RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A Cone, a Heme sphere and a Cylinder have equal bases and heights. What is the ratio of their volumes.
A.1:2:3
B.1:2:4
C.3:2:3
D.4:2:3
Answer: A.1:2:3
Explanation: Volume of cone=(1/3)*pi*r^2*h
Volume of hemisphere=(2/3)*pi*r^3
Volume of cylinder=pi*r^2*h
Since base and height of all three figures are same and for hemisphere h=r
So ther volumes are in the ratio (1/3:(2/3):1=1:2:3
ANSWER:A
Question: The city of Boston decided to reconstruct its major tunnels. It estimated the job would require 612 mini projects spread evenly over an 18 month plan of completion. Only 108 mini projects had been successfully completed after 7 months. At this time, the construction was behind schedule by how many projects?
A.34
B.96
C.130
D.204
Answer: C.130
Explanation: Project/month : 612/18 = 34
Project in 6 month to be completed = 34*7 =238
Lag :238-108 = 130
C is the answer
Question: In how many ways can 6 black and 2 white chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
A.12
B.1440
C.720
D.360
Answer: B.1440
Explanation: 6 black chess pieces can be arranged in 6! ways and 2 white pieces can be arranged in 2! ways.
W_W_W_W
Number of ways = 6!*2! = 720 * 2 = 1440
Answer B
Question: Company workers decided to raise Rs. 3 lakhs by equal contribution from each. Had they contributed Rs. 50 each extra, the contribution would have been Rs. 3.25 lakhs. How many workers were they?
A.300
B.400
C.500
D.600
Answer: C.500
Explanation: Explanation:
N * 50	= (325000 - 300000) = 25000
N = 25000 / 50
= 500
Option C
Question: On dividing a number by 357, we get 37 as remainder.On dividing the same number by 17, what will be the remainder ?
A.4
B.3
C.8
D.7
Answer: B.3
Explanation: Let x be the number and y be the quotient.Then,
x=357*y+37
=(17*21*y)+(17*2)+3
=17*(21y+2)+3.
Required number =3.
Answer is B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 36 km/hr. What is the length of the platform?
A.160
B.240
C.288
D.277
Answer: A.160
Explanation: Speed = 36 * 5/18 = 10 m/sec.
Length of the train = 10 * 20 = 200 m.
Let the length of the platform be x m . Then,
(x + 200)/36 = 10=> x = 160 m.
Answer: A
Question: B can be divided by 11 with no remainder. Which of the following expressions could be divided by 11 leaving a remainder of 1?
A.B-20.
B.B-12.
C.B-9.
D.B-10.
Answer: D.B-10.
Explanation: We could use the following logic:
since Bis a multiple of 11, we could very well say B= 11K (where K is 1,2...n).
The condition here should now be
11K + 1 = <operation> such that it gives us an integer
11k +1 = B-20 => B= 11K + 21 Not divisible by 11
11K +1 = B-12 => B= 11K + 31 Not Divisible by 11
11K +1 = B -9 => B= 11K + 10 Not Divisible by 11
11K +1 = B-10 => B= 11K + 11Divisible by 11
11K +1 = B-13 => B= 11K + 14 Not Divisible by 11
Answer therefore is B-10 (D)
Question: How many three letter words are formed using the letters of the word MARCH?
A.A)150
B.B)140
C.C)130
D.D)120
Answer: D.D)120
Explanation: The number of letters in the given word is five.
The number of three letter words that can be formed using these four letters is 5P4
= 5 * 4 *3* 2 = 120.
Answer:D
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
A.18
B.28
C.21
D.17
Answer: D.17
Explanation: D
17 hrs
The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Question: The Royal Hawaiian Hotel decorates its Rainbow Christmas Tree with non-flashing white lights and a series of colored flashing lights - red, blue, green, orange, and yellow. The red lights turn red every 20 seconds, the blue lights turn blue every 30 seconds, the green lights turn green every 45 seconds, the orange lights turn orange every 60 seconds, and yellow lights turn yellow every 1 minute and 20 seconds. The manager plugs the tree in for the first time on December 1st precisely at midnight and all lights begin their cycle at exactly the same time. If the five colored lights flash simultaneously at midnight, what is the next time W all five colored lights will all flash together at the exact same time?
A.0:03 AM
B.0:04 AM
C.0:06 AM
D.0:12 AM
Answer: D.0:12 AM
Explanation: Time taken by each light to on
Red = 20 secs
Blue = 30 secs
Green = 45 secs
Orange = 60 secs
Yellow = 80 secs
We need to take LCM to find the time all five colored lights will flash together.
