mathewhe/aqua_rat huggingface dataset:
Question: How many multiples of 2 are there between 1 and 50, exclusive?
(A) 21
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: 24
multiples of 2 between 1 and 50 exclusive.
from 2 * 1 upto 2*24, (1,2,3,4,...,24). Hence, 24 multiples !
correct option is C
Answer: (C) 24
Question: What is the next number in the sequence below? 1 4 9 16 25 36 49 64 81 100 __ ?
(A) 64
(B) 46
(C) 81
(D) 100
(E) 121
Rationale: as the series of numbers are squares of numbers
1^2=1
2^2=4
3^2=9
and so on
therefore 11^2=121
ANSWER:E
Answer: (E) 121
Question: If 20% of a = b, then b% of 20 is the same as:
(A) 4% of a
(B) 5% of a
(C) 20% of a
(D) 10% of a
(E) None of these
Rationale: 20% of a = b
(20/100)a = b.
b% of 20 =(b/100)x 20=(20/100)a x	(1/100)x 20=(4/100)	a = 4% of a.
Answer:4% of a.
Answer: (A) 4% of a
Question: The ratios of areas of two squares, one having its diagonal double than the other is
(A) 4:7
(B) 4:2
(C) 4:0
(D) 4:1
(E) 4:6
Rationale: Answer: D) 4:1
Answer: (D) 4:1
Question: The security gate at a storage facility requires a five-digit lock code. If the lock code must consist only of digits from 1 through 7, inclusive, with no repeated digits, and the first and last digits of the code must be even, how many lock codes are possible?
(A) 120
(B) 240
(C) 360
(D) 720
(E) 1440
Rationale: X-X-X-X-X --> there are 3 even digits from 1 to 7, inclusive thus options for the first and the last X's are: 3-X-X-X-2. Other X's can take following values: 3-5-4-3-2 --> 3*5*4*3*2=360.
Answer: C.
Answer: (C) 360
Question: when W is divided by 13, the reminder is 0. if W is three more than it value and when divided by 11 its remainder is 0. what is the value of W ?
(A) 13
(B) 52
(C) 39
(D) 26
(E) 35
Rationale: W is divided by 13 so that is multiple of 14 as 13,26,39...
W+3 is divided by 11 the remainder is 0 so it is divisible by 11. Consider from option let us take the number is 13 it is divisible by 14 but 13+3 is not divisible by 11 so it is not answers so let us take 2nd option 52 which is divisible by 13 and 52+3=55 is divisible by 11 so ans is B
Answer: (B) 52
Question: Kunal walks 10 km towards North. From there he walks 6 Km towards South. Then, he walks 3 Km towards east. How far and in which direction is he with reference to his starting point ?
(A) 5 km north
(B) 5 km south
(C) 5 km east
(D) 5 km north-east
(E) 7 km south-east
Rationale: Clearly, Kunal moves from A 10 Km northwards upto B, then moves 6 Km southwards upto C, turns towards east and moves 3 km upto D.
Then AC = (AB-BC) = 4 Km
So AD is 5 Km also with reference to starting point Kunal's direction is North-East.
ANSWER D
Answer: (D) 5 km north-east
Question: Find the fourth proportional to 22.8 , 36.2 and 40.8?
(A) 60.1
(B) 65.86
(C) 66.48
(D) 64.78
(E) 65.04
Rationale: Formula= Fourth proportional =(b x c)/a
a=22.8 , b=36.2 and c=40.8
(36.2 x 40.8)/22.8=64.78
D
Answer: (D) 64.78
Question: 2/3rd of the boys and 3/4th of the girls of a school participate in a function. If the no.of participating students is 550, out of which 150 are girls, what is the total no.of students in the school?
(A) 500
(B) 600
(C) 800
(D) 900
(E) 1200
Rationale: Let total number of boys be x and total number of girls be y. y=400=>x = 600and^= I50=>y = 200 Now, x + y = 800
C
Answer: (C) 800
Question: If x and y are integers, what is the least positive number of 24x+9y?
(A) 1
(B) 3
(C) 4
(D) 6
(E) 9
Rationale: 24x+9y = 3(8x+3y) which will be a minimum positive number when 8x+3y = 1.
8(-1) + 3(3) = 1
Then 3(8x+3y) can have a minimum positive value of 3.
The answer is B.
Answer: (B) 3
Question: Kanul spent $500 in buying raw materials, $400 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount?
