers is 15 and their L.C.M. is 420. If one of the numbers is 375, then the other is:
Options:
A)12.21
B)283
C)16.8
D)318
E)32.4
Rationale: Other number =	(15 x 420)/375 = 16.8.
ANSWER :C
Answer: C
Question: Find compound interest on Rs. 7500 at 4% per annum for 2 years, compounded annually.
Options:
A)Rs.512
B)Rs.552
C)Rs.612
D)Rs.622
E)None
Rationale: Solution
Amount	= Rs[7500x(1+4/100)²]
=Rs.(7500x26/25x26/25)
= Rs.8112.
C.I	= Rs(8112 - 7500)
=Rs.612.
Answer C
Answer: C
Question: In how many possible ways you can write 3240 as product of 3 positive integers x,y,z .
Options:
A)420
B)450
C)350
D)320
E)380
Rationale: 3240=2^3*3^4*5
we have to distribute three 2 to three numbers : 3+3-1C3-1=5C2=10
similarly for 3 and 5
therefore total=10*15*3=450
ANSWER:B
Answer: B
Question: In how many ways can a committee consisting of three men and four women be formed from a group of six men and seven women?
Options:
A)(7C4)(6C9)
B)(7C4)(6C5)
C)(7C4)(6C3)
D)(7C4)(8C3)
E)(7C3)(6C3)
Rationale: The group contain six men and seven women
Three men can be selected from six men in 6C3 ways.
Four women can be selected from seven women in 7C4 ways.
Total number of ways = (7C4)(6C3).
Answer:C
Answer: C
Question: When positive integer N is divided by positive integer J, the remainder is 12. If N/J = 134.08, what is value of J?
Options:
A)22
B)56
C)78
D)150
E)175
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 134.08
Here 134 is the quotient.
Given that Remainder = 12
So, 134.08 = 134 + 12/J
So, J = 150 ANS D
Answer: D
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 140?
Options:
A)65
B)77
C)25
D)18
E)12
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100 = (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (140 - 75) = 65 points to C.
Answer:A
Answer: A
Question: The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?
Options:
A)12%
B)20%
C)25%
D)30%
E)35%
Rationale: Sol. Required change = (20*100)/(100-20)=25%
C
Answer: C
Question: If x and y are positive integers such that x/y = 4.25, which of the following numbers could be y?
Options:
A)5
B)4
C)3
D)17
E)50
Rationale: With the given information, we are trying to find the value of y.
To achieve this we must convert the given decimal to a fraction and reduce it to it's lowest integer form.
Take the decimal x/y = 4.25 and because it's in the hundreds decimal place, put the given value (x/y = 4.25/1) and multiply it by 100.
Take the resulting fraction (x/y = 425/100) and reduce it to it's lowest form.
Both of the numbers are divisible by 25.
The result is x/y = 17/4.
Thus y = 4.
The correct answer is B.
Answer: B
Question: The area of Circle O is added to its diameter. If twice the circumference of Circle O is then subtracted from this total, the result is 8. What is the radius of Circle O?
Options:
A)2/π
B)2
C)3
D)4
E)5
Rationale: area+diameter-2*circumference=8
pi*r^2+2r=8+2*2pi*r
isolate r and get r(pi*r+2)=8+4pi*r
r=(8+4pi*r)/(pi*r+2) =>4(pi*r+2)/(pi*r+2)
r=4
D
Answer: D
Question: A set of data consists of the following 9 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
Options:
A)-1 and 9
B)4 and 4
C)3 and 5
D)2 and 6
E)0 and 8
Rationale: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding -1 and 9 , results in a value that would change the SD to the least. Hence A
Answer: A
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs.10 of money?
Options:
A)1500
B)1992
C)9921
D)1000
E)2789
Rationale: P = 10(100/10)2
=> P = 1000
Answer: D
Answer: D
Question: If a is the smallest positive integer such that 3,150 multiplied by a is the square of an integer, then a must be
Options:
A) 2
B) 5
C) 6
D) 7
E) 14
Rationale: Solution:
This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.
Let’s start by prime factorizing 3,150.
3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2
3,150 = 2^1 x 3^2 x 5^2 x 7^1
(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)
We also are given that 3,150 multiplied by a is the square of an integer. We can write this as:
2^1 x 3^2 x 5^2 x 7^1 x a = square of an integer
According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, a = 7 x 2 = 14
Answer is E.
Answer: E
Question: Which is the middle even number between 1 and 9?
