mathewhe/aqua_rat huggingface dataset:
Question: A container has a capacity of 20 gallons and is full of spirit. 5 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 5 times. Find how much spirit is left in the resulting mixture finally?
(A) (257/525) gallons
(B) 1.5552 gallons
(C) 1.5 gallons
(D) 1.25 gallons
(E) None of these
Rationale: There is a direct formula to calculate such repetition:
Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:
Left QTY / 20 = (20 -5)^5 / 20^5
Left QTY = 20 (15/20)^5
Left QTY = 20 ( 3/5 )^5
Left QTY = 1.5552
Answer is B
Answer: (B) 1.5552 gallons
Question: A 6% stock yields 8%. The market value of the stock is:
(A) Rs. 48
(B) Rs. 75
(C) Rs. 96
(D) Rs. 133.33
(E) none
Rationale: For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs. (100/8 * 6) = Rs. 75.
Market value of Rs. 100 stock = Rs. 75.
Answer = B
Answer: (B) Rs. 75
Question: W, X, Y, Z are integers. The expression X - Y - Z is even and the expression Y - Z - W is odd. If X is even what must be true?
(A) U
(B) W
(C) E
(D) H
(E) R
Rationale: Sol: X is even so Y, Z both are even or both are odd.
Now Y - Z in both cases even. So (Y - Z ) - W = odd happens only when w is odd
Ans: W is odd
Answer:B
Answer: (B) W
Question: A train 130 meters long completely crosses a 320-meter long bridge in 30 seconds. What is the speed of the train in km/h?
(A) 42 km/h
(B) 46 km/h
(C) 50 km/h
(D) 54 km/h
(E) 58 km/h
Rationale: speed = distance / time = (130 + 320)/30 = 450/30 (m/s) * 3600/1000 = 54 km/h
The answer is D.
Answer: (D) 54 km/h
Question: The simple form of the ratio 7/6:3/2 is?
(A) 5:8
(B) 7:9
(C) 5:9
(D) 5:3
(E) 5:1
Rationale: 7/6 : 3/2 = 7:9
Answer: B
Answer: (B) 7:9
Question: To be eligible for retirement benefits at the Norman Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 68. If x, where x <68, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y?
(A) xy=68
(B) x+y=68
(C) 2x+y=68
(D) 2x+2y=68
(E) x+2y=68
Rationale: We are told that when a certain employee was hired he was x years old and that the he needed minimum y years to be eligible for benefits.
Now,after y years of employment, when the employee will be be eligible for benefits, the employee will be x+y years old and will have y years of employment, thus{age after y years}+{employment years}=(x+y)+y=x+2y=68.
Answer: E
Answer: (E) x+2y=68
Question: A pupil's marks were wrongly entered as 35 instead of 23. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
(A) 30
(B) 80
(C) 20
(D) 25
(E) 24
Rationale: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (35 - 23)
=> X/2 = 12
=> X = 24.
ANSWER:E
Answer: (E) 24
Question: In how many ways 6 Indians and 1 Englishmen can be seated in a row so that they are alternate?
(A) 120
(B) 265
(C) 144
(D) 720
(E) 256
Rationale: number of ways = 6!*1! = 720
Answer is D
Answer: (D) 720
Question: A family has two children. find the probability that both the children are girls given that at least
one of them is a girl?
(A) 1/3
(B) 4/7
(C) 4/9
(D) 4/11
(E) 5/7
Rationale: Let b stand for boy and g for girl. The sample space of the experiment is
S = {(g, g), (g, b), (b, g), (b, b)}
Let E and F denote the following events :
E : ‘both the children are girls’
F : ‘at least one of the child is a girl’
Then E = {(g,g)} and F = {(g,g), (g,b), (b,g)}
Now E n F = {(g,g)}
Thus P(F) = 3/4
and P (E n F )= 1/4
Therefore P(E|F) = P(E ∩ F)/P(F) = (1/4)/(3/4) = 1/3
A)
Answer: (A) 1/3
Question: A man buys two cycles for 1200 each, he sells first cycle at a loss of 20% ,if he desires to get a profit of 15% on whole for how much should he sell his 2nd cycle?
