mathewhe/aqua_rat huggingface dataset:
Question: A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 160 kilometers?
(A) 8 gallons
(B) 4 gallons
(C) 6 gallons
(D) 5.5 gallons
(E) 10 gallons
Rationale: Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 160 kilometers?
160 / 40 = 4 * 1 gallon = 4 gallons correct answer B
Answer: (B) 4 gallons
Question: If 240 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
(A) 16
(B) 40
(C) 20
(D) 18
(E) 22
Rationale: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (240 *4/24) = 40
ANSWER:B
Answer: (B) 40
Question: If x = 1- 3t and y = 2t - 3, then for what value of t does x = y?
(A)  5/2
(B)  3/2
(C)  2/3
(D)  4/5
(E)  0
Rationale: We are given x = 1 – 3t and y = 2t – 3, and we need to determine the value for t when x = y. We should notice that both x and y are already in terms of t. Thus, we can substitute 1 – 3t for x and 2t – 3 for y in the equation x = y. This gives us:
1 – 3t = 2t – 3
4 = 5t
4/5 = t
The answer is D.
Answer: (D)  4/5
Question: Each of six different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
(A) 1/8
(B) 1/36
(C) 1/4
(D) 3/8
(E) 1/2
Rationale: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 6 is 1/6.
Probability of choosing another right key is 1/6.
since the question is asking for 2 right keys , probability is multiplication of both = 1/6 * 1/6 = 1/36.
Ans B
Answer: (B) 1/36
Question: Simplify
16−[5−(6+2(7−8−5¯¯¯¯¯¯¯¯¯¯¯))]
(A) 23
(B) 25
(C) 28
(D) 30
(E) 32
Rationale: Explanation:
=16−[5−(6+2(7−8+5))]
(Please check due to overline, sign has been changed)
=16−[5−(6+2×4))]
=16−[−9]=16+9=25
Option B
Answer: (B) 25
Question: In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?
(A) 2/15*P
(B) 3/5*P
(C) 3/4*P
(D) 5/6*P
(E) 13/15*P
Rationale: no of people polled who did not answer “yes” to both questions = P - no of people polled who answered “yes” to both questions
no of people who answered yes for the 2nd question = 1/3 * 2/5 * P = 2/15*P
no of people polled who did not answer “yes” to both questions = P - 2/15*P = 13/15*P
Hence, E will be the answer.
Answer: (E) 13/15*P
Question: A sum of 14,400 amounts to 16,600 in 3 years at the rate of simple interest. What is the rate of interest?
(A) 2%
(B) 1%
(C) 6%
(D) 5%
(E) 8%
Rationale: D
5%
S.I. = (16600 - 14400) = 2200.
Rate = (100 x 2200)/(14400x3)% = 5%
Answer: (D) 5%
Question: Jake took a bus from home to market, that travels at 10 kmph. While walking back at 2 kmph,
halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 50 kmph. Find the average speed.
(A) 1.17 kmph
(B) 1.67 kmph
(C) 0.69 kmph
(D) 1.45 kmph
(E) none of these
Rationale: Let the distance be 2x(one way)
Time taken by bus = 2x/10, by walking =x/2, by cycling = x/50 hours
:. Average speed = Total Distance/Total time
= 2x / x/5 + x/2 + x/50
= 2 *60 / 12+30+1.2
= 1.67
ANSWER:B
Answer: (B) 1.67 kmph
Question: Lexy walks 5 miles from point A to point M in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
(A) 40
(B) 80
(C) 120
(D) 160
(E) 180
Rationale: Lexy walks 5 miles from point A to point M in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Average speed = total distance/total time
We know the total distance is 5+5 (going from A to M then from M to A)
Time = distance/speed
Time = 5/15
Time = 1/3 hour
Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.
This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.
Answer: D). 160
Answer: (D) 160
Question: Which of the following MUST yield an integer when divided by 7?
(A) The sum of Seven consecutive positive integers.
(B) The square of a prime number.
(C) The sum of two odd integers.
(D) The product of three consecutive odd numbers.
(E) The difference between a multiple of 8 and a multiple of 3.
Rationale: For option A: Let the numbers be (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3).