Options:
A)10
B)25
C)5
D)8
E)6
Rationale: 1+x = 9-x
2 x = 8
X = 4
Now 1+x = 5
ANSWER:C
Answer: C
Question: A person lent a certain sum of money at 5% per annum at simple interest and in 8 years the interest amounted to $480 less than the sum lent. What was the sum lent?
Options:
A)700
B)800
C)900
D)1000
E)1100
Rationale: P - 480 = (P*5*8)/100
P = 800
The answer is B.
Answer: B
Question: If, 4 years ago, Jamie was half as old as he is now, how old will he be in x years?
Options:
A)x + 10
B)x + 5
C)x + 8
D)x – 5
E)2x
Rationale: let his age be a. a-4=a/2 hence a=8. 8 years hence, a =x+8
Answer C
Answer: C
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)8 months
B)2 months
C)6 months
D)4 months
E)5 months
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Answer:E
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: E
Question: Multiply: (x-4)(X+5)
Options:
A)xpower2 + 5x-20
B)xpower2 - 4x - 20
C)xpower2 - x - 20
D)xpower2 + x - 20
E)x - 20
Rationale: (x-4)(x+5)=x(X+5)-4(x+5), = xpower2 + 5x - 4x - 20, =xpower2 + x - 20 . the correct answer : (D)
Answer: D
Question: A train 100 m long crosses a platform 125 m long in 15 sec; find the speed of the train?
Options:
A)55 kmph
B)52 kmph
C)57 kmph
D)54 kmph
E)59 kmph
Rationale: D
54 kmph
D = 100 + 125 = 225
T = 15
S = 225/15 * 18/5 = 54 kmph
Answer: D
Question: Andrew earns $2000 a month from his job. His income increased and now makes $2125 a week. What is the percent increase?
Options:
A)6.25%
B)5.25%
C)7.25%
D)4.25%
E)12.5%
Rationale: Increase = (125/2000)*100 = (1/16)*100 = 6.25%.
A
Answer: A
Question: In a kilometer race, If A gives B a 40m start, A wins by 19sec. But if A gives B a 30 sec start, B wins by 40 m. Find the time taken by B to run 5,000m?
Options:
A)2275
B)2375
C)2475
D)2575
E)2675
Rationale: Let A travells 1000m in x sec and b in (x+19)sec
Therefore, speed of B is 1000/(x+19)
B travel 960m in x sec from here equation of speed=960/x
speed of B is constant so boht the speed equation for B are equal
960/x = 1000/(x+19)
On solving we get x=456sec
Time taken by B for 5000m : 5000/(960/456)=2375
ANSWER:B
Answer: B
Question: In a certain warehouse, 70 percent of the packages weigh less than 75 pounds, and a total of 48 packages weigh less than 25 pounds. If 80 percent of the packages weigh at least 25 pounds, how many of the packages weigh at least 25 pounds but less than 75 pounds?
Options:
A)8
B)64
C)120
D)102
E)144
Rationale: If 80% of the packages weigh at least 25 pounds
This means that 20% of the packages weigh LESS THAN 25 pounds
Let T = TOTAL number of packages
So, 20% of T = # of packages that weigh LESS THAN 25 pounds
48 packages weigh LESS THAN 25 pounds
GREAT. So, 20% of T = 48
Rewrite to get: 0.2T = 48
Solve:T = 240
70% of the packages weigh less than 75 pounds
So, 70% ofT= number of packages that weigh less than 75 pounds
70% of240=168, so168packages weigh less than 75 pounds
OF THOSE168packages that weigh less than 75 pounds,48packages weigh less than 25 pounds.
So, the number of packages that weight BETWEEN 25 and 75 pounds =168-48= 120 = C
Answer: C
Question: What is the ratio between perimeters of two squares one having 8 times the diagonal then the other?
Options:
A)3: 6
B)3: 3
C)3: 8
D)8: 1
E)3: 2
Rationale: d = 8d d = d
a√2 = 8d a√2 = d
a = 8d/√2 a = d/√2 => 8: 1
Answer: D
Answer: D
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
Options:
A)7%
B)9%
C)4 percent
D)2%
E)4%
Rationale: 150 = (750*5*R)/100
R = 4%
Answer: C
Answer: C
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 150 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
Options:
A)110
B)146
C)152
D)162
E)170
Rationale: The probability of survival for each of the first 3 months of life is 1-1/10=9/10, so of 150 newborn 150*9/10*9/10*9/10=~110 is expected to survive.
Answer: A.
Answer: A
Question: If Albert’s monthly earnings rise by 26%, he would earn $693. If, instead, his earnings rise by only 20%, how much (in $) would he earn this month?
