divelab/Sys2Bench huggingface dataset:
Question: A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)6 kmph
B)5 kmph
C)2 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 85/(2 1/2) = 34 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (34 - 18)/2 = 8 kmph
Answer:D
Answer: D
Question: In a games hour 4 different types of players came to the ground? cricket 22, hokey 15, football 21, softball 19. How many players are present in the ground?
Options:
A)70
B)52
C)62
D)77
E)79
Rationale: total number of players= 22+15+21+19= 77
Answer is D
Answer: D
Question: A man buy a book in Rs50 & sale it Rs90. What is the rate of profit ???
Options:
A)10%
B)80%
C)30%
D)25%
E)28%
Rationale: cp=50
sp=90
profit=90-50=40
%=40/50*100=80%
ANSWER:B
Answer: B
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?
Options:
A)179 km/hr
B)197 km/hr
C)120 km/hr
D)109 km/hr
E)187 km/hr
Rationale: Let speed of the car be x km/hr.
Then, speed of the train = 150/100 x = 3/2 x km/hr.
75/x - 75/(3/2 x) = 125/(10 * 60)
75/x - 50/x = 5/24 = 120 km/hr.
Answer: C
Answer: C
Question: A car has been driven with an average speed of 30 kilometers per hour during the first 30 kilometers of a journey. Upon reaching the 30th kilometer, the car then travels at 45 kilometers per hour for the next 30 kilometers. Find out the average speed of the car if it has not been stopped at all during the journey.
Options:
A)35
B)36
C)37.5
D)38
E)40
Rationale: Avg speed = Total distance/ total time taken
= 60 km/ 100 min
= .6 km/m
= .6 * 60 per hour
= 36 km
ANSWER:B
Answer: B
Question: If k > 0, x + k = y, and y + 5k = z, what is the ratio between z - x and y - x ?
Options:
A)2 to 1
B)3 to 1
C)4 to 1
D)5 to 1
E)6 to 1
Rationale: y-x = k
z-y = 5k
Let's add the two equations together:
z-x = 6k
The ratio of z-x to y-x is 6:1.
The answer is E.
Answer: E
Question: For how many integers n is 1^n+2 = (n+2)^1?
Options:
A)0
B)1
C)2
D)None of these
E)3
Rationale: If n=0
1^0+2 = (0+2)^1
1^2 = 1 ; 2^1 =2 not ok
If n=1
1^1+2 =1 ; (1+2)^1=3^1=3 not OK
So, Answer : D
Answer: D
Question: How many different sevevn letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
Options:
A)65
B)11!/(2!*2!*2!)
C)56
D)23
E)11!/(3!*2!*2!*2!)
Rationale: E- -R
We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.
We should consider two cases:
1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.
2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.
Total = 56 + 3 = 65.
Answer: A.
Answer: A
Question: The average age of A and B is 22 years. If C were to replace A, the average would be 44 and if C were to replace B, the average would be 33. What are the age of A, B and C?
Options:
A)11,33,55
B)20, 20, 18
C)22, 44, 33
D)44, 88, 66
E)None of the above
Rationale: Given A + B = 44â€¦(i)
C + B = 88 â€¦ (ii)
A + C = 66â€¦(iii)
(i) + (ii) + (iii) â‡’ A + B + C =99 â€¦(iv)
from (i) and (iv), we get
C = 55 years
âˆ´ B = 33 years and A = 11years
Answer A
Answer: A
Question: Of the 70 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: Neither Car nor Garage
= Total - Garage - (Swim - Common)
= 70 - 50 - (40-35) = 70-55 = 15
Answer B
Answer: B
Question: In how many different ways can the letters of the word ‘SMART’ be arranged?
Options:
A)120
B)354
C)126
D)214
E)124
Rationale: A
120
The word SMART has 5 distinct letters.
Number of arrangements = 5!
= 5 × 4 × 3 × 2 × 1 = 120
Answer: A
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.14200 after a year?
