divelab/Sys2Bench huggingface dataset:
Question: Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).
Options:
A)2 hours 2 minutes
B)3 hours 5 minutes
C)4 hours 6minutes
D)5 hours 7 minutes
E)7 hours 9 minutes
Rationale: In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill
1/5 + 1/8 = 13 / 40 of a tank
Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving
(13/40) t = 1
t = 40 / 13 = 39/13 + 1/13 hours
= 3 hours and (1/13)*60 minutes
= 3 hours 5 minutes (rounded to the nearest minute)
correct answer B
Answer: B
Question: John and Jacob set out together on bicycle traveling at 15 and 12 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John two hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 15 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)
Options:
A)7
B)7 1/3
C)7 1/2
D)4
E)7 1/2
Rationale: John's speed - 15 miles/hr
Jacob's speed - 12 miles/hr
After 40min (i.e 2/3hr), distance covered by John = 15x2/3 = 10 miles.
Jacob continues to ride for a total of 2 hour and 40min (until John's bike is repaired). Distance covered in 2 hour 40min (i.e 8/3hr) = 12x8/3 = 32 miles.
Now, when John starts riding back, the distance between them is 22 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 15-12 = 3 miles/hr.
Thus, to cover 22 miles at 3 miles/hr, John will take 22/3 = 7 1/3 hours
Answer B
Answer: B
Question: The average of first five prime numbers which are odd is?
Options:
A)15.5
B)15.7
C)15.2
D)7.8
E)15.1
Rationale: Sum of first 5 prime no. which are odd = 39
Average = 39/5 = 7.8
Answer:D
Answer: D
Question: Cole drove from home to work at an average speed of 60 kmh. He then returned home at an average speed of 90 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
Options:
A)66
B)70
C)72
D)75
E)78
Rationale: Let the distance one way be x
Time from home to work = x/60
Time from work to home = x/90
Total time = 2 hrs
(x/60) + (x/90)= 2
Solving for x, we get x = 72
Time from home to work in minutes= (72)*60/60 = 72 minutes
Ans= C
Answer: C
Question: Suppose you work for a manufacturing plant that pays you $12.50 an hour plus $0.16 for each widget you make. How many widgets must you produce in a 40 hour week to earn $750 (before payroll deductions)?
Options:
A)1600
B)1625
C)1650
D)1655
E)1675
Rationale: total pay = 40*$12.50 + $0.16*x = 760
x = 260 / 0.16 = 1625
The answer is B.
Answer: B
Question: The product of all the prime numbers less than 20 is closest to which of the following powers of 10?
Options:
A)10^9
B)10^8
C)10^7
D)10^6
E)10^5
Rationale: Quickly approximate
2, 3, 5, 7, 11, 13, 17, 19
Make groups
2*5 = 10
3*17 = 50 (approximately)
7*13 = 100 (approximately)
11*19 = 200 (approximately)
So you make 7 zeroes (the 2 and the 5 also make a 0). When you multiply all these, the answer will be close to 10^7
ANSWER:C
Answer: C
Question: Dick and Jane each saved $1,000 in 1989. In 1990 Dick saved 15 percent more than in 1989, and together he and Jane saved a total of $2,000. Approximately what percent less did Jane save in 1990 than in 1989?
Options:
A)3%
B)5%
C)10%
D)15%
E)18%
Rationale: 1990
Dick saved = $ 1150
Jane saved = $ 850 (jane saved $150 less than she did the prior year)
Jane saved approximately $150/1000$ (15%) less in 1990
Answer: D
Answer: D
Question: The average of 11numbers is 500. Out of 11numbers the average of first 6no. is 50, and last 6numbers is 60 then find 6th number?
Options:
A)95
B)80
C)110
D)120
E)72
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*50+6*60-11*50 = 110
Answer is C
Answer: C
Question: If w is 40 percent less than q, q is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
Options:
A)4%
B)18%
C)36%
D)40%
E)50%
Rationale: GIven w= 0.6q, q=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. E is the correct answer.