Options:
A)643
B)652
C)660
D)690
E)693
Rationale: =693/1.26∗1.2
=660=660
Answer is C
Answer: C
Question: If a and b are prime numbers, which of the following CANNOT be the sum of a and b?
Options:
A)5
B)9
C)23
D)16
E)13
Rationale: All answer choices but C are odd. In order odd number to be the sum of two prime numbers one must be even, so 2, and another odd.
Now, 23=2+21. Since 21 is not a prime then 23 cannot be written as the sum of two prime numbers.
Answer: C
Answer: C
Question: A train 440 meters long is running with a speed of 50 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
A)40.33 sec
B)41.33 sec
C)42.33 sec
D)40 sec
E)44.64 sec
Rationale: D = 440 + 180 =620
S = 50 * 5/18 = 13.88889 mps
T = 620/13.88889 = 44.64
E
Answer: E
Question: A = {0, 1, 3, 6, -8}
B = {-1, 2, -4, 7,-5}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
Options:
A)1/4
B)1/3
C)2/5
D)9/25
E)1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 3/5*2/5 = 6/25;
P(negative, negative) = 1/5*3/5 = 3/25.
P = 6/25 + 3/25
= 9/25
Answer: D
Answer: D
Question: The profit earned by selling an article for Rs 900 is double the loss incurred when the same article is sold for Rs.490. At what price should the article be sold to make 25% profit?
Options:
A)136
B)187
C)600
D)750
E)733
Rationale: Explanation:
Let C.P be Rs. x
900 - x = 2(x - 450)
=> x = Rs.600
C.P = 600 gain required is 25%
S.P = [(100+25)*600]/100
= Rs.750
Answer: D
Answer: D
Question: Ten years ago, the age of Anand was one-third the age of Bala at that time. The present age of Bala is 10 years more than the present age of Anand. Find the present age of Anand?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 10 = 1/3 (b - 10) --- (1)
b = a + 10
Substituting b = a + 12 in first equation,
a - 10 = 1/3 (a + 0) => 3a - 30 = a
=> 2a = 30=> a = 15.
ANSWER:D
Answer: D
Question: A group of men can complete a job in X hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of X.
Options:
A)5.5 days
B)6.5 days
C)7.5 days
D)8.5 days
E)9.5 days
Rationale: If there are m men
job requires mX man hours.
job completed in first 4 hrs = m*4 =4m
job completed in next 4 hrs = 4*m/2 = 2m
job completed in next 4 hrs = 4.m/4 = m
job completed in last 4 hrs = 4.m/8= m/2
4m+2m+m+m/2 = mX
x= 7+1/2 = 7.5 days
ANSWER:C
Answer: C
Question: The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 24 hours and a standard deviation of 6 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
Options:
A)30
B)20
C)18
D)12
E)16
Rationale: Given: mean=24 and SD=6.
The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=18and 2 SD below the mean ismean-2*SD=12, so the number of hours that Pat watched television was between 12 and 18 hours.
Answer: E
Answer: E
Question: Mary completes a piece of work in 160 days, Rose completes the same work in 240 days. If both of them work together, then the number of days required to complete the work is?
Options:
A)92
B)94
C)96
D)98
E)100
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 160 × 240/400 = 96 days
Answer is C
Answer: C
Question: David paid $5,000 for 100 shares of stock X and $3,000 for 100 shares of stock Y. He later sold the same shares of both stocks, gaining 3/8 the amount he paid for stock Y. If the prices he had paid for the stocks had been reversed and everything else remained the same, then the net result would have been:
Options:
A)A gain 1.67 times as much.
B)A loss 2 times as much
C)A loss 3 times as much
D)A loss 1.5 times as much
E)No Loss No Gain
Rationale: A = 5000; B = 3000; Profit = (3/8)*3000 = 1125
After prices are reversed:
A = 3000; B =5000; Profit = (3/8)*5000 =1875
1875 --> Gain of 1.67 times 1125
Answer: A
Answer: A
Question: Eight identical machines can produce 360 aluminum cans per hour. If all of the machines work at the same constant rate, how many cans could 5 such machines produce in 4 hours?
Options:
A)675
B)900
C)1,800
D)5,900
E)7,500
Rationale: 8 machines/ 360 cans = 5 machines/ x cans
8x= 1800
x=225
(225)(4 hours)= 900 cans. The answer is B.
Answer: B
Question: The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
Options:
A)Rs.8790
B)Rs.8721
C)Rs.8891
D)Rs.8768
E)Rs.8730
Rationale: Actual price = 95% of 90% of 85% of Rs. 12000
= 95/100 * 90/100 * 85/100 * 12000
= Rs.8721.
