divelab/Sys2Bench huggingface dataset:
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
Options:
A)16 : 5
B)14 : 5
C)16 : 7
D)19 : 5
E)None of these
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed = 4.75 : 1.25 = 19 : 5.
ANSWER:D
Answer: D
Question: A walks around a circular field at the rate of one round per hour while B runs around it at the rate of three rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other after ___ minutes?
Options:
A)11 min
B)12 min
C)10 min
D)15 min
E)30 min
Rationale: Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two.
Relative speed of A and B = 3 - 1 =2 rounds per hour.
Time taken to complete one round at this speed = 1/2 hr = 30 min.
E
Answer: E
Question: 0, 1, 5, 14, 30, ____
Options:
A)25
B)35
C)45
D)65
E)55
Rationale: 0,1,5, 14, 30,.....
0+1*1=1
1+2*2=5
5+3*3=14
14+4*4=30
So 30+5*5=55
ANSWER:E
Answer: E
Question: What is the least number of digits (including repetitions) needed to express 10^300 in decimal notation?
Options:
A)a) 4
B)b) 100
C)c) 301
D)d) 1000
E)e) 1001
Rationale: 10^n is a decimal number with a 1 followed by n zeros.
So 10^300 will include 300 0's + 1 digit for 1 = 301
So the answer is C.
Answer: C
Question: A train 120 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
Options:
A)67 kmph
B)50 kmph
C)55 kmph
D)60 kmph
E)70 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 120/((x+5)×5/18)=6 <=> 30 (x + 5) = 2160 <=> x = 67
Speed of the train is 67 kmph.
Answer: Option A
Answer: A
Question: A boat can move upstream at 25 kmph and downstream at 31 kmph, then the speed of the current is?
Options:
A)3
B)6
C)7
D)54
E)8
Rationale: US = 25
DS = 31
M = (31 - 25)/2 = 3.Answer:A
Answer: A
Question: 9 - 3 ÷ 1/3 + 1 = ?
Options:
A)1
B)3
C)6
D)9
E)12
Rationale: 9 - 3 1/3 + 1
=9-3÷1/3+1
=9-(3X3) +1
=9-9+1
=1
CORRECT ANSWER : A
Answer: A
Question: In the last set of tests, a student scored marks in each of 5 subjects in the ratio 4:5:6:7:8 and got an overall average score of 72%. If a mark of 50% in a subject is a pass and the maximum marks of each subject is the same, how many subjects did the student pass?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The tests scores are 4k, 5k, 6k, 7k, and 8k.
The sum of the test scores is 30k.
The average test score is 30k/5 = 66. Then k = 11.
The test scores are 44, 55, 66, 77, and 88.
The student passed 4 subjects.
The answer is D.
Answer: D
Question: A basket contains 7 apples, of which 1 is spoiled and the rest are good. If we select 2 apples from the basket simultaneously and at random, what is the probability that the 2 apples selected will include the spoiled apple?
Options:
A)1/5
B)2/7
C)2/9
D)3/5
E)4/11
Rationale: The total number of ways to choose 2 apples is 7C2 = 21
The number of ways that include the spoiled apple is 6C1 = 6
P(the spoiled apple is included) = 6/21 = 2/7
The answer is B.
Answer: B
Question: Find the number of elements in the power set of {1,2}
Options:
A)4
B)0
C)2
D)3
E)5
Rationale: Power set is the set of subsets of {1,2}
That is { {1,2}, {1}, {2}, f}
ANSWER:A
Answer: A
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 8 is
Options:
A)189
B)197
C)221
D)227
E)230
Rationale: In that case, the Sophie prime numbers greater than 8 are 11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be A.
Answer: A
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)28 cm2
B)27 cm2
C)29 cm2
D)25 cm2
E)35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2
= 35 cm2
Answer: E
Answer: E
Question: A newly-wed couple is using a website to design an eBook Wedding Album to distribute to their friends and families. The template they have chosen has places for 3 large photos and 19 smaller photos. The couple has 5 large photos they could use for those three slots, and 21 smaller photos they could use for those 19 slots. Given these choices, how many different possible albums could they create?