LCM = 720 secs
=12 mins
=0.12 AM
Ans = D
Question: Rs.100 doubled in 5 years when compounded annually. How many more years will it take to get another Rs.200 compound interest?
A.10 years
B.5 years
C.7.5 years
D.15 years
Answer: B.5 years
Explanation: Explanatory Answer
Rs.100 invested in compound interest becomes Rs.200 in 5 years.
The amount will double again in another 5 years.
i.e., the amount will become Rs.400 in another 5 years.
So, to earn another Rs.200 interest, it will take another 5 years.
Answer B
Question: In a certain province in France there are 9 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
A.36
B.105
C.330
D.14
Answer: A.36
Explanation: 1 city needs 8 roads to connect directly to the rest => 9 city needs 9*8 roads.
One road is counted twice => the number of road needed is 9*8/2 = 36
Answer A
Question: If X gets 25% more than Y and Y gets 20% more than Z, the share of Z out of Rs.925 will be:
A.Rs. 300
B.Rs. 200
C.Rs. 250
D.Rs. 350
Answer: C.Rs. 250
Explanation: Z share = Z,
Y = 1.2Z
X = 1.25Ã—1.2Z,
X+Y+Z =925
(1.25Ã— 1.2+1.2+1)Z=925
3.7Z=925, Z=250
Answer: . C
Question: In a survey of 330 employees, 104 of them are uninsured, 54 work part time, and 12.5 percent of employees who are uninsured work part time. If a person is to be randomly selected from those surveyed, what is the probability that the person will neither work part time nor be uninsured?
A.37/66
B.8/41
C.9/348
D.1/8
Answer: A.37/66
Explanation: ---------UI----------------NUI-------Total
PT----(12.5/100)*104 = 13----------- --54
NPT---104-13-------------- x--------276
Total--104----------------------------330
we have to find not part time and not uninsured . in other words not part time and insured = x/330 = (276-104+13)/330
= 37/66
Answer is A.
Question: On 8th Dec, 2007 is Saturday falls. What day of the week was it on 8th Dec. 2006 ?
A.Sunday
B.Thursday
C.Tuesday
D.Friday
Answer: D.Friday
Explanation: Solution
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
∴ 8th Dec, 2006 is Friday Answer D
Question: Daniel went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
A.19.7
B.20
C.21.3
D.21.5
Answer: A.19.7
Explanation: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
A
Question: Two trains of equal are running on parallel lines in the same direction at 47 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
A.50
B.88
C.66
D.55
Answer: D.55
Explanation: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 47 - 36 = 11 km/hr.
= 11 * 5/18 = 55/18 m/sec.
2x/36 = 55/18 => x = 55.
Answer:D
Question: J can dig a well in 16 days. P can dig a well in 24 days. J, P, H dig in 8 days. H alone can dig the well in How many days?
A.229
B.29
C.27
D.48
Answer: D.48
Explanation: Assume the total work = 48 units.
Capacity fo J = 48 / 16 = 3 units / day
Capacity of P = 48 / 24 = 2 units / day
Capacity of J, P, H = 48 / 8 = 6 units / day
From the above capacity of H = 6 - 2 - 3 = 1
So H takes 48 / 1 days = 48 days to dig the well
Answer:D
Question: 6 workers should finish a job in 8 days. After 3 days came 4 workers join them. How many days D do they need to finish the same job?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: Let Rate of one worker be R
=> (6*R)*8 = 1 (Rate * Time = work)
=> R = 1/48
=> Work remaining after 3 days
1 - (3*6)/48 = 30/48
After 4 ppl joined in
((6+4)*Time)/48 = 30/48
Time D = 3 days to finish the task
IMO A
Question: To fill a tank, 100 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four-fifth of its present ?
A.100
B.125
C.150
D.175
Answer: B.125
Explanation: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 100x.
New capacity of bucket = 4/5 x
Therefore, Required number of buckets = (100x)/(4x/5)
= (100x) x 5/4x
= 500/4
= 125
Answer is B.
Question: If population of certain city increases at the rate of 5%. If population in 1981 was 185220, then population in 1978 was?
A.160000
B.228788
C.266891
D.267689
Answer: A.160000
Explanation: X * (105/100) * (105/100) * (105/100) = 185220
X = 185220/1.157625
X = 160000
Answer:A
Question: A and B can do a work in 2 days, B and C in 4 days and C and A in 6 days. In how many days will the work be completed, if all three of them work together?
A.10/12
B.16/28
C.24/11
D.42/16
Answer: C.24/11
Explanation: One day work of A and B = 1/2
One day work of B and C = 1/4
One day work of C and A = 1/6
2(A + B + C) = 1/2 + 1/4 + 1/6.