Options:
A)3630
B)9232
C)4260
D)2387
E)2813
Rationale: 6300:4200:10500
3:2:5
3/10 * 14200 = 4260
Answer: C
Answer: C
Question: Donna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much do they have in their wallets?
Options:
A)Donna $10 -Chris $45 -Austin $90
B)Donna $20-Chris $13 -Austin $60
C)Donna $30 -Chris $34-Austin $70
D)Donna $40 -Chris $56 -Austin $100
E)Donna $50 -Chris $23 -Austin $80
Rationale: Let the amount in Chris’s wallet be $x
Donna has $7 more than Chrish's wallet = $(x + 7)
Austin has 3 times than Donna's wallet = $3(x + 7)
According to the problem, Donna, chris, and Austin have a total of $93 in their wallets.
Therefore,
x + (x + 7) + 3(x + 7) = 93
x + x + 7 + 3x + 21 = 93
5x + 28 = 93
- 28 -28 (subtract 28 from both sides)
5x = 65
or, 5x/5 = 65/5 (Divide both sides by 5)
x = 13
Amount in Chris wallet = $x = $13
Amount in Donna's wallet = $(x + 7) = $(13 + 7) = $20
Amount in Austin 's wallet = $3(x + 7) = $3(13 + 7) = $3(20) = $ 60
Answer: Amount in Chris’s wallet: $13
Amount in Donna's wallet: $20
Amount in Austin's wallet: $60
correct answer B
Answer: B
Question: if m is a positive integer greater than 8, which of the following must be divisible by 4?
Options:
A) m(m-1)(m+2)(m+3)
B) m(m-1)(m+3)(m+4)
C) m(m-3)(m+2)(m+4)
D) m(m-3)(m+2)(m+3)
E) m(m+1)(m+3)(m+4)
Rationale: D.
For any integer m, D is the only answer choice which will always be divisible by 4.
A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice ism* [(m-1)OR(m+3)] * [(m-2)OR(m+2)] * [(m-3)OR(m+1)]. (answer D)
Answer: D
Question: An athlete runs 200 metres race in 24 seconds. What is his speed?
Options:
A)20 km/hr
B)30 km/hr
C)25 km/hr
D)35 km/hr
E)40 km/hr
Rationale: speed = dist/time = 200/24
200/24 * 18/5 = 40*3/4 = 30 km/hr
ANSWER B
Answer: B
Question: A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?
Options:
A)288
B)225
C)277
D)272
E)150
Rationale: Speed = 90 * 5/18 = 25 m/sec
Length of the train = speed * time = 25 * 9
= 225 m
Answer: B
Answer: B
Question: A bag contains 9 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
Options:
A)4/7
B)2/3
C)5/8
D)9/14
E)5/7
Rationale: Total number of balls = 9+5 = 14
number of white balls = 9
Probability = 9/14
Answer is D
Answer: D
Question: Find the cost of fencing around a circular field of diameter 36 m at the rate of Rs.3.50 a meter?
Options:
A)438
B)395
C)378
D)279
E)222
Rationale: 2 * 22/7 * 18 = 113
113 * 3 1/2
= Rs.395
Answer: B
Answer: B
Question: A trader sells 45 meters of cloth for Rs. 4500 at the profit of Rs. 12 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)Rs. 80
B)Rs. 85
C)Rs. 88
D)Rs. 100
E)None of these
Rationale: SP of 1m of cloth = 4500/45 = Rs. 100
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 100 - Rs. 12 = Rs. 88.
ANSWER:C
Answer: C
Question: If 4 women can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in?
Options:
A)1/5 day
B)1 day
C)2 days
D)3 days
E)4 days
Rationale: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.
B)
Answer: B
Question: If n is the product of three consecutive integers, and n is divisible by 3, which of the following is not necessarily a divisor of n ?