(A) 1600
(B) 1700
(C) 1800
(D) 1900
(E) 1950
Rationale: 1st cycle sold at a loss of 20%, so the Sp of 1st cycle= 1200*(1-20/100)=960
Total CP for 2 cycles= 1200*2=2400
Desired SP for 2 cycles= 2400*(1+15/100)=2760
so, SP of 2nd cycle= 2760-960=1800
ANSWER:C
Answer: (C) 1800
Question: 7^1+7^2+7^3+...........+7^2015 find out how many numbers present which unit place contain 3 ?
(A) 502
(B) 503
(C) 504
(D) 505
(E) 506
Rationale: 7^3,7^7,7^11,7^15,7^19.........7^2015 contains last digit=3.
Now,we see
3,7,11,15....2015 are in AP
tn=a+(n-1)d
2015=3+(n-1)4
2015=3+4n-4
4n=2016
n=504
ANSWER:C
Answer: (C) 504
Question: There is enough provisions for 600 men in an army camp for 25 days. If there were 300 men less, how long will the provision last?
(A) 35 days
(B) 40 days
(C) 45 days
(D) 50 days
(E) 55 days
Rationale: Exp: We have, M1D1 = M2D2
600*25= 300* D2
D2 = 600*25/300 = 50 days.
Answer: D
Answer: (D) 50 days
Question: In three years, Janice will be three times as old as her daughter. Six years ago, her age was her daughter’s age squared. What would be the age of Janice Daughter after 3 years
(A) 18
(B) 36
(C) 40
(D) 42
(E) 45
Rationale: Let Jane's age be J and daughters' age be D...
Given J + 3 = 3(D + 3 ) => J - 6 = 3D -> Eq1.
Given J-6 = (D-6)^2 --> Eq 2..
sub J-6 value in eq 2... 3D = D^2 - 12D + 36.
0 = D^2 - 15D + 36 => D = 12 or D = 3.
When D = 12 we get from eq 1... J+3 = 45 => J =42..
When D = 3 ..we get from eq 1.. J+3 = 18 => J = 15...
IMO option A is correct answer..
Answer: (A) 18
Question: Given that x and y are nonnegative integers, compute the number of pairs (x; y) such that
5x + y = 20.
(A) 1
(B) 5
(C) 10
(D) 15
(E) 20
Rationale: For x = 0,1,2,3,4, there is a valid y, giving the answer 5 .
correct answer B
Answer: (B) 5
Question: If the speed of the boat in still water is 12km/hr and the speed of the stream is 5km/hr. Find the time taken to travel 34kms down stream.
(A) 4 hrs.
(B) 1 hrs.
(C) 3 hrs.
(D) 2 hrs.
(E) 5 hrs.
Rationale: DS =speed of the boat + speed of the stream 5+12 =17km/hr. Time taken to cover 34km down stream =34/17 =2hrs. Answer : D
Answer: (D) 2 hrs.
Question: The sum of 5 hours 45 minutes and 55 minutes is approximately what percent of a day?
(A)  approx 27%
(B)  16%
(C)  24%
(D)  approx 18%
(E)  approx 72%
Rationale: Since the question is asking for an approximate percentage
5:45 + 0:45 ~ 6:30 hours
% of day = 6.5*100/24 = 7*100/24 ~ 27%
Answer is A.
If you had 27 and 29 as options you would probably need to do more accurate calculations. In this particular case while approximating values we increase both numerator and denominator so our calculations should be close
Answer: (A)  approx 27%
Question: Before being simplified, the instructions for computing income tax in country R were to add 5 percent of one's annual income to the average(arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in country R's currency, for a person in that country whose annual income is I?