2(A + B + C) = 11/12
(A + B + C) = 11/24
Number of days required = 24/11 days.
Answer: C
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.227m
B.180m
C.176m
D.126m
Answer: B.180m
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 20%?
A.17 per kg
B.18 per kg
C.16.5 per kg
D.16 per kg
Answer: B.18 per kg
Explanation: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 120% of 3000 = (120⁄100 × 3000) = 3600
∴ Rate of S.P. of the mixture = (3600⁄200) per kg
= 18 per kg.
Answer B
Question: On Thursday Mabel handled 90 transactions. Anthony handled 10% more transactions than Mabel, Cal handled 2/3rds of the transactions that Anthony handled, and Jade handled 16 more transactions than Cal. How much transactions did Jade handled?
A.80
B.81
C.82
D.83
Answer: C.82
Explanation: Solution:
Mabel handled 90 transactions
Anthony handled 10% more transactions than Mabel
Anthony = 90 + 90 × 10%
= 90 + 90 × 0.10
= 90 + 9
= 99
Cal handled 2/3rds of the transactions than Anthony handled
Cal = 2/3 × 99
= 66
Jade handled 16 more transactions than Cal.
Jade = 66 + 16
= 82
Jade handled = 82 transactions.
Answer: C
Question: 10 men and 15 women together can complete a work in 3 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
A.1 2/7 days
B.64 2/7 days
C.1 7/7 days
D.1 8/7 days
Answer: B.64 2/7 days
Explanation: 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/3
15 women's 1 day work = (1/3- 10/100) = 7/30
1 woman's 1 day work = 7/450
1 woman alone can complete the work in 64 2/7 days.
Answer:B
Question: If 40% of a number exceeds 20% of it by 12, then find the number?
A.60
B.50
C.47
D.55
Answer: A.60
Explanation: Use the elimination method to find the correct option.
Of all the options only 60 fits
40% of 60 = 24
20% of 60 = 12
24 - 12 = 12
Required number is 60.
ANSWER:A
Question: If a job is complete in X days by A, what will be A's one day work?
A.1/x
B.x
C.10
D.5
Answer: A.1/x
Explanation: A can complete a work in x days.
so one day work of a is 1/x.
Answer is option A
Question: Weights of two friends Ram and Shyam are in the ratio 7:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased?
A.19%
B.10%
C.22%
D.16%
Answer: C.22%
Explanation: Solution:
given ratio of Ram and Shayam's weight = 7:5
Hence, (x-15)/(15-10) = 7/5
Or, x = 22%.
Answer: Option C
Question: The average age of Lion,Tiger & Elephant were 4 years ago was 30 years and the age of lion and elephant were 6 years ago was 20 years. The present age of the Tiger is?
A.52 years
B.45 years
C.30 Years
D.50 Years
Answer: D.50 Years
Explanation: Sum of the present ages of Lion,Tiger & elephant = (30*3+4*3) = 102 years.
Sum of the present ages of X,Y = (20*2+6*2) = 52 years
Present age tiger = (102 - 52) = 50 years.
Answer : D
Question: In how many R ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
A.6
B.12
C.18
D.24
Answer: C.18
Explanation: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning R= 24 - 6 = 18
Answer: C
Question: The average of 25 results is 19. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?
A.74
B.75
C.103
D.78
Answer: C.103
Explanation: Solution: Sum of 1st 12 results = 12*14
Sum of last 12 results = 12*17
13th result = x (let)
Now,
12*14+12*17+x = 25*19
Or, x = 103.
Answer: Option C
Question: A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, one-third were right handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left handed players who were not at practice?
A.1/3
B.2/3
C.7/5
D.5/7
Answer: C.7/5
Explanation: Say the total number of players is 18, 9 right-handed and 9 left-handed.
On a certain day, two-thirds of the players were absent from practice --> 12 absent and 6 present.
Of the players at practice that day, one-third were right-handed --> 6*1/3=2 were right-handed and 4 left-handed.
The number of right-handed players who were not at practice that day is 9-2=7.
The number of left-handed players who were not at practice that days is 9-4=5.
The ratio = 7/5.
Answer: C.
Question: When n is divided by 27, the remainder is 4. What is the remainder when n + 16 is divided by 7?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: Assume n = 23
Remainder (n/27) = 4
n+16 = 39
Remainder (39/7) = 4
Option C
Question: A car takes 6 hours to cover a distance of 720 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.60
B.50
C.80
D.70
Answer: C.80
Explanation: Time = 6
Distance = 720
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 720/9 = 80 Kmph
Answer C.