Options:
A)18
B)20
C)24
D)22
E)26
Rationale: IF ONE NO. IS 4 THEN OTHER CONSEQUTIVE NO. ARE 1*2*3=6 , 2*3*4=24 , 3*4*5 =60
24 IS NOT A DIVISOR OF N
C
Answer: C
Question: After Naomi received her order, she found that she could make a scarf from one skein of the yarn
that cost $5.99 a skein. After taking into account the discount, taxes, and shipping for the yarn, how
much would it cost to make five scarves?
Options:
A)$40.45
B)$60.45
C)$10.45
D)$20.45
E)$30.45
Rationale: $5.99 x 5 = $29.95
.10 x $29.95 = 2.995 rounds to $3.00
$29.95 - $3.00 = $26.95 discounted price
$26.95 x 1.13 = $30.45 with tax and shipping
correct answer E
Answer: E
Question: In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 25, what is the greatest possible value of B x A?
Options:
A)0
B)15
C)20
D)25
E)35
Rationale: I also was confused when I was looking forabove number:D
As far as I understood, 25 is a factor of AB. In other words, the values of B (units digits can be 5 or 0. Better to have option for 5 in this case to havebigger result). Now let's try 25x1 (A=2, B=5 respectively we have =10). But we don't have this number in answer choices, move on. (avoid even multiples of 2,4,6,8 etc (we will have 0 in units thus making our result 0)
25x3 = 75 (A=7 B=5 respectively. Hey! that's 35. This is the greatest possible value of B x A
IMO E.
Answer: E
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 38° is?
Options:
A)30m2
B)40m2
C)47.7m2
D)50m2
E)55m2
Rationale: 38/360 * 22/7 * 12 * 12
= 47.7 m2
Answer:C
Answer: C
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
Options:
A)neither profit nor loss
B)1%
C)2%
D)3%
E)4%
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
ANSWER:A
Answer: A
Question: How many numbers from 2 to 9 are exactly divisible by 2?
Options:
A)A)2
B)B)3
C)C)5
D)D)4
E)E)8
Rationale: 2/2 = 1 and 9/2 = 4
4 - 1 = 3
3 + 1 = 4 Numbers.
Answer : D
Answer: D
Question: 18.05 Ã— 0.001 = ?
Options:
A)0.1805
B)0.01805
C)1.805
D)0.001805
E)None of these
Rationale: 18.05 Ã— 0.001 = ?
or,? = 0.01805
Answer B
Answer: B
Question: If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 2 = ?
Options:
A)2
B)4
C)8
D)16
E)32
Rationale: 4 Ø 2 = 2^4/2^2 = 4
4 Ø 2 = 2^4/2^2 = 4
The answer is B.
Answer: B
Question: The average of 10 numbers is calculated as 21. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Options:
A)A)16
B)B)18
C)C)19
D)D)22
E)E)24
Rationale: Explanation:
10 * 21 + 36 – 26 = 220=>220/10 = 22
D)
Answer: D
Question: Danny obtained 76, 65, 82, 67 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
Options:
A)A)87
B)B)99
C)C)68
D)D)82
E)E)73
Rationale: Average = (76 + 65 + 82 + 67 + 75)/5
= 365/5
= 73.
Answer:E
Answer: E
Question: In an examination, 300 students appeared. Out of these students; 29 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
Options:
A)51
B)37
C)54
D)99
E)01
Rationale: The number of students with first division = 29 % of 300 = 29/100 × 300 = 8700/100 = 87
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (87 + 162) = 51
Answer:A
Answer: A
Question: 1,245
1,254
1,425
.....
....
+5,421
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1,2,4,5 exactly once in each integer. What is the sum of these 24 integers?
Options:
A)74,446
B)79,992
C)83,338
D)86,662
E)91,114
Rationale: In each of the units, tens, hundreds, and thousands place, each digit will appear 6 times.
Then the sum equals 6(1111)+6(2222)+6(4444)+6(5555) = 79,992
The answer is B.