Answer: E
Question: The greatest common factor of positive integers m and n is 9. What is the greatest common factor of (2m^2, 2n^2)?
Options:
A)9
B)81
C)162
D)324
E)405
Rationale: m = 9j and n = 9k, where the greatest common factor of j and k is 1.
2m^2 = 2*9*9*j^2 and 2n^2 = 2*9*9*k^2
The greatest common factor of 2m^2 and 2n^2 is 2*9*9 = 162
The answer is C.
Answer: C
Question: Two pipes A and B can fill a tank in 5 hrs and 20 hrs respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
Options:
A)5 hr
B)4 hr
C)6 hr
D)3 hr
E)7 hr
Rationale: Explanation:
Pipe A can fill 1/5 of the tank in 1 hr
Pipe B can fill 1/20 of the tank in 1 hr
Pipe A and B together can fill 1/5+1/20=1/4 of the tank in 1 hr
i.e., Pipe A and B together can fill the tank in 4 hours
Answer: Option B
Answer: B
Question: If
1 = 6
2 = 12
3 = 18
4 = 24
5 = 30
Then 6 = ?
Hint: Its a logic Riddle not a mathematical riddle
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: A
1
As stated
1=6 => 6=1
Answer: A
Question: Which of the following is a prime number ??
Options:
A)33
B)81
C)32
D)93
E)11
Rationale: E
11
Clearly, 11 is a prime number.
Answer is E
Answer: E
Question: A city council will select 2 of 8 available firefighters and 1 of 6 available police officers to serve on an advisory panel. How many different groups of 3 could serve on the panel?
Options:
A)36
B)72
C)168
D)216
E)432
Rationale: OA C
8C2 * 6C1
using the combination formula to choose 2 from 8 and 1 from 6
Answer: C
Question: The angle between the minute hand and the hour hand of a clock when the time is 8:30
Options:
A)33
B)75
C)29
D)27
E)299
Rationale: Explanation:
Angle traced by hour hand in \inline \frac{17}{2} hrs = \inline \left ( \frac{360}{12}\times \frac{17}{2} \right )^{o} = 255
Angle traced by min hand in 30 min = \inline \left ( \frac{360}{60}\times 30 \right )^{o} = 180
\inline \therefore Required angle = (255 - 180) = \inline 75^{o}
Answer: B) 75
Answer: B
Question: If x^2 − 2x − 15 = (x + r)( x + s) for all values of x, and if r and s are constants, then which of the following is a possible value of r − s?
Options:
A)8
B)2
C)− 2
D)− 3
E)− 5
Rationale: Given: x^2 − 2x − 15 = (x + r)( x + s)
Factor to get: (x - 5)(x + 3) = (x + r)( x + s)
Rewrite as: (x + -5)(x + 3) = (x + r)( x + s)
So, it's possible that r = -5 and s = 3
Here, r - s = (-5) - 3
= -8
Try REVERSING the factorization:
x^2 − 2x − 15 = (x + r)( x + s)
Factor to get: (x + 3)(x - 5) = (x + r)( x + s)
Rewrite as: (x + 3)(x + -5) = (x + r)( x + s)
So, it's possible that r = 3 and s = -5
Here, r - s = 3 - (-5)
= 8
Answer: A
Answer: A
Question: the sum of the ages of 5 children born at the intervals of 3 year each is 50 year. what is the age of the youngest child ?
Options:
A)4 year
B)8 year
C)10 year
D)None of these
E)9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 ⇔ 5 x = 20 ⇔ x= 4.
∴ Age of the youngest child = x = 4 years. Answer A
Answer: A
Question: Working together, John and Jack can type 30 pages in one hour. If they would be able to type 35 pages in one hour if Jack increases his typing speed by 25%, what is the ratio of Jack's normal typing speed to that of John?
Options:
A)3/2
B)2/1
C)5/2
D)4/3
E)1/3
Rationale: Lets say John types x pages an hour and Jack types y pages an hour.