Question: Anthony and Michael sit on the six member board od directors for compnay X. If the board is to be split up into 2 three-person subcommittees, what percent of all the possible subcommittees that include Michael also include Anthony?
A.20%
B.30%
C.40%
D.50%
Answer: C.40%
Explanation: First approach:
Let's take the group with Michael: there is a place for two other members and one of them should be taken by Anthony, as there are total of 5 people left, hence there is probability of 2/5=40%.
Second approach:
Again in Michael's group 2 places are left, # of selections of 2 out of 5 5C2=10 - total # of outcomes.
Select Anthony - 1C1=1, select any third member out of 4 - 4C1=4, total # =1C1*4C1=4 - total # of winning outcomes.
P=# of winning outcomes/# of outcomes=4/10=40%
Third approach:
Michael's group:
Select Anthony as a second member out of 5 - 1/5 and any other as a third one out of 4 left 4/4, total=1/5*4/4=1/5;
Select any member but Anthony as second member out of 5 - 4/5 and Anthony as a third out of 4 left 1/4, total=4/5*1/4=1/5;
Sum=1/5+1/5=2/5=40%
Fourth approach:
Total # of splitting group of 6 into two groups of 3: 6C3*3C3/2!=10
# of groups with Michael and Anthony: 1C1*1C1*4C1=4
P=4/10=40%
Answer: C.
Question: A man decides to buy a nice horse. He pays $60 for it, and he is very content with the strong animal. After a year, the value of the horse has increased to $70 and he decides to sell the horse. But already a few days later he regrets his decision to sell the beautiful horse, and he buys it again. Unfortunately he has to pay $80 to get it back, so he loses $10. After another year of owning the horse, he finally decides to sell the horse for $90. What is the overall profit the man makes?
A.20 profit
B.10 profit
C.25 profit
D.30 profit
Answer: A.20 profit
Explanation: 70-60=10 profit
90-80=10 profit
---------------------
Total=20 profit
ANSWER:A
Question: When throwing 2 dices, and looking at the sum of numbers on the dices - what is the probability to have a sum which is smaller than 5?
A.1/9
B.1/6
C.1/2
D.1/3
Answer: B.1/6
Explanation: a dice is composed of 6 numbers - 1,2,3,4,5,6.
When trowing 2 dices - there are 36 options (6X6=36).
If we want the sum of two dices to be< 5 there are those options: (1,1), (1,2), (2,1), (1,3), (3,1), (2,2) - total of 6 options.
Therefore - the probability to have a sum which is smaller than 5 is 6/36=1/6.
Answer:B
Question: Anup start a bike at 6am. and rides it at 60kmph. Raghu started at 7pm with his car at 80kmph. When will Raghu overtake Anup?
A.8:30am
B.9:40am
C.10:00am
D.12:00pm
Answer: C.10:00am
Explanation: Suppose bike is overtaken by car xhrs after 6am
Distance covered by the bike in x hrs = distance covered by the car in x-1 hr
60x = 80(x-1)
20x = 80
x = 4 hrs
Required time = 6+4 = 10:00am
Answer is C
Question: Sandy invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 2 times the original investment. What is the value of n?
A.12.5
B.18.5
C.24.5
D.30.5
Answer: A.12.5
Explanation: n* 0.08 * principal + principal = 2 * principal
n * 0.08 = 1
n = 12.5 years
The answer is A.
Question: If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trip whose distance in miles is the whole number y?
A.(x+xy)/125
B.(4x + 4xy)/5
C.(4x+xy)/500
D.(4x+xy)/5
Answer: B.(4x + 4xy)/5
Explanation: let Y be 1 mile
x= 20 cents
as per given info
in 1 mile we have 4 quarter mile
so for the first mile x=20 cents and x/5 cents =20/5=4 cents for every additional quarter mile
so total =20+4+4+4=32 cents charge for complete ride.
we just substitute our values in the given options and we get our ans B.
Question: It is known that no more than 4 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
A.35
B.105
C.12
D.210
Answer: C.12
Explanation: The question states that there are no more than 4 children in the party. Thus, the possibility is that there could be 1, 2, 3 or 4 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 4).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4), i.e.,12
Answer (C)
Question: The average marks obtained by 120 cndidates in a certainexaminationis 35.if the average marks of passed candidate is 39 and that of the failedcandidates is 15,what is the number of candidates who passed the examination
A.14 years
B.14 years 5 month
C.14 years 8 month
D.15 years 1 month
Answer: C.14 years 8 month
Explanation: (d) Let No. of passed candidates are x
So, x * 39 + (120 – x) 15= 120 * 35
x = 100
2.(a) Total increase = 8 * 2 = 16 years
So, total age of two women = 35 + 45 +16= 96
Average age of two women=96/2=48 years
3(d) Total decrease = 20 * 2 = 40 month
= 3 years 4 month
So, age of new boy = 18 years – 3 years 4 month
= 14 years 8 month
C
Question: What is the smallest integer X such that 2X+2 is divisible by 33, 44, 55, and 666?