Answer: B
Question: A man spends 15% of his income in house rent, 25% of the rest on his children’s education, 20% of the rest miscellaneous causes. If he now posses Rs. 2988 then his income is?
Options:
A)A)Rs.3625
B)B)Rs.4625
C)C)Rs.4585
D)D)Rs.5655
E)E)Rs.6225
Rationale: X * (85/100) * (75/100) * (80/100) = 2988
X * 0.85 * 0.75 * 0.8=2988
X = 2988/0.48
X = 6225
ANSWER:E
Answer: E
Question: How many times do the hands of a clock coincide in a day?
Options:
A)29
B)28
C)22
D)88
E)27
Rationale: Explanation:
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they
coincide only once, i.e., at 12 o'clock).
The hands overlap about every 65 minutes, not every 60 minutes.
The hands coincide 22 times in a day.
Answer: C) 22
Answer: C
Question: A bat is bought for Rs.410 and sold at a gain of 20% find its selling price
Options:
A)s.430/-
B)s.492/-
C)s.400/-
D)s.580/-
E)s.600/-
Rationale: 100 % ------> 410
120 % ------> 120*410/100
Selling price = Rs.492/-
B
Answer: B
Question: The speed of a car is 10 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)79 kmph
B)85 kmph
C)35 kmph
D)23 kmph
E)14 kmph
Rationale: S = (10 + 60)/2
= 35 kmph
Answer:C
Answer: C
Question: If 0.10 of a number is equal to 0.070 of another number, the ratio of the numbers is :
Options:
A)2 :3
B)3 :4
C)7:10
D)20 : 3
E)30:7
Rationale: 0.10A = 0.070B
-> A/B = 0.07/0.10 = 7/10
:. A : B = 7 : 10
ANSWER:C
Answer: C
Question: Mr. Smith calculated the average of 10three digit numbers. But due to a mistake he reversed the digits of a number and thus his average increased by 49.5. The difference between the unit digit and hundreds digit of that number is :
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Since the average increased by 49.5 and there were a total of 10 numbers, it means the incorrect number was 49.5 greater than the correct number.
Say, the correct number was abc (where a, b and c are the digits of the 3 digit number)
Then the incorrect number was cba.
100c + 10b + a - (100a + 10b + c) = 495
99c - 99a = 99(c - a) = 495
495 = 99*5 = 99(c - a)
So c - a = 5
Answer (C)
Answer: C
Question: A man is 28 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
Options:
A)20 years
B)21 years
C)22 years
D)24 years
E)26 years
Rationale: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 28) years
=> (x + 28) + 2 = 2(x + 2)
=> x + 30 = 2x + 4
So, x = 26
Answer: Option E
Answer: E
Question: An uneducated retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?
Options:
A)12.50%
B)12%
C)13.50%
D)13%
E)11%
Rationale: Let C.P =Rs 100.
then ,marked price =Rs100
S.P=75% of Rs 150=Rs112.50
Hence,gain%=12.50%
Option A
Answer: A
Question: Look at this series: 97, 97, 97, 87, 87, 87, 67, 67, 67 ... What number should come next?
Options:
A)47
B)57
C)45
D)48
E)55
Rationale: Explanation:
In this series, each number 20 is subtracted from previous number to arrive at the next number.
Answer: Option B
Answer: B
Question: Group A has 3 boys and 4 girls, group B has 2 boys and 2 girls and group C has 4 boys and 4 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
Options:
A)13/4
B)19/28
C)9/15
D)29/35
E)77/27
Rationale: Group A has 3 boys and 4 girls; 7
Group B has 2 boys and 2 girls; 4
Group C has 4 boys and 4 girls. 8
Selected group should have one girl and two boys.
Girl from A, boy from B, boy from C: 4/7*2/4*4/8 = 1/7;
Boy from A, girl from B, boy from C: 3/7*2/4*4/8 = 3/28;
Boy from A, boy from B, girl from C: 3/7*2/4*4/8 = 3/7.