(A) $1010
(B) $1025
(C) $1125
(D) $1100
(E) $1000
Rationale: Let the total amount be x
then, (100-10)% of x = 500+400
90% of x = 900
90x/100 = 9000/9
x = $1000
Answer is E
Answer: (E) $1000
Question: A ship can travel with aspeed of 10km/hr in still water. If the speed of the stream is 10km/hr, find the time taken by the boat to go 60km downstream.
(A) 3 hrs
(B) 5 hrs
(C) 6 hrs
(D) 7 hrs
(E) 9 hrs
Rationale: Speed downstream = (10 + 10) km/hr = 45 km/hr.
Time taken to travel 68 km downstream = 60/20 hrs = 3 hrs.
A
Answer: (A) 3 hrs
Question: Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 20 hrs
(B) 22 hrs
(C) 23 hrs
(D) 24 hrs
(E) 21 hrs
Rationale: 1/( 1/36 +1/45) = 180/9 = 20 hrs
ANSWER:A
Answer: (A) 20 hrs
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity R of the pool?
(A) 9000 cubic meters
(B) 10500 cubic meters
(C) 11750 cubic meters
(D) 12000 cubic meters
(E) 12500 cubic meters
Rationale: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Answer: (D) 12000 cubic meters
Question: A boat can move upstream at 25 kmph and downstream at 45 kmph, then the speed of the current is?
(A) 10 kmph
(B) 7 kmph
(C) 8 kmph
(D) 9 kmph
(E) 4 kmph
Rationale: US = 25
DS = 45
M = (45 - 25)/2 = 10
Answer:A
Answer: (A) 10 kmph
Question: If f(x) = 2x + 3, & g(x) = (x - 3)/2, then what is the value of, fo(fo(go(go(fo(fo(go(go................(fo(fo(go(gof(x) )))).....)))))) ?
(A) 3
(B) 2
(C) 9
(D) 7
(E) 1
Rationale: f(x) = 2x + 3
g(x) = (x - 3)/2
gof(x) = 2x+3−32=x2x+3−32=x
gogof(x) = x−32x−32
fogogof(x) = 2(x−32)+32(x−32)+3 = 2x−6+622x−6+62 = x
fofogogof(x) = 2x + 3
This means, when we apply two times g(x) and two time f(x) on f(x) we get f(x). This pattern continues, Hence the answer is option (D).
Answer: (D) 7
Question: If the price of petrol increases by 30, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
(A) 25%
(B) 23%
(C) 16.67%
(D) 33.33%
(E) None of these
Rationale: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+30) i.e 130.
Now, his consumption should be reduced to :-
=(130−100)/130 ∗ 100.
Hence, the consumption should be reduced to 23%.
Answer : B
Answer: (B) 23%
Question: Sam buys 10 apples for $1. At what price should he sell a dozen apples if he wishes to make a profit of 25%?
(A) $0.125
(B) $1.25
(C) $0.25
(D) $1.5
(E) $1.8
Rationale: Explanatory Answer
The cost price of 1 apple = $1/10 or $0.10.
As Sam wishes to make a profit of 25%, his selling price per apple should be 0.10 + 25% of 0.10 = 0.1 + 0.025 = $0.125.
If the selling price of 1 apple is $0.125, the selling price of a dozen apples = 12 * 0.125 = $1.5
Choice D
Answer: (D) $1.5
Question: The rate of a certain chemical reaction is directly proportional to the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B present is increased by 50 percent, which of the following is closest to the percent change in the the concentration of chemical A required to keep the reaction rate unchanged.
(A) 100 % decrease
(B) 50% decrease
(C) 40% decrease
(D) 30% increase
(E) 60% increase
Rationale: Let's say here is the formula of how A and B affects the reaction speed:
rate = A/B
After the concentration B is increased by 50%, the percentage of B
become 1.5B, to keep 'rate' the same, need to have 1.5A.
Which means A increased by 50%
Answer : B
Answer: (B) 50% decrease
Question: Two numbers have a H.C.F of 11 and a product of two numbers is 1991. Find the L.C.M of the two numbers?
(A) 140
(B) 181
(C) 160
(D) 170
(E) 180
Rationale: L.C.M of two numbers is given by
(Product of the two numbers) / (H.C.F of the two numbers) = 1991/11 = 181.
ANSWER:B
Answer: (B) 181
Question: How many liters of water must be added to 14 liters of milk and water containing 10% water to make it 30% water?
(A) 1 liter
(B) 2 liters
(C) 3 liters
(D) 4 liters
(E) 5 liters
Rationale: By rule of alligation:
30% - 10% = 20%
100% - 30% = 70%
Quantity of pure water : Quantity of the mixture = 2 : 7
There are 14 liters of mixture, so we need to add 4 liters of pure water.
The answer is D.