We know that x+y=30
Jack increase speed by 25% means he will type 1.25y pages an hour.
So we get x+1.25y=35
We need to know the ratio of Jack's speed to John's speed. This is going to be proportional to the number of pages each can type in an hour, hence (y/x).
Subtracting both : 0.25y=5 so y=20 ... so x=10
(y/x)=2/1
Answer is (B)
Answer: B
Question: A man divides his property so that his son’s share to his wife’s and the wife’s share to his daughter are both in the ratio 3 : 1. If the daughter gets 10,000 less than the son, find the total worth of the property.
Options:
A)16,200
B)16,250
C)16,500
D)15,300
E)None of these
Rationale: Let Son’s share = S;
Daughter’s share = D;
and Wife’s share = W.
Also, S : W = W : D = 3 : 1
∴ S : W : D = 9 : 3 : 1
then S = 9x , D = x
and 9x – x = 10,000 ⇒ x = 1250
∴ Total worth of the property = (9 + 3 + 1)x = 13x
= 13 × 1250 = 16,250
Answer B
Answer: B
Question: A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 17% profit. He gains 10 % on the whole. Find how much is sold at 7% profit?
Options:
A)70 lbs
B)40 lbs
C)30 lbs
D)50 lbs
E)60 lbs
Rationale: 100(x)(7/100)+(100(1-x)) (17/100)=100(10/100)
7x+17-17x=10
-10 x=-7
x=7/10
100lbs x (7/10) = 70 lbs
ANSWER:A
Answer: A
Question: A can do a work in 12days. When he had worked for 3days, B joinedhim. If they complete the work in 3more days, in how manydays can Balone finish the work?
Options:
A)3
B)4
C)6
D)7
E)8
Rationale: sax Work done by Afar 3 days : i
J
.. Remzming war — 1
.Work done by (A + B) for 1 day :
. Work done by a for 1 day
6 days
C
Answer: C
Question: The sum of first five prime numbers is?
Options:
A)11
B)18
C)26
D)28
E)None of these
Rationale: Required sum = (2+3+5+7+11)=28.
Correct Option : D
Answer: D
Question: Naomi drives to the beauty parlor in 60 minutes. On the way back, her average speed is half the average speed as it was to the way to the parlor. How much time will it take Naomi to travel two round trips to the beauty parlor?
Options:
A)3 hours.
B)4 hours.
C)4 hours and 20 minutes.
D)5 hours and 50 minutes
E)6 hours.
Rationale: s1=2s2
since, speed is inversely proportional to time
we have,
s1/s2=2/1=t2/t1
therefore , the time taken for one trip = 60+120 = 180 minutes
total = 180*2 =360 minutes = 6 hours
ANSWER:E
Answer: E
Question: If the price of 20 toys is 540, then what will the price of 15 toys ?
Options:
A)144
B)405
C)117
D)287
E)112
Rationale: One toy price = 540/20 = 27
15 toy price = 15 * 27 = 405
Answer : B
Answer: B
Question: A clock loses two minutes every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days?
Options:
A)11:54:40 AM
B)11:56:24 AM
C)12:16:40 PM
D)11:22:24 AM
E)12:06:36 PM
Rationale: Clock loses: 2 minute in 3 hours = 16 minutes in 24 hours = 64 minutes in 4 days.
Clock gains: 1% in the subsequent 6 days = 1% in 6*24*60 minutes = 86.40 minute in 6 days;
Net gain in 10 days = 86.40 - 64 = 22.4 minutes.
11AM + 22.4 minutes = 11:22 and 4/10th of a minute or 24 seconds.
Answer: D.
Answer: D
Question: A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Options:
A)120
B)140
C)240
D)320
E)100
Rationale: Let x be the number of kilograms he sold in the morning.Then in the afternoon he sold 2x kilograms. So, the total is
x+2x=3x. This must be equal to 360.