Sum = 1/7 + 3/28 + 3/7 = 19/28.
Answer: B.
Answer: B
Question: A restaurant meal cost $40 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between
Options:
A) $43 and $47
B) $39 and $4 1
C) $38 and $40
D) $37 and $39
E) $36 and $37
Rationale: Hence it will be between 40 * (1+10/100) and 40 * (1+15/100).
i.e b/w 44 and 46. Hence the answer A (b/w 43 and 47).
Answer: A
Question: The arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5, respectively. What value is exactly 2 standard deviations less than the mean?
Options:
A)10.5
B)11
C)11.5
D)12
E)12.5
Rationale: The value which isexactlytwo SD less than the mean is:mean-2*SD=14.0-2*1.5=11.
Answer: B.
Answer: B
Question: Worker A takes 4 hours to do a job. Worker B takes 10 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
Options:
A)20/9
B)40/9
C)40/14
D)60/9
E)80/9
Rationale: one day work of A = 1/4
one day work of B = 1/10
so one day work of A and B together = 1/4 + 1/10 = 14/40
so total days required = 40/14
ANSWER:C
Answer: C
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)12 sec
B)30 sec
C)27 sec
D)87 sec
E)15 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer:B
Answer: B
Question: We can rent a car for x dollars per day for the first 3 days and then y dollars for each additional day. How much will it cost to rent a car for z days, where z>3?
Options:
A)x + zy
B)3y+(z-3)x
C)3x + 3zy
D)3x+(z-3)y
E)3x + zy
Rationale: The first 3 days cost 3x.
The next (z-3) days cost (z-3)y.
The total cost is 3x+(z-3)y.
The answer is D.
Answer: D
Question: The average of 11 numbers is 12.9. If the average of first six is 12.5 and that of the last six is 11.4 the sixth number is?
Options:
A)10.5
B)11.5
C)12.5
D)13.5
E)14.5
Rationale: 1 to 11 = 11 * 12.9 = 141.9
1 to 6 = 6 * 15.5 = 93
6 to 11 = 6 * 11.4 = 68.4
93 + 68.4 = 161.4 – 149.9 = 11.5
6th number = 11.5
ANSWER:B
Answer: B
Question: A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
Options:
A)4 km/hr
B)6 km/hr
C)7 km/hr
D)8 km/hr
E)2 km/hr
Rationale: Rate downstream =16/2 kmph = 8 kmph.
Rate upstream =16/4	kmph = 4 kmph.
Speed in still water =	1/2	(8 + 4) kmph = 6 kmph.
ANSWER:B
Answer: B
Question: A sum of Rs. 4500 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest?
Options:
A)37%
B)25%
C)35%
D)6%
E)20%
Rationale: S.I. = (9000 - 4500) = Rs. 4500\
Rate = (100 * 4500) / (4500* 4)
= 25%
Answer: B
Answer: B
Question: The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 462 the Other is
Options:
A)330
B)300
C)270
D)150
E)350
Rationale: The other number
= L.C.M * H.C.F/given number
= 2310*30/462 = 150
Answer is D.
Answer: D
Question: Crew A can build a complete car in 20 minutes and Crew B can build a complete car in 25 minutes. If both crews work independently and start at the same time, what is the shortest amount of time Q it could take for 10 cars to be complete?
Options:
A)111 1/9 minutes
B)115 2/5 minutes
C)116 minutes
D)120 minutes
E)125 minutes
Rationale: A builds 4 cars in 80 min
B builds 4 cars in 100 min
So A builds another car in another 20 min (i.e total 5 cars)
B builds another car in another 25 minutes (i.e, total 5 cars)
However, A can build another car in next 20 min (i.e total 6 cars)
So total time Q= 125 min by B, which is > 120 min by A
B - 4 cars, A - 6 cars
Answer = D
Answer: D
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 11 cm.