Options:
A)2,100
B)4,200
C)5,040
D)20,520
E)84,000
Rationale: MAGOOSHOFFICIAL SOLUTION:
For the large photos, we need 5C3, which we calculated in the article:
5C3 = 10
For the smaller photos, we need 21C19, which by symmetry must equal 21C2, and we have a formula for that. In fact, in the article above, we already calculated that 21C2 = 210.
Now, by the FCP, we just multiply these: total number of possible albums = 10*210 = 2100.
Answer = A
Answer: A
Question: Two cars start from the same places in opposite directions. One is going towards north at 60 kmph and the other is going towards south 40kmph. What time will they take to be 100km apart?
Options:
A)1hr
B)2hrs
C)3hrs
D)4hrs
E)5hrs
Rationale: To be (60+40) km apart, they take 1 hour
To be 100 km apart, they take 1/100 *100 = 1 hr
Answer is A
Answer: A
Question: Two teams are distributing information booklets. Team A distributes 60% more boxes of booklets than Team Z, but each box of Team A’s has 60% fewer booklets than each box of Team Z’s. Which of the following could be the total number of booklets distributed by the two groups?
Options:
A)2,000
B)3,200
C)4,100
D)4,800
E)4,900
Rationale: Let x be the no of booklets in each box that team distributes. So, Team A has 60% fewer - 0.4x.
Let y be the no. of boxes distributed by team Z. So, Team A distributes 60% more - 1.6y
Total booklets distributed by team A = xy
Total booklets distributed by team Z=0.64xy
Total booklets distributed = xy+0.64xy=1.64xy
As no. of booklets can only be integer, plugging the answer choice equal to 1.64xy should give an integer.
Choice A - 1.64xy=2000; xy=2000/1.64 = doesn't provide an integer value.
Similarly all answer choices, except choice C, fail to provide an integer value.
Choice C = 4100/1.64= 2500 and is the correct answer.
Answer: C
Question: Which of the following can be expressed as a terminating decimal?
Options:
A)1/25 + 1/35
B)1/225 + 1/1,250
C)1/11,000 + 1/13,000
D)1/75 + 1/35
E)1/125 + 1/8
Rationale: In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first.
A. 1/25 + 1/35 = 12/175 = 12/25*1/7
1/7 does is not a terminating decimal.
E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000
This is a terminating decimal and our answer.
Correct Option: E
Answer: E
Question: The average score in an examination of 10 students of a class is 60. If the scores of the top five students are not considered, the average score of the remaining students falls by 5. The pass mark was 40 and the maximum mark was 100. It is also known that none of the students failed. If each of the top five scorers had distinct integral scores, the maximum possible score of the topper is
Options:
A)87
B)95
C)99
D)100
E)103
Rationale: If the value of all other except the largest is 55..
Largest will be 60*10-55*9=600-495=105..
However the top 5 are distinct and the smallest of these can be 55, so remaining THREE will be 1,2,&3 more so total combined value will be 1+2+3 or 6 more..
Therefore the largest will be 6 less than max possible..... 105-6=99
ANSWER:C
Answer: C
Question: Oranges are bought at 7 for Rs.3. At what rate per hundred must they be sold to gain 33%?
Options:
A)57
B)58
C)59
D)54
E)55
Rationale: 7 oranges bought for rs 3
1 orange cost =3/7
therefore for 100 oranges =100*(3/7)
gain =33%
300/7+(33/100)*300/7=rate per hundred he want to sell
ans :57
ANSWER:A
Answer: A
Question: The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 10%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?
Options:
A)45
B)40
C)35
D)47.61
E)30
Rationale: Let the price of tea and coffee be x per kg in June.
Price of tea in July = 1.2x
Price of coffee in July = 0.9x .
In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50
1.2x(1/2) + 0.9x(1/2) = 50
=> x =47.61
D
Answer: D
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that all the four bulbs are defective?
Options:
A)1/126
B)1/122
C)1/129
D)1/136
E)1/126
Rationale: Out of nine, five are good and four are defective. Required probability
= ⁴C₄/⁹C₄
= 1/126
Answer:E
Answer: E
Question: The average of 12 result is 55. Average of the first 6 of them is 42 and that of the last 6 is 48. Find the 8th result?
Options:
A)35
B)564
C)526
D)48
E)50
Rationale: Sum of all the 12 results = 12 * 55 = 660
Sum of the first 6 of them = 6 * 42 = 252
Sum of the last 6 of them = 6 * 48 = 288
So, the 8th number = 600 + 252 - 288= 564.