Answer: (D) 4 liters
Question: What is the units digit of (5!*4! + 6!*5!)/2?
(A) 4
(B) 3
(C) 0
(D) 1
(E) 2
Rationale: (5!*4! + 6!*5!)/2
=5!(4! + 6!)/2
=120 ( 24 + 720)/2
=(120 * 744)/2
= 120 * 372
Units digit of the above product will be equal to 0
Answer C
Answer: (C) 0
Question: In the kitchen of a busy restaurant, it takes M minutes to wash P pots. At this rate, how many hours does it take to wash 10P pots?
(A) M/10
(B) 6/M
(C) 600M
(D) M/6
(E) 10M
Rationale: The time it takes to wash 10P pots is 10M minutes which is 10M / 60 = M/6 hours.
The answer is D.
Answer: (D) M/6
Question: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 50,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
(A) $ 280,000
(B) $ 320,000
(C) $ 360,000
(D) $ 400,000
(E) $ 540,000
Rationale: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 50,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.
So the amount invested will get doubled thrice.
So, 50000 *2^3 =400000
Hence, the answer is D.
Answer: (D) $ 400,000
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 30% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
(A) 1/2 m
(B) 1/3 m
(C) 1/4 m
(D) 1/5 m
(E) 1/6 m
Rationale: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/3.
Answer: B.
Answer: (B) 1/3 m
Question: the distance between parallel sides of the hexagon is 9. determine the length of the hexagon
(A) 18*sqrt3
(B) 18*sqrt2
(C) 18*sqrt4
(D) 19*sqrt3
(E) 17*sqrt3
Rationale: Length of each side of regular hexagon will be 3*sqrt3. total length ( perimeter) of regular hexagon will be 18*sqrt3
ANSWER:A
Answer: (A) 18*sqrt3
Question: If the compound interest on a certain sum of money for 3 years at 10% per annum be Rs. 993, what would be the simple interest?
(A) Rs. 880
(B) Rs. 890
(C) Rs. 895
(D) Rs. 900
(E) None
Rationale: Let P = Principal
A - Amount
We have a = P(1 + R/100)3 and CI = A - P
ATQ 993 = P(1 + R/100)3 - P
? P = 3000/-
Now SI @ 10% on 3000/- for 3 yrs = (3000 x 10 x 3)/100
= 900/-
Answer: D.
Answer: (D) Rs. 900
Question: If 30% of a number is equal to one-third of another number, what is the ratio of first number to the second number ?
(A) 2:5
(B) 3:7
(C) 10:9
(D) 7:3
(E) None of these
Rationale: Explanation :
Let 30% of A=1/3B
Then, 30A/100=1B/3
=> 3A/10=B/3
=> A:B= 10 : 9
Answer : C
Answer: (C) 10:9
Question: Mohan's salary was first increased by 20% and then decreased by 20%. If his present salary is Rs. 7200, then what was his original salary?
(A) Rs. 8000
(B) Rs. 7500
(C) Rs. 7400
(D) Rs. 7200
(E) None of these
Rationale: Let Mohan's salary be Rs.100.
When increased by 20%, Mohan's salary = Rs.120
Again when decreased by 20%, Mohan's salary = 120 - 24 = Rs. 96.
But present salary is Rs. 7200
for, 96 ---> 100 ; 7200 ---> ?
Required salary is 7200/96 * 100 = Rs. 7500
ANSWER:B
Answer: (B) Rs. 7500
Question: Find number which is 70% less than 60.
(A) 18
(B) 22
(C) 28
(D) 26
(E) 98
Rationale: Explanation:
70% less is 30% of the given number
Therefore, 30% of 60 is 18.
ANSWER: A
Answer: (A) 18
Question: If 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others, then what is the total number of handshakes
(A) 41
(B) 42
(C) 43
(D) 44
(E) 45
Rationale: n(n-1)/2 =10*9/2
=45
ANSWER:E
Answer: (E) 45
Question: Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage W.
(A) 16.8%
(B) 17.4%
(C) 17.9%
(D) 18.5%
(E) 19.1%
Rationale: Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653
653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible
Cost price = 20*21 + 8*17 = 420 + 136 = 556
Profit = 653 - 556 = 97
Profit% W= (97/556)*100 = 17.4%
Answer: B
Answer: (B) 17.4%
Question: If rupee one produces rupees nine over a period of 45 years, find the rate of simple interest?
(A) 22 1/7 %
(B) 22 3/2 %
(C) 22 1/8 %
(D) 20 %
(E) 22 1/2 %
Rationale: 9 = (1*45*R)/100
R = 20 %
Answer:D
Answer: (D) 20 %
Question: 300 + 5 × 8 = ?