(A) 50 + I/200
(B) 50 + 3I/100
(C) 50+ 11I/200
(D) 100+ I/50
(E) 100+ 3I/100
Rationale: Income of a person is I
5 percent of ones annual income = 5I/100
100 units of Country R's currency = 100
1 percent of one's annual income = I/100
Average of 100 units and 1 percent annual income = 50 + I/200
Sum of average and 5 percent = 5I/100 + 50 + I/200
= 50 + 11I/200
So answer is C.
Answer: (C) 50+ 11I/200
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ?
(A) 4966
(B) 2477
(C) 2877
(D) 2676
(E) 1881
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4966
Answer: A
Answer: (A) 4966
Question: The area of a rectangle is 460 square metres. If the length is 15% more than the breadth, what is the breadth of the rectangular field ?
(A) 18 meter
(B) 20 meter
(C) 22 meter
(D) 25 meter
(E) 30 meter
Rationale: Explanation:
Let breadth =x metres.
Then length =(115x/100)metres.
=x∗115x/100=460
x2=(460x100/115)x2=400x=20
ANSWER IS B
Answer: (B) 20 meter
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 30 hrs and a machine of type S does the same job in 15 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) A)3
(B) B)4
(C) C)5
(D) D)9
(E) E)12
Rationale: Rate of machine R =1/30
Rate of machine S =1/15
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/30 +x/15 =1/2
x3/30=1/2
x=30/6=5
So no of machine R is 5
Answer C
Answer: (C) C)5
Question: x percent of y percent of z is decreased by y percent What is the result?
(A) (100xyz - xy^z2) / 1,000,000
(B) (xz - y) / 100
(C) (xz - y) / 10,000
(D) (xyz - 2y) / 100
(E) (xyz - 2y) / 10,000
Rationale: We're told that X percent of Y percent of Z is DECREASED by Y percent. We're asked for the result of all of this math.
IF....
X = 10
Y = 50
Z = 100
First, 50% of 100 = 50
Next, 10% of 50 = 5
Finally, 5 decreased by 50% of itself is 2.5
So we're looking for an answer that equals 2.5 when X=10, Y=50 and Z=100.
Answer A. (100xyz - xy^2z) / 1,000,000 = (5,000,000 - 2,500,000)/1,000,000 = 2,500,000/1,000,000 = 2.5 This is a MATCH
A
Answer: (A) (100xyz - xy^z2) / 1,000,000
Question: How much time will take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 7
(B) 4
(C) 5
(D) 3
(E) 2
Rationale: Time = (100 * 81) / (450 * 4.5) = 4 years'
Answer:B
Answer: (B) 4
Question: Working individually, Jane can bake cakes for 4 hours and Roy can bake cakes in 5 hours. If Jane and Roy work together but independently at the task for 2 hours, at which point Roy leaves, how many remaining hours will it take Jane to complete the task alone?
(A) 1/2
(B) 2/5
(C) 3/4
(D) 1/4
(E) 1/5
Rationale: In first 2 hrs Roy will finish 2/5 = 2/5 of work and Jane will finish 2/4 work so total 2/5 + 1/2 = 9/10 work is finished and 1-9/10 = 1/10 work remaining. Now Jane will take (1/10)*4 = 2/5 hrs to finish it.
So answer is B.
Answer: (B) 2/5
Question: Two bus stations are 600 km apart. if two separate buses depart from both stations and travel towards each other, at what time will they meet each other, given that the first bus left at 12 p.m. and travels at a speed of 60 kmph while the second bus left at 1 p.m. and travels at a speed of 40 kmph.
(A) 2.40 p.m.
(B) 8.40 p.m.
(C) 5.40 p.m.
(D) 7.40 p.m.
(E) 6.40 p.m.
Rationale: Suppose they meet x hours after 12 p.m.
Distance moved by first bus in x hours + distance moved by 2nd bus in x-1 hrs = 600
60x+40(x-1) =600
60x+40x-40= 600
100x= 640
x = 6.4
So they meet 6.4 hr after 12 p.m. which is at 6.40 p.m.
Answer is E
Answer: (E) 6.40 p.m.
Question: A Caterpillar crawls a distance with speed of 21inches/min in the one direction and after feeding moves back in the same direction with 7inches/min and what is the average speed of it?