B
Answer: B
Question: After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Explanation:
i) Let the ages of the five members at present be a, b, c, d & e years.
And the age of the new member be f years.
ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1)
iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years
So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2)
==> a + b + c + d + e = 5x + 15
==> a + b + c + d = 5x + 15 - e ------ (3)
iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above,
The new average is: (5x + 15 - e + f)/5
Equating this to the average age of x years, 3 yrs, ago as in (2) above,
(5x + 15 - e + f)/5 = x
==> (5x + 15 - e + f) = 5x
Solving e - f = 15 years.
Thus the difference of ages between replaced and new member = 15 years. Answer: D
Answer: D
Question: If x = a!, which of these following values of a is the least possible value (in this list) for which the last 8 digits of the integer x will all be zero?
Options:
A)21
B)29
C)37
D)41
E)80
Rationale: 2*5 will give one 0 at the end. We need 2^8*5^8 to get 8 zeroes at the end.
There are many 2's, so we need to find the first 8 appearances of 5.
These multiples of 5 are: 5, 10, 15, 20, 5*5, 30, 35...which gives us 8.
To have at least 8 zeroes at the end, a => 35.
The answer is C.
Answer: C
Question: Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?
Options:
A)$42
B)$46
C)$48
D)$49
E)$41
Rationale: C
$48
Sravan's one day's work = 1/25 - 1/75 = 2/75
Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75
Sravan completed 16/75th of total work.
So, his share is 16/75 * 225 = $48.
Answer: C
Question: If logx y =100 and log2 x =10, then the values of y is
Options:
A)2(10)
B)2 (100)
C)2 (1000)
D)2 (10000)
E)None of these
Rationale: Solution
log2 x	= 10
x= 210
logx y	= 100
y= x100
=(210)100
y‹=›2(1000)
Answer D
Answer: D
Question: P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
Options:
A)9 days
B)9 (3/5) days
C)11 1/5 days
D)13 days
E)13 1/7
Rationale: Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
B)
Answer: B
Question: In how many ways can a committee consisting of 4 men and 5 women be formed from a group of 7 men and 7 women?
Options:
A)7C4 7C5
B)4C7 5C7
C)7C5 9C4
D)9C4 7C5
E)NONE
Rationale: Group consisting of 7 men and 7 women
4 men can be selected from 7 men in 7C4 ways
5 women can be selected from 7 women in 7C5 ways
Therefore, Total number of ways= 7C4 7C5
ANSWER:A
Answer: A
Question: Each week, Harry is paid x dollars per hour for the first 24 hours and 1.5x dollars for each additional hour worked that week. Each week, James is paid x dollars per per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 41 hours If Harry and James were paid the same amount last week, how many hours did Harry work last week ?
Options:
A)35
B)36
C)37
D)38
E)39
Rationale: 42x=24x+1.5x(H-24)
==> 42=24+1.5(H-24)
==> H-24 = 18/1.5=12=> H = 36
Answer is B
Answer: B
Question: At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/8 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?
Options:
A)8 greater
B)17 fewer
C)28 fewer
D)36 fewer
E)44 fewer
Rationale: Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/8* 480 =60
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of remaining students)
thus 60-68 =-8>>> therfore answer is 8 greater
A
Answer: A
Question: To produce an annual income of Rs. 800 from a 8% stock at 90, What is the amount of stock needed?
Options:
A)10000
B)11000
C)12000
D)13000
E)14000
Rationale: Since face value is not given, take it as Rs.100.
As it is an 8% stock, income (dividend) per stock = Rs.8
ie, For an income of Rs.8,amount of stock needed = Rs.100
For an income of Rs.800, amount of stock needed = 100×800/8=10000
Answer is A.
Answer: A
Question: In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
Options:
A)66 kg
B)67 kg
C)68 kg
D)69 kg
E)None of these
Rationale: Explanation:
Let Arun’s weight by X kg.
According to Arun, 65 < X < 72
According to Arun’s brother, 60 < X < 70.
According to Arun’s mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required average = [66+67+68/3]=[201/3]=67kg
Answer B
Answer: B
Question: The difference in compound interest earned on a deposit (compounded annually) in year 1 and year 2 is $ 40. Had the interest rate been three times its present value, the difference would have been how much?