Options:
A)335 cm2
B)209 cm2
C)285 cm2
D)825 cm2
E)725 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (11)
= 209 cm2
Answer: B
Answer: B
Question: Three fair coins are labeled with a zero (0) on one side and a one (1) on the other side. Jimmy flips all three coins at once and computes the sum of the numbers displayed. He does this over 1000 times, writing down the sums in a long list. What is the expected standard deviation of the sums on this list?
Options:
A)1/2
B)3/4
C)√3/2
D)√5 /2
E)5/4
Rationale: variance of binomial distribution is n*p*(1-p), n = 3, p = 1/2
variance = 3*1/2*(1-1/2)= 3/4
stddev = sqrt(variance) = sqrt(3)/2
After many trials sample standard deviation is close to theoretical standard deviation = sqrt(3)/2.
C is the answer.
Answer: C
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A do the work if he is assisted by B and C on every third day?
Options:
A)22 days
B)15 days
C)77 days
D)99 days
E)11 days
Rationale: A's 2 day's work = (1/20 * 2) = 1/10
(A + B + C)'s 1 day work = (1/20 + 1/30 + 1/60) = 1/10
Work done in 3 days = (1/10 + 1/10) = 1/5
Now, 1/5 work is done in 3 days.
Whole work will be done in (3 * 5) = 15 days.
Answer: B
Answer: B
Question: How many positive 5-digit integers have the odd sum W of their digits?
Options:
A)9*10^2
B)9*10^3
C)10^4
D)45*10^3
E)9*10^4
Rationale: We are looking at numbers between 10000 and 99999 both inclusive.
There are 90000 numbers.
Now for
10000 : sum of digits is odd;
10001 :sum of digits is even;
10002 : sum of digits is odd ; so on and so forth. So every alternate number is such that the sum of digit is odd.
(Exception for the above statement :
When it is 10009 the sum is even and for 10010 again the sum is even; But if you look at 10019 :sum is odd; 10020 : sum is odd
and this pattern continues so basically the number of odd sum of digits and even sum of digits are equal)
This means exactly half of the numbers will have odd sum W of their digits. i.e 45000
Answer :D
Answer: D
Question: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 13 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
Options:
A) 2,060
B) 1,320
C) 545
D) 315
E) 286
Rationale: 13*12*11/3*2*1 = 286
E
Answer: E
Question: A committee of 6 is chosen from 8 men and 5 women so as to contain at least 2 men and 3 women. How many different committees could be formed if two of the men refuse to serve together?
Options:
A)635
B)700
C)1404
D)2620
E)3510
Rationale: 8 Men - 5 Women
Choose 6 ( two cases)
Case 1:2 men, 4 women
No of ways to choose 2 men out of 8 is 8C2 . This includes that one case in which the two men who refuse to serve together are included. So men can be chosen in 8C2 - 1 ways.
No. of ways to choose 4 women out of 5 is 5C4.
Number of ways of choosing 2 men and 4 women = (8C2 - 1)*(5C4) = 27*5 = 135
Case 2: 3 men, 3 women
No of ways to choose 3 men out of 8 is 8C3. No of ways to choose those two men together is 6C1 (You choose them and choose one more to make 3). So men can be chosen in 8C3 - 6C1 ways.
No of ways to choose 3 women out of 5 is 5C3.
Number of ways of choosing 3 men and 3 women = (8C3 - 6C1)*(5C3) = 500
Total number of ways = 135 + 500 = 635
ANSWER:A
Answer: A
Question: John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $70. What is the percent decrease?
Options:
A)20%
B)30%
C)40%
D)50%
E)60%
Rationale: The is always the difference between our starting and ending points. In this case, itâ€™s 100 â€“ 70 = 30. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (30/100)*100 = (0.3)*100 = 30%.
B
Answer: B
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
Options:
A)34
B)39
C)42
D)45
E)49
Rationale: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Answer: C