A.X = 53186760
B.X = 26593379
C.X = 73260
D.X = 36629
Answer: D.X = 36629
Explanation: 33 = 3 * 11
44 = 2 * 2 * 11
55 = 5 * 11
666 = 2 * 3 * 3 * 37
So 2X+2 = 2 * 2 * 3 * 3 * 5 * 11 * 37 = 73260, and X = (73260 - 2)/2 = 36629, which is option D.
Question: The area of a rectangular plot is 15 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
A.10 metres
B.5 metres
C.7.5 metres
D.Data inadequate
Answer: B.5 metres
Explanation: L × B = 15 × B
∴ L = 15 m
and L – B = 10
∴ B = 15 – 10 = 5 m
Answer B
Question: Given that x = 2^b – (8^35 + 16^5), which of the following values for b yields the lowest value for |x|?
A.104
B.105
C.106
D.107
Answer: B.105
Explanation: 8^35 + 16^5 = 2^105 + 2^20
Compared to 2^105, the value of 2^20 is negligible.
2^105 - (2^105 +2^20) will minimize the value of |x|.
The answer is B.
Question: For any real number x, the operatoris defined as:
(x) = x(2 − x)
If p + 1 =(p + 1), then p =
A.-2
B.0
C.1
D.2
Answer: C.1
Explanation: (x) = x(2 − x)
(p + 1) = (p + 1)(2 - p - 1) = (1-p)(p+1)
We are given that p + 1 =(p + 1)
Therefore (1-p)(p+1) = (p + 1)
Or (p + 1) + (p-1)(p+1) = 0
(p + 1)(p - 1) = 0
p = -1,p=1
Option C
Question: In the Hillside summer camp there are 50 children. 80% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 10% of the total number of children in the camp. How many more boys must she bring to make that happen?
A.55
B.50
C.40.
D.30.
Answer: B.50
Explanation: Given there are 50 students , 80% of 50 = 40 boys and remaining 10 girls.
Now here 80% are Boys and 20% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 20 or 20%..
If we add 50 to existing 40 then the count will be 90 and the girls number will be 10 as it.
Now boys are 90% and girls are 10%. ( out of 100 students = 90 boys + 10 girls ).
IMO option B is correct.
Question: 12 men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: 1 man's 1 day work = 1/108
12 men's 6 day's work = 1/9 * 6 = 2/3
Remaining work = 1 - 2/3 = 1/3
18 men's 1 day work = 1/108 * 18 = 1/6
1/6 work is done by them in 1 day.
1/3 work is done by them in 6 * 1/3 = 2 days.
Answer: A
Question: If |p+q|=|p-q|, then p*q must be equal to:
A.0
B.-2
C.-1
D.1
Answer: A.0
Explanation: Solution 1: Distance perspective
|p-q| = |p+q| ==> The distance of p and q is equal to the distance of p and -q.
<=======(-q)=======0=======(q)======>
Only 0 is the value that has a distance equal to q and -q.
Solution 2:
|p-q| = |p+q| (square both)
p^2 -2pq + q^2 = p^2 + 2pq + q^2
4pq = 0
pq = 0
Answer: A
Question: In what time a sum of money double itself at 7% per annum simple interest?
A.33 1/8%
B.33 1/3%
C.14 2/7%
D.32 1/3%
Answer: C.14 2/7%
Explanation: P = (P*7*R)/100
R = 14 2/7%
Answer: C
Question: Franklin has s pairs of shoes, which is 1/5 as many as Bailey and twice as many as Smith. In terms of s, how many pairs of shoes do the three of them have combined?
A.7/2*s
B.2s
C.13/2*s
D.4s
Answer: C.13/2*s
Explanation: == s +5s + s/2 ==> 6s + 1/2 s = 13/2*s
Ans .C
Question: On 3,000 invested at a simple interest rate 6 p.c.p.a, 900 is obtained as interest in certain years. In order to earn 1,600 as interest on 4,000 in the same number of years, what should be the rate of simple interest?
A.7 p.c.p.a.
B.8 p.c.p.a.
C.9 p.c.p.a.
D.Data inadequate
Answer: B.8 p.c.p.a.
Explanation: Time = 900×100/3000×6 = 5 years
Rate = 1600×100/5×4000 = 8%
Answer B