Options:
A)40/3
B)40
C)120
D)360
E)420
Rationale: CASE 1:
Deposit = $x;
Rate of increase = r.
Interest yearned in 1 year = xr. Deposit in 1 year = x + xr.
Interest yearned in 2 year = (x + xr)r.
The difference = (x + xr)r - xr = xr^2 = 40.
CASE 2:
Deposit = $x;
Rate of increase = 3r.
Interest yearned in 1 year = x(3r). Deposit in 1 year = x + 3xr.
Interest yearned in 2 year = (x + 3xr)3r.
The difference = (x + 3xr)3r - 3xr = 9xr^2. Since from CASE 1 we know that xr^2 = 40, then 9xr^2 = 9*40 = 360.
Answer: D
Answer: D
Question: Carrie likes to buy t-shirts at the local clothing store. They cost $9.95 each. One day, she bought 20 t-shirts. How much money did she spend?
Options:
A)$150
B)$248.75
C)$199
D)$171.6
E)$190
Rationale: $9.95*20=$199. Answer is C.
Answer: C
Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 2 hour to row to a place and come back, how far is the place?
Options:
A)2.4 km
B)4.8 km
C)3.4 km
D)4.4 km
E)5.6 km
Rationale: Explanation:
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph
Let the required distance be x km
Total time taken = 2 hour
â‡’ x/6+x/4=2
â‡’2x+3x=24
â‡’5x=24
â‡’x=4.8 km
Answer: Option B
Answer: B
Question: A van takes 5 hours to cover a distance of 600 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?
Options:
A)80
B)84
C)88
D)92
E)96
Rationale: (3/2)*5 = 7.5 hours
600 / 7.5 = 80 kph
The answer is 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 eldest child ?
Options:
A)16 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 â‡” 5 x = 20 â‡” x= 4.
âˆ´ Age of the eldest child = x+12 = 4 +12 =16 years. Answer A
Answer: A
Question: A batsman makes a score of 110 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
Options:
A)40
B)50
C)60
D)45
E)56
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+110 = 11x
x = 110-50 = 60
Answer is C
Answer: C
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Options:
A)47200
B)48000
C)42000
D)50400
E)65400
Rationale: Explanation:
The word 'CORPORATION' has 11 letters. It has the vowels 'O','O','A','I','O' in it and these 5 vowels should always come together. Hence these 5 vowels can be grouped and considered as a single letter. that is, CRPRTN(OOAIO).
Hence we can assume total letters as 7. But in these 7 letters, 'R' occurs 2 times and rest of the letters are different.
Number of ways to arrange these letters
=7!2!=7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—12Ã—1=2520=7!2!=7Ã—6Ã—5Ã—4Ã—3Ã—2Ã—12Ã—1=2520
In the 5 vowels (OOAIO), 'O' occurs 3 and rest of the vowels are different.
Number of ways to arrange these vowels among themselves =5!3!=5Ã—4Ã—3Ã—2Ã—13Ã—2Ã—1=20=5!3!=5Ã—4Ã—3Ã—2Ã—13Ã—2Ã—1=20
Hence, required number of ways
=2520Ã—20=50400=2520Ã—20=50400
ANSWER IS D
Answer: D
Question: In a factory, there are 80% technicians and 20% non-technicians. If the 80% of the technicians and 20% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
Options:
A)62%
B)68%
C)52%
D)22%
E)42%
Rationale: Total = 100
T= 80 NT= 20
80*(20/100)=24 80*(20/100)=24
16 + 16 = 32 => 100 - 32 = 68%
Answer:B
Answer: B
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,80,000 as total savings, how much has he saved in Public Provident Fund?
Options:
A)81000
B)85000
C)75000
D)72000
E)77000
Rationale: Let savings in National Savings Certificate = x
and savings in Public Provident Fund = (180000 - x)
1/3x=1/2(180000−x)
⇒2x=3(180000−x)
⇒2x=540000−3x
⇒5x=540000
⇒x=540000/5=108000
Savings in Public Provident Fund = (180000 - 108000) = 72000
Answer is D.