(A) 11.5 inch/ min
(B) 10.5 inch/ min
(C) 12.5 inch/ min
(D) 13.5 inch/ min
(E) 14.5 inch/ min
Rationale: average speed = 2*21*7/(21+7) = 2*21*7/28 = 21/2 = 10.5 inch/ min
ANSWER:B
Answer: (B) 10.5 inch/ min
Question: The remainder obtained when a prime number greater than 8 is divided by 8 is
(A) a) 1 or 3
(B) b) 1 or 5
(C) c) 3 or 5
(D) d) 4 or 5
(E) e) 5
Rationale: The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 8, i.e. 13 and 11:
13/8 = 1 + remainder of 5
11 / 8 = 1 + remainder of 3
This is already sufficient to see that answer choice b) is correct.
C
Answer: (C) c) 3 or 5
Question: After working for 6 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
(A) 20 days
(B) 24 days
(C) 27 days
(D) 21 days
(E) 26 days
Rationale: A
20 days
1/3 ---- 6
1 -------? A = 18
R = 1/18 * 60/100 = 1/30
1 ----- 1/30
2/3 ----? => 20 days
Answer: (A) 20 days
Question: 70,76, 74,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times.
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74.
Answer: C.
Answer: (C) 3
Question: A student is ranked 6th from right and 5th from left. How many students are there in totality ?
(A) 10
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: From right 6 , From left 5
Total = 6+5-1 = 10
ANSWER:A
Answer: (A) 10
Question: The diagonals of a rhombus are 17 cm and 20 cm. Find its area?
(A) 176
(B) 186
(C) 150
(D) 170
(E) 172
Rationale: 1/2 * 17 * 20
= 170
Answer:D
Answer: (D) 170
Question: (1^3 + 2^3 + 3^3 + ... + 10^3) = x?
(A) 360
(B) 380
(C) 420
(D) 440
(E) 450
Rationale: We know that (1^3 + 2^3 + 3^3 + ... + n^3) =	1	2n(n + 1)
6
Putting n = 10, required sum = 1	x 10 x 10 x 21 = 2100/5
420
C
Answer: (C) 420
Question: Caleb spends $68.50 on 50 hamburgers for the marching band. If single burgers cost $1.00 each and double burgers cost $1.50 each, how many double burgers did he buy?
(A) 5
(B) 10
(C) 37
(D) 40
(E) 45
Rationale: Solution -
Lets say, Single hamburgersxand Double hamburgersy
Given that,
x+y=50 and 1x+1.5y=68.50. By solving the equations y=37. ANS C.
Answer: (C) 37
Question: A train passes a station platform in 30 sec and a man standing on the platform in 12 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 227
(B) 240
(C) 200
(D) 178
(E) 270
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 12= 180 m.
Let the length of the platform be x m . Then,
(x + 180)/30= 15 => x = 270 m.
Answer:E
Answer: (E) 270
Question: A certain list of 100 data has an average (arithmetic mean) of 5 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 100 data with standard deviation less than d?
(A) -5 and 0
(B) 0 and 0
(C) 0 and 5
(D) 0 and 10
(E) 5 and 5
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 5 and 5 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
Answer: E.
Answer: (E) 5 and 5
Question: how many five digit numbers are there such that two left most digits are even and remaining are odd and 4 digit should not be repeated.
(A) 950
(B) 960
(C) 970
(D) 980
(E) 990
Rationale: even numbers are 2,4,6,8 and odd 1,3,5,7,9
so choice for first 2 digit 4 and 4
and for last 3 digit 5 ,4 ,3 coz not repeated
so ans 4*4*5*4*3 = 960
ANSWER:B
Answer: (B) 960
Question: In a chess competition involving some men and women, every player needs to play exactly one game with every other player. It was found that in 45 games, both the players were women and in 190 games, both players were men. What is the number of games in which one person was a man and other person was a woman?