3x=360
x=360/3
x=120
Therefore, the salesman sold 120 kg in the morning and 2*120=240 kg in the afternoon.
Answer is C.
Answer: C
Question: If the bus had traveled 60 kmh faster than it actually did, the trip of 120 km would have lasted 1 hour less. Find the speed of the bus.
Options:
A)55 kmh
B)30 kmh
C)80 kmh
D)60 kmh
E)75 kmh
Rationale: Time = Distance/Speed
Difference in time = 1 hr
120/x - 120/(x + 60) = 1
Substitute the value of x from the options. --> x = 60 --> 120/60 - 120/120 = 2 - 1 = 1
Answer: D
Answer: D
Question: The sum of two numbers is 95. Their difference is 5. The bigger number is
Options:
A)20
B)50
C)30
D)35
E)45
Rationale: X + Y = 95
X - Y = 5
Adding 2X = 100 ==> X = 50 and Y = 95 - 50 = 45
Bigger number is X = 50
Answer B.
Answer: B
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is
Options:
A)1/13
B)2/13
C)1/26
D)1/52
E)None
Rationale: Solution
Here, n(S) = 52
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E)	= n(E) / n(S)
= 2/52
‹=›1/26.
Answer C
Answer: C
Question: Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 34, what is the minimum possible range in scores of the three test-takers?
Options:
A)a 17
B)b) 34
C)c) 35
D)d) 45
E)e) 80
Rationale: It is finding the minimum range between all their scores, if all test taker scores are between 0 and maximum range we will have:
A- 0 and 17
B- 0 and 28
C- 0 and 35
therefore the minimum range is 34, it cant be any lower however you play with the numbers.
B
Answer: B
Question: You buy a piece of land with an area of âˆš400, how long is one side of the land plot?
Options:
A)28
B)29
C)30
D)20
E)32
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 400.
Answer D
Answer: D
Question: #p is defined as 2p-20 for any number p. What is p, if #(#(#p))=12?
Options:
A)–108
B)19
C)10
D)16
E)18
Rationale: #p = 2p-20 --->#(#p) = 2(2p-20)-20 = 4p-60 and thus #(4p-60) = 2(4p-60)-20 = 8p-140 = 12 ---> 8p= 152 ---> p = 19, B is the correct answer.
Answer: B
Question: If 2^z is a factor of 25!, which of the following could be the value of z?
I. 22
II. 23
III. 24
Options:
A)I ​ only
B)II only
C)I​ and II
D)I, II, and III
E)None
Rationale: 25! contains all numbers from 1 to 25. To find the factor with the highest power of 2, we count the number of multiples of 2,4,8 and 16
Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22
A is the answer.
Answer: A
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
Options:
A)1976 sq m
B)2176 sq m
C)4312 sq m
D)1269 sq m
E)2679 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:C
Answer: C
Question: If 4 men can colour 48 m long cloth in 2 days, then 2 men can colour 36 m long cloth in
Options:
A)1 day
B)2 days
C)3 days
D)4 days
E)5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 2 = 3 day.
C
Answer: C
Question: A sum of Rs.4700 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)Rs.2520
B)Rs.3055
C)Rs.3320
D)Rs.2760
E)None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4700[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4700 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7755
So the interest = 7755 - 4700 = Rs.3055
ANSWER:B
Answer: B
Question: A dress on sale in a shop is marked at $X. During the discount sale its price is reduced by 15%. Staff are allowed afurther 10% reduction on thedis counted price. If a staff member buys thedress what will she have to pay in terms of X?
Options:
A)0.560X
B)0.560X
C)0.765X
D)0.608X
E)0.895X
Rationale: If the price is reduced by 15 %, then the new price will be 0.85D
If this new price is further reduced by 10%, the discounted price will be 0.9 x 0.85X = 0.765X
C
Answer: C
Question: Cost of 2 bats and 3 balls is Rs.1300. The cost of 3 bats and 2 balls is Rs.1200. The cost of each balls is more than that of each bat by?