(A) 820
(B) 340
(C) 420
(D) 209
(E) None of these
Rationale: 300 + 5 × 8 = ?
or, ? = 300 + 40 = 340
Answer B
Answer: (B) 340
Question: The first term in a sequence is 1 and the second term is 7. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 25th term in the sequence?
(A) 2.5
(B) 3
(C) 4
(D) 25
(E) 100
Rationale: The third term is 4 since this is the average of 1 and 7.
Then the next terms will all be 4 since the average stays at 4.
The answer is C.
Answer: (C) 4
Question: The ratio between the number of sheep and the number of horses at the Stewar farm is 4 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??
(A) 18
(B) 28
(C) 32
(D) 56
(E) 58
Rationale: et no of sheep and horses are 4k and 7k
no of horses= 12880/230=56
now 7K=56 and k=8
no of sheep=(4*8) =32
ANSWER:C
Answer: (C) 32
Question: There is a 20% chance that Ella will visit Finland this year, while there is a 70% chance that she will visit Mexico this year. What is the probability that Ella will visit either Finland or Mexico this year, but NOT both?
(A) 58%
(B) 60%
(C) 62%
(D) 64%
(E) 66%
Rationale: P(Finland but not Mexico)=0.2*0.3=0.06
P(Mexico but not Finland)=0.7*0.8=0.56
P(Finland or Mexico but not both)=0.06+0.56=0.62
The answer is C.
Answer: (C) 62%
Question: Jaclyn buys $10 000 worth of debentures in a company. She earns 9.5% p.a. simple interest, paid to her quarterly (that is, every 3 months). If the agreed period of the debenture was 18 months: calculate the amount of interest Jaclyn will earn for each quarter
(A) 237.5
(B) 234
(C) 289.5
(D) 345
(E) None of these
Rationale: Explanation:
I=(p x r x t)/100
= 10000*9.5/100*(18/12)^1/6 = 237.5
Answer: A
Answer: (A) 237.5
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:
(A) 11:5
(B) 3 : 2
(C) 1:2
(D) 3:5
(E) 7:8
Rationale: Answer: Option B
Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 23 ==> 27 x + 17 y = 23 x + 23 y ==> 4 x = 6 y ==> x/y = 3/2.
Answer: (B) 3 : 2
Question: What sum of money will produce Rs.90 as simple interest in 4 years at 3 1/2 percent?
(A) 263
(B) 500
(C) 367
(D) 642.9
(E) 339
Rationale: 90 = (P*4*7/2)/100
P = 642.9
Answer: D
Answer: (D) 642.9
Question: The distance between Delhi and Mathura is 150 kms. A starts from Delhi with a speed of 25 kmph at 5 a.m. for Mathura and B starts from Mathura with a speed of 40 kmph at 6 p.m. from Delhi. When will they meet?
(A) 11
(B) 77
(C) 8
(D) 10
(E) 12
Rationale: D = 150 – 25 = 125
RS = 40 + 25 = 65
T = 125/65 = 2 hours
6 a.m. + 2 = 8 a.m..Answer: C
Answer: (C) 8
Question: A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time R it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?
(A)  0.8(80 – y)
(B)  0.8 + 0.0025y
(C)  80/y – 1.25
(D)  80/1.25y
(E)  80 – 0.25y
Rationale: This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <=> 1/12,5 weeks per house * 40 houses = 40/12,5 = 80/25 = 320/100 = 3,2 weeks.
Which means finishing all houses at normal rate R=> 2*4 = 8 weeks. Faster rate = 4+3,2 = 7,2 weeks.
7,2/8 = 9/10 = 0,9. Insert y=40 in equations and it is clear that only (B) gives us 0,9.
Answer: (B)  0.8 + 0.0025y
Question: there is park of length 100 m and width 80m.there is path in middle of park across the length and breadth crossing each other.the breadth of path 3m.what % of park used for path?
(A) 5.53
(B) 6.63
(C) 4.43
(D) 8.61
(E) 5.81
Rationale: area of park=100*80=8000m2.
area of path=100*3+80*3-3*3=300+240-9=540-9=531m2.
%of path=531/8000*100=6.6375%
answer B
Answer: (B) 6.63
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 20 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has now how many candies initially?
(A) 36
(B) 48
(C) 50
(D) 55
(E) 60
Rationale: T = R
T - 24 ;R + 24
R + 24 = 5 ( T - 24 )
R + 24 =5T - 120
R - 5T = - 144
We knowR = T, so
R - 5T = - 144
Or, R - 5R = -144
Or, - 4R = - 144
Or, R = 36( This is the initital no of Candies Rebecca had)
Answer will be (A) 36
Answer: (A) 36
Question: One fast typist type some matter in 4hrs and another slow typist type the same matter in 6hrs. If both do combine in how much time they will take to finish.