(A) 40
(B) 120
(C) 180
(D) 200
(E) 220
Rationale: This is similar to handshake problem, If there are NN people, then number of handshakes = 1+2+...N=N∗(N−1)/2
No. of Women be xx and given x∗(x−1)/2=45 This gives x=10
|||y No. of Men : solve y∗(y−1)/2=190. This gives y=20
so total Men vs. Women = 10*20 = 200. Answer is D
Answer: (D) 200
Question: How many numbers between 200 and 700 begin or end with 5?
(A) 20
(B) 60
(C) 140
(D) 110
(E) 120
Rationale: How many numbers between 200 and 700 begin or end with 5?
Just think that those numbers are:
i) The ones ending in 5: 205, 215, 225, ... , 695 --> 50 numbers
ii) The ones beginning in 3: 300, 301, 302, 303, ... , 393, ... , 399 --> 100 numbers
BUT 10 out of the first 50 numbers are repeated in the second set.
THEREFORE, the solution is 140 numbers.
Answer: C
Answer: (C) 140
Question: If a(a - 5) = 6 and b(b -5) = 6 where a ≠ b, then a + b =
(A) −48
(B) −2
(C) 2
(D) 9
(E) 5
Rationale: i.e. if a = -1 then b = 6
or if a = 6 then b = -1
But in each case a+b = -1+6 = 5
Answer: option E
Answer: (E) 5
Question: A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $340,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment?
(A) $1,416
(B) $1,733
(C) $3,466
(D) $13,333
(E) $20,796
Rationale: 0.04x + 0.09y = 340000 [1]
0.04x = 0.80 * 340000 = 272000 [2]
272000 + 0.09y = 340000 --> 0.09y = 64000 [3]
272000 / 12 = 22666.67 [4]
64000 / 12 = 5666.67 [5]
Adding [4,5] we get: 28333.33 [6]
Dividing [6] / 2 to get an average we get 1.416,ANS A
Answer: (A) $1,416
Question: Gasoline varies in cost from $0.93 to $1.13 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?
(A) $15.13
(B) $15.30
(C) $15.72
(D) $16.01
(E) $16.23
Rationale: Solution:
We know that the per gallon cost of gasoline varies from $0.93 - $1.13.
Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.
Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.
So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).
Case 1: for 30 gallons the cost is 30*0.93 to 30*1.13 which is $27.90 to $33.90
Case 2: for 20 gallons the cost is 20*0.93 to 20*1.13 which is $18.60 to $22.60
Thus, the maximum cost of the 480 mile trip is $33.90 and minimum is $18.60
so the difference is $33.90 - $18.60 = $15.30
Answer: B
Answer: (B) $15.30
Question: Ramesh purchased a refrigerator for Rs. 14500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 34778
(B) 26888
(C) 20350
(D) 17600
(E) 12778
Rationale: Price at which the TV set is bought = Rs. 14,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 18125
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 18125 + 375 = Rs. 18500
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 18500 * 110/100
= Rs. 20350
Answer: C
Answer: (C) 20350
Question: A man starts walking at 3 pm . ha walks at a speed of 4 km/hr on level ground and at a speed of 3 km/hr on uphill , 6 km/hr downhill and then 4 km/hr on level ground to reach home at 9 pm. What is the distance covered on one way
(A) 10km
(B) 12km
(C) 14km
(D) 16km
(E) 18km
Rationale: avg speed=2*3*6/(3+6)=4
so speed of man=4km/hr
distance=4*6=24km
since we want one way distance it will be
24/2 =12km
ANSWER:B
Answer: (B) 12km
Question: If 3 people a,b,c can do a work simultaneously in 6 days. a and b can do work in 10 days. b and c can do work in 15 days. c and a can do the same work in 20 days.In how many days that a can complete the same work alone?
(A) 20
(B) 25
(C) 30
(D) 24
(E) 19
Rationale: a+b+c=1/6(one day work)
a+b=1/10;b+c=1/15;c+a+1/20
b=1/15-c;c=1/20-a;---------(2)
substitute equation 2 in a+b=1/10
a=1/10-b;a=1/10-1/15+c;
a=1/10-1/15+1/20-a;
2a=1/10-1/15+1/20;
a=1/24(one day work)
That is the no of days that a can work alone is 24 days
The option D is answer
Answer: (D) 24
Question: How many prime numbers exist between 200 and 220?