Options:
A)50
B)100
C)110
D)120
E)130
Rationale: 2Bats + 3Ball = 1300 --- (1)
3Bats + 3Ball = 1200 --- (2)
Subtracting 2nd from 1st, we get
-Bats + Ball = 100 => Ball - Bats = 100
B
Answer: B
Question: If 11 and 13 are prime numbers, which of the following CANNOT be the sum of a and b?
Options:
A)24
B)48
C)72
D)47
E)96
Rationale: ans =D
Answer: D
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
Options:
A)3 : 5 : 2
B)3 : 5 : 5
C)6 : 10 : 5
D)8 : 12 : 4
E)Data inadequate
Rationale: Explanation:
Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer is C
Answer: C
Question: A shop keeper had some books. He sells 40% books and still has 420 books. Originally, he had
Options:
A)588 books
B)600 books
C)620 books
D)700 books
E)None of these
Rationale: Explanation :
Suppose originally he had x books.
Then,(100-40)% of x = 420.
=>60/100x = 420
=>x = (420 100 / 60
=>x=700.
Answer : D
Answer: D
Question: There were totally 100 men.81 are married.75 have T.V, 85 have radio,70 have A.C. How many men have T.V, radio, A.C and also married?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: 100-(100-81)-(100-75)-(100-85)-(100-70)= 100-19-25-15-30=100-89=11
ANSWER:A
Answer: A
Question: When 200 is divided by positive integer x, the remainder is 5. What is the remainder when 395 is divided by x?
Options:
A)2
B)3
C)4
D)6
E)5
Rationale: if 200/x leaves a reminder 5 then (200-5) i.e. 195 is divisible by x
So (200+195)/x leaves a reminder rem(200/x)+rem(195/x)=> 5+0=5
Answer :E
Answer: E
Question: A = {2, 3, 5, 7, 11}
B = {2, 4, 6, 17}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
Options:
A)15
B)16
C)19
D)20
E)36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 20
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
D
Answer: D
Question: A 270m long train running at the speed of 120kmph crosses another train running in opposite direction at the speed of 80kmph in 9 second. What is the length of the other train?
Options:
A)150m
B)230m
C)290m
D)310m
E)420m
Rationale: Relative speed = 120+80 = 200*5/18 = 500/9 m/s
Let the length of the other train be x meters
x+270/9 = 500/9
x = 230m
Answer is B
Answer: B
Question: A sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest. What is the rate of interest?
Options:
A)2%
B)1%
C)7%
D)5%
E)8%
Rationale: C
7%
S.I. = (21200 - 15600) = 5600.
Rate = (100 x 5600)/(15600x5)% = 7%
Answer: C
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is
Options:
A)1/9
B)1/7
C)1/5
D)1/6
E)1/3
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: C
Question: (540 + ?) × 3/5 - 120 = 483
Options:
A)A)465
B)B)450
C)C)540
D)D)20
E)E)120
Rationale: Explanation:
=> (540 + ?) × 3/5 - 120 = 483
=> (540 + ?) × 3/5 = 483 + 120
=> (540 + ?) × 3/5 = 603
=> ? = 603 × 5/3 - 540 = 1005 - 540 = 465
Answer: Option A
Answer: A
Question: Lilly has 10 fish and Rosy has 14 fish. In total, how many fish do they have in all?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: 10+14=24
The answer is D.
Answer: D
Question: What quantity of water should be added to reduce 20 liters of 80% acidic liquid to 20% acidic liquid?
Options:
A)30liters
B)50liters
C)60liters
D)70liters
E)80liters
Rationale: Acid in 20 liters = 80% of 20 = 16 liters
Suppose x liters of water be added.
Then 16 liters of acid in 20+x liters of diluted solution
20% of 20+x = 16
20+x = 80
x = 60liters
Answer is C
Answer: C
Question: Ashis's height is 25% more than Babji, by how much percent Babji's height is less than Ashis.