(A) 10 hr
(B) 1 hr
(C) 2 hr 24 mins
(D) 3 hr 4 mins
(E) 4 hr 10 mins
Rationale: Fast's 1 hr work = 1/4
slow's 1 hr work = 1/6
1/4 + 1/6 = 5/12
they ll finish in 12/5hrs= 2 2/5 ==> 2 hr 24 mins
ANSWER:C
Answer: (C) 2 hr 24 mins
Question: Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?
(A) 5544
(B) 2288
(C) 6776
(D) 1877
(E) 1981
Rationale: Let the rate of interest during the second year be R%. Given,
4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544
R = 10%
Answer:A
Answer: (A) 5544
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.5 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
(A) 24 years
(B) 44 years
(C) 34 years
(D) 40 years
(E) 84 years
Rationale: 40 years
If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 5 = 11
4A + 5 = 9
9(5A + 5)=11(4A + 5)
A = 10
Thomasâ€™s current age = 4A
= 40 years.
D
Answer: (D) 40 years
Question: 120 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?
(A) 1~10
(B) 10~20
(C) 20~30
(D) 45~55
(E) 55~65
Rationale: 120 = 2^3*3*5
There are factors in each range except for 45~55
The answer is D.
Answer: (D) 45~55
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
(A) 30 minutes
(B) 45 minutes
(C) 1 hour
(D) 1 hour 15 min
(E) None
Rationale: Sol.
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 D
Answer: (D) 1 hour 15 min
Question: The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?
(A) 249
(B) 247
(C) 245
(D) 2882
(E) 212
Rationale: Speed = 45 * 5/18 = 25/2 m/sec.
Time = 30 sec
Let the length of bridge be x meters.
Then, (130 + x)/30 = 25/2
x = 245 m.
Answer: C
Answer: (C) 245
Question: I. a2 - 7a + 12 = 0,
II. b2 - 3b + 2 = 0 to solve both the equations to find the values of a and b?
(A) if a < b
(B) if a ≤ b
(C) if the relationship between a and b cannot be established
(D) if a > b
(E) if a ≥ b
Rationale: I.(a - 3)(a - 4) = 0
=> a = 3, 4
II. (b - 2)(b - 1) = 0
=> b = 1, 2
=> a > b
ANSWER:D
Answer: (D) if a > b
Question: Martha has the unique talent of being able to guess other people’s height and weight. For every three people that Martha meets, she consistently guesses the people’s correct height two times, and for every seven people that she meets, she consistently guesses the people’s correct weight five times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?
(A) 8/27
(B) 2/5
(C) 49/81
(D) 98/125
(E) 7930/9261
Rationale: Probability that she guesses the height correctly P(h)=2/3
Probability that she guesses the weight correctlyP(w)=5/7
Probability that she guesses both weight and height correctly(P(h)*P(w))=2/3 * 5/7= 10/21
Now the Q asks about the probability of this happening atleast once.
We calculate it by finding the probability of not being able to guess in any of the three occasions.
Probability of not being able to guess any no. of times =1-10/21=11/21
For all three occasions P(A)=11/21 * 11/21 * 11/21=1331/9261
Probability of the event happening atleast once=1- P(A)=1-1331/9261=7930/9261
Ans should be E
Answer: (E) 7930/9261
Question: If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?
(A) 78 days.
(B) 99 days.
(C) 49 days.
(D) 48 days.
(E) 67 days.
Rationale: B
99 days.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (9*6*88/1) = (6*8*d/1)
on solving, d = 99 days.
Answer: (B) 99 days.
Question: The moon revolves around the earth at a speed of approximately 1.04 kilometers per second. This approximate speed is how many kilometers per hour?
(A) 60
(B) 61.2
(C) 3,744
(D) 3,600
(E) 3,672
Rationale: moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 1.04*3600=3744kilometers per hour.
Option C is correct
Answer: (C) 3,744
Question: By selling an article at $800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) $580
(B) $450
(C) $480
(D) $400
(E) $440
Rationale: C
$480
SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = $160
SP = CP - Loss = 640 - 160 = $480
Answer: (C) $480
Question: A train 300 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 298 m
(B) 279 m
(C) 500 m
(D) 289 m
(E) 1000 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (300 + x)/60 = 65/3
x = 1000 m.
Answer: E
Answer: (E) 1000 m