(A) None
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: All the even numbers goes out of the window.
201,207,213,219 - Sum of digits = 3 so divisible by 3
All the numbers ending with 5 is obviously not prime
ANSWER:B
Answer: (B) 1
Question: An airline passenger is planning a trip that involves three connecting flights that leave from airports A, B and C, respectively. The First flight leaves Airport A every Hour, beginning at 8:00 a.m., and arrives at Airport B 2nd a half hours later. The second flight leaves Airport B every 20minutes, beginning at 8:00a.m, and arrives at Airport C 1h 10 minutes later. The third flight leaves Airport C every hour, beginning at 8.45 a.m. What is the least total amount of time the passenger must spend between flights if all flights keep to their schedules?
(A) 25min
(B) 1hr 5min
(C) 1hr 15min
(D) 2hr 20min
(E) 3hr 40min
Rationale: Following way may not be a pure mathematical approach to solve it but it got me the result within a minute.
A: Flight leaves every hour; 8,9,10,11,12,1,2,3
B: Flight leaves every 20min; 8:20,8:40,9,9:20,9:40,10,10:20,10:40,11
C: Flight leaves every hour: 8:45,9:45,10:45,11:45,12:45
Passenger leaves at 8:00AM from A; reaches B@ 10:30am - he will catch 10:40am flight from B{10 minutes spent at airport B}; reaches c after 1hour10minutes @11:50AM;his next flight at C is at 12:45 - he waits another 55minutes;
Total wait = 10+55= 65 minutes = 1hour 5 mins
Ans:B
Answer: (B) 1hr 5min
Question: Divide Rs.118000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6?
(A) A = 30000 B = 40000 C = 48000
(B) A = 30000 B = 40000 C = 48030
(C) A = 30000 B = 40070 C = 48000
(D) A = 30000 B = 40000 C = 48300
(E) A = 30200 B = 40000 C = 48000
Rationale: Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
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A:B:C = 15:20:24
We can divide Rs.118000 in this ratio.
Share of A = 15/59 * 118000 = 30000
Share of B = 20/59 * 118000 = 40000
Share of C = 24/59 * 118000 = 48000
Answer: A
Answer: (A) A = 30000 B = 40000 C = 48000
Question: If 0 < x ≤ 2, then which one of the following is the maximum value of (x – 1)^2 + x ?
(A) –2
(B) –1
(C) 0
(D) 2
(E) 3
Rationale: If you cannot spot that the maximum value of (x – 1)^2 + x for 0 < x ≤ 2 is when x=2 --> (x – 1)^2 + x = 2 you can do the following:
Since 0 < x ≤ 2, then (x – 1)^2 + x is positive --> discard A, B and C.
For the same reason: (x – 1)^2 is a non-negative fraction less than 1.
Thus (x – 1)^2 + x = (non-negative fraction less than 1) + (0 < x ≤ 2) < 3. Discard E.
Only D is left.
Answer: D.
Answer: (D) 2
Question: Find the odd man out
2, 5, 14, 41, 122, 365, 1125
(A) 2
(B) 14
(C) 41
(D) 365
(E) 1125
Rationale: 1*3-1 = 2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3-1 = 122
122*3-1= 365
365*3-1= 1094
ANSWER:E
Answer: (E) 1125
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) Rs.7500
(B) Rs.7502
(C) Rs.7529
(D) Rs.7596
(E) Rs.7506
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18)
= 4:3:3
B's share = 25000 * 3/10
= Rs.7500.
Answer:A
Answer: (A) Rs.7500
Question: How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
(A) 8 years
(B) 4 years
(C) 7 years
(D) 6 years
(E) 2 years
Rationale: Explanation:
Time = (100 x 81)/(450 x 4.5) years
= 4 years.
Answer: B
Answer: (B) 4 years