Answer: B
Answer: B
Question: John has 10pairs of dark blue socks and 10pairs of black socks. He keeps them all in the same bag. If he picks out 3socks at random, then what is the probability thathe will get a matching pair?
Options:
A)1
B)3
C)4
D)5
E)6
Rationale: If he draws any combination of 3 socks he will definitely have the matching pair of either colour.
A
Answer: A
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)8
B)7
C)9
D)6
E)5
Rationale: Let B joined for x months. Then
85000×12:42500×(x)=3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
⇒850×4=425x
⇒x=8
Answer is A.
Answer: A
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3200, A will get:
Options:
A)Rs.1200
B)Rs.1500
C)Rs. 1920
D)Rs.2000
E)None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3000/25 = 128
So, A’s amount = 120 × 15 = Rs.1920.
Answer: Option C
Answer: C
Question: The reciprocal of the hcf and lcm of two are 1/13 and 1/312 .if one of the number is 24 then other no. is
Options:
A)126
B)136
C)146
D)156
E)169
Rationale: reciprocal of the hcf and lcm of two are 1/13 and 1/312
so, HCF = 13 , LCM = 312
LCM * HCF = product of two numbers = a*b => b = LCM * HCF / a
so, other = 13*312 / 24 = 169
ANSWER:E
Answer: E
Question: Of the 170 people at a party, 70 were women, and 30 women tried the appetizer. If 60 people did not try the appetizer, what is the total number of men who tried the appetizer?
Options:
A)40
B)50
C)60
D)70
E)80
Rationale: Total people at party=170
Women=70
so Men 170-70=100
No. of pple who tried appetizer=170-60 (given info)=110
No of women who tried appetizer=30
So Remaining ppl(men) who tried the appetizer =110-30=80
Correct Option E
Answer: E
Question: Priya covers journey from kavali to nellore by car at average speed of 70 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?
Options:
A)50 Km/hr
B)50.90 Km/hr
C)50.95 Km/hr
D)52 Km/hr
E)53 km/hr
Rationale: Explanation:
Average speed = 2 xy/x+y
= 2*70*40/110
= 50.90 Km/hr
Answer: Option B
Answer: B
Question: A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
Options:
A)12/15
B)37 1/2
C)3/7
D)4/9
E)5/2
Rationale: Explanation :
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
ANSWER:B
Answer: B
Question: In a games hour 4 different types of players came to the ground? cricket 15, hokey 12, football 13, softball 15. How many players are present in the ground?
Options:
A)70
B)52
C)55
D)49
E)50
Rationale: total number of players= 15+12+13+15= 55
Answer is C
Answer: C
Question: Bucket P has thrice the capacity as Bucket Q. It takes 60 turns for Bucket P to fill the empty drum. How many turns it will take for both the buckets P&Q, having each turn together to fill the empty drum?
Options:
A)45
B)53
C)54
D)46
E)63
Rationale: If caoacity of Q is x units, then capacity of P is 3x and capacity of drum is 60*3x = 180 x.
It will take 180x/4x = 45 turns it will take for both the buckets P&Q, having each turn together to fill the empty drum.
ANSWER:A
Answer: A
Question: Find the lowest positive integer that can be divided by all the even numbers between 14 and 21.
Options:
A)4581
B)5040
C)3682
D)1231
E)1563
Rationale: The even numbers between 14 and 21 are 14,16,18,20.
Find the LCM of these numbers
LCM=2^4*7*3^2*5
The answer is B)
Answer: B
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options:
A)101
B)209
C)301
D)405
E)91
Rationale: Required number of ways = 6C1*4C3 + 6C2*4C2 + 6C6*4C1 + 6C4
= 24+90+80+15
= 209
Answer is B
Answer: B
Question: In a recent election, Geoff received 15 percent of the 6,000 votes cast. To win the election, a candidate needed to receive more than x% of the vote. If Geoff needed exactly 3,571 more votes to win the election, what is the value of x ?
Options:
A) 74.5
B) 54
C) 56
D) 60
E) 63
Rationale: Word problems are tricky in somehow more than other problem because you have the additional step to translate.
Breaking the problem: Geoff how many votes he receives ?? 900 votes
he needs 3571 more votes so : 900+3571= 4471
Now what's the problem wants ?? a x %........4471 is what % of total votes 6000........translating: 4471 = x/100 * 6000 ---
x= 74.5 %..........A
Answer: A