Options:
A)30%
B)25%
C)75%
D)20%
E)None of these
Rationale: Explanation :
Solution: Babji is less than Ashis by (25/(100+25) * 100)% = 20%
Answer : D
Answer: D
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 210 m long?
Options:
A)34 Seconds
B)22 Seconds
C)21 Seconds
D)24 Seconds
E)29 Seconds
Rationale: Distance travelled = 140 + 210m = 350m
Speed = 60 * 5/8 = 50/3m
Time = 350 * 3/50 = 21 Seconds
ANSWER C
Answer: C
Question: Incomes of two companies A and B are in the ratio of 5 : 8. Had the income of company A been more by 35 lakh, the ratio of their incomes would have been 5 : 4. What is the income of company B?
Options:
A)80 lakh
B)56 lakh
C)40 lakh
D)60 lakh
E)None of these
Rationale: Let the incomes of two companies A and B be 5x and 8x respectively.
From the question,
5x+35/8x=5/4 ⇒ 20x + 140 = 40x
∴ x = 7
∴ Income of company B = 8x = 56 lakh
Answer B
Answer: 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?
Options:
A)Rs.250
B)Rs.300
C)Rs.320
D)Rs.340
E)Rs.400
Rationale: 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
A
Answer: A
Question: If N is the least positive integer that is divisible by every integer from 3 to 10 inclusive, then N/7 is =
Options:
A) 360
B) 720
C) 2520
D) 3960
E) 6720
Rationale: The integer should be divisible by: 3, 4, 5, 6, 7, 8, 9 and 10, that is 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5. The least common multiple of these integers is the product of 7, 5, 3^2 and 2^3. Then, N/7 is (7 * 5 * 3^2 * 2^3)/7 = 5*9*8 = 360.
Answer: A.
Answer: A
Question: If A got 70 marks and B got 60 marks, then what percent of A's mark is B's mark?
Options:
A)A)60%
B)B)85.7%
C)C)65%
D)D)75%
E)of these
Rationale: A's marks = 70 ; B's marks = 60.
Let x% of A = B => x/100 *70 = 60
=> x = (60 * 100)/80 = 85.7
B's marks is 85.7% of A's marks.
ANSWER:B
Answer: B
Question: A male leader is to be selected from a class of students having 15 boys and 20 girls. In how many ways can select?
Options:
A)50 ways
B)7/3 ways
C)3/7 ways
D)35 ways
E)15 ways
Rationale: The number of boy student in the class is 15. Therefore required number of selection =15. Answer : E
Answer: E
Question: How many seconds will a 500 meter long train moving with a speed of 63 km/hr, take to cross a man walking with a speed of 3 km/hr in the direction of the train ?
Options:
A)42
B)50
C)30
D)28
E)26
Rationale: Explanation:
Distance = 500m
Speed = 63 -3 km/hr = 60 km/hr = 600/36 m/s = 50/3 m/s
Time taken = distance/speed = 500/(50/3) = 30 s
Answer: Option C
Answer: C
Question: Kid have 8 black balls and 8 white balls. He is trying to arrange a ball in a row then in how many ways can he arrange these balls in a row so that balls of different colors alternate?
Options:
A)3×(4!)^2
B)1×(9!)^3
C)2×(8!)^2
D)2×(8!)
E)2×6^2
Rationale: 8 black balls can be arranged in 8! ways ...(A)
Now we need to arrange white balls such that white balls and black balls are positioned alternatively. i.e., we can arrange 8 white balls either in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I as shown below.
8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H in 8! ways.
8 white balls can be arranged in the 8 positions marked as B,C,D,E,F,G,H,I in 8! ways.
8 white balls can be arranged in the 8 positions marked as A,B,C,D,E,F,G,H or in the 8 positions marked as B,C,D,E,F,G,H,I in 8!+8!=2×8! ways ...(B)
From (A) and (B),
required number of ways =8!×2×8!=2×(8!)^2
C
Answer: C