Answer: D
Question: The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then
Options:
A)None of these
B)x = y + z
C)2x = y + z
D)x = 2y + 2z
E)x = y + 2z
Rationale: Explanation:
Average of 6 numbers = x
=> Sum of 6 numbers = 6x
Average of the 3 numbers = y
=> Sum of these 3 numbers = 3y
Average of the remaining 3 numbers = z
=> Sum of the remaining 3 numbers = 3z
Now we know that 6x = 3y + 3z
=> 2x = y + z
Answer: Option C
Answer: C
Question: In how many ways 2 students can be chosen from the class of 20 students?
Options:
A)190
B)180
C)240
D)390
E)None
Rationale: Solution: Number of ways = 20C2 = 20!/(2! 18!)
= 20*19/2
= 190.
Answer: Option A
Answer: A
Question: 1939392 * 625
Options:
A)1212120010
B)1212120000
C)1212120011
D)1212121010
E)1212121000
Rationale: Explanation:
Trick: when multiplying with
5n
5n
then put n zeros to the right of multiplicand and divide the number with
2n
2n
So using this we can solve this question in much less
time.
1939392×5(4)=1939392000016=1212120000
Option B
Answer: B
Question: In how many different number of ways 4 man and 3 woman can sit on a bench such that girls always sit together.
Options:
A)700
B)720
C)730
D)750
E)770
Rationale: Option 'B'
Answer: B
Question: Two employees X and Y are paid a total of Rs. 440 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)s.150
B)s.200
C)s.250
D)s.350
E)s.400
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 440
But x = 120% of y = 120y/100 = 12y/10
âˆ´12y/10 + y = 440
â‡’ y[12/10 + 1] = 440
â‡’ 22y/10 = 440
â‡’ 22y = 4400
â‡’ y = 4400/22 = 400/2 = Rs.200
B)
Answer: B
Question: Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case
Options:
A)4
B)7
C)9
D)13
E)15
Rationale: Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4.
ANSWER IS A
Answer: A
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)6
B)5
C)7
D)8
E)2
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer:C
Answer: C
Question: A cube of side one meter length is cut into small cubes of side 20 cm each. How many such small cubes can be obtained?
Options:
A)2878
B)2778
C)1000
D)120
E)125
Rationale: Along one edge, the number of small cubes that can be cut
= 100/20 = 5
Along each edge 20 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 5 * 5 * 5 = 125
Answer: E
Answer: E
Question: A man sold 18 toys for Rs. 25200, gaining thereby the cost price of 3 toy find the cost price of a toy
Options:
A)s. 600
B)s. 800
C)s.500
D)s.900
E)s. 1200
Rationale: Let the cost of one toy = X.
Then, cost of 18 toys = 18X.
Gain = 3X.
SP of 18 toys = Rs. 25200.
Gain = SP â€“ CP
3X = 25200 â€“ 18X
21X = 25200
X = Rs. 1200.
ANSWER : OPTION E
Answer: E
Question: If in a certain sequence of consecutive multiples of 50, the median is 625, and the greatest term is 850, how many terms that are smaller than 625 are there in the sequence?
Options:
A)5
B)7
C)8
D)12
E)13
Rationale: Since the median is 625 we know there must be a even number of integers because 50 is not a multiple of 625.
So the list around 625 must go. 600 (625) 650 700 750 800 850
Since we know there are 5 numbers greater than 625 then there must be 5 numbers less then 625.
A
Answer: A
Question: 23,8,34,81,33,...
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: 23 : 2^3=8
34 : 3^4=81
33 : 3^3=27
ANSWER:D
Answer: D
Question: If 2ab - 3c = 2a(b - c), which of the following must be true?
Options:
A) a=3/2 and c=0
B) a=1/2 and b=2
C) b=1 and c=0
D) a=1 or b=0
E) a=1/2 or c=0
Rationale: 2ab-3c = 2a (b-c)
2ab - 3c = 2ab - 2ac
3c= 2ac
2ac-3c = 0
c(2a-3) = 0
Either c = 0; or a = 3/2
A is the answer
Answer: A
Question: Anita has 360 apples. There are 60 students are studying in her class. She would like to give each student the same amount of apples, how much should she give to each student?
Options:
A)12
B)6
C)9
D)15
E)7
Rationale: 360/60 = 6
The answer is B.
Answer: B