Now, (x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3) = 7(x). Hence A is true. No need to check other answers since there can only be one correct answer.
So, Ans(A).
Answer: (A) The sum of Seven consecutive positive integers.
Question: When 2/3 of the garments in the shipment were inspected, 18 of the garments passed inspection and the remaining 2 garments failed. How many of the un inspected garments must pass inspection in order that 80 percent of the garments in the shipment pass?
(A) 6
(B) 9
(C) 8
(D) 7
(E) 5
Rationale: B = 9
2/3x= 20
x=30
for 80% approval we need 24 garments approved.
already approved = 18
we need 6 more.
Answer : A
Answer: (A) 6
Question: In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of
(A) 5363
(B) 6240
(C) 2368
(D) 1987
(E) 2732
Rationale: To obtain Rs. 10, investment
= Rs. 96.
To obtain Rs. 650, investment =
= Rs. 6240.
Answer: B
Answer: (B) 6240
Question: When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
(A) 671
(B) 661
(C) 673
(D) 681
(E) 693
Rationale: When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.
The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.
Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625 = 671
ANSWER:A
Answer: (A) 671
Question: George went to a fruit market with certain amount of money. With this money he can buy either 50 oranges or 40 mangoes. He retains 8% of the money for taxi fare and buys 20 mangoes. How many oranges can he buy?
(A) 21
(B) 30
(C) 20
(D) 16
(E) 12
Rationale: Let the amount of money be 200
Let cost of 1 Orange be 4
Let cost of 1 mango be 5
He decides to retain 8% of 200 = 16 for taxi fare, so he is left with 184
He buys 20 mangoes ( @ 5) so he spends 100
Money left is 84 (184 - 100)
No of oranges he can buy = 84/4 =>21
So, George can buy 21 Oranges.
A
Answer: (A) 21
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 9 a.m.
(B) 10 a.m.
(C) 10.30 a.m.
(D) 11 a.m.
(E) 11.30 a.m.
Rationale: Explanation:
Suppose they meet x hours after 7 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
=> 45x = 135
=> x = 3.
So, they meet at 10 a.m.
ANSWER IS B
Answer: (B) 10 a.m.
Question: John want to buy a $100 Trouser at the store, but he think itâ€™s too expensive. Finally, it goes on sale for $50. What is the percent decrease?
(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€“ 50 = 40. The â€œoriginalâ€ is our starting point; in this case, itâ€™s 100. (50/100)*100 = (0.5)*100 = 50%.
D
Answer: (D) 50%
Question: If x/y =2/5, then (x-y)/x?
(A) -1/2
(B) -1/3
(C) 1/3
(D) -3/2
(E) 5/2
Rationale: we have this law of fraction:
a/b=c/d= (a-c)/(b-d)
x/y=2/5 ---> x/2=y/5= (x-y)/(2-5)=(x-y)/(-3) ---> (x-y)/x= -3/2
Answer: D
Answer: (D) -3/2
Question: A composer’s guild is planning its spring concert, and nine pieces have been submitted for consideration. The director of the guild knows that they will only have time to present two of them. If the pieces can be played in any order, how many combinations of pieces are possible?
(A) 40
(B) 21
(C) 36
(D) 54
(E) 16
Rationale: Combination question..
9C2 = 36..
IMO option C is correct..
Answer: (C) 36
Question: A train running at the speed of 50 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 125 m
(B) 150 m
(C) 187 m
(D) 167 m
(E) 197 m
Rationale: Speed = 50 * 5/18 = 125/9 m/sec
Length of the train = speed * time = 125/9 * 9
= 125 m
Answer: A
Answer: (A) 125 m
Question: A shopkeeper sold an article for 600 after giving 20% discount on the labelled price and made 20% profit on the cost price. What would have been the percentage profit,had he not given the discount’?
(A) 25%
(B) 30%
(C) 23%
(D) 50%
(E) None of these
Rationale: Cost price =600×100/120= 500
S.P. at no discount = 600×100/80 = 750
∴ % profit = 250×100/500 = 50 %
Answer D
Answer: (D) 50%
Question: If the range of the set of numbers {140, 80, 135, 110, 175, 145, x, 123, 136} is 105, which of the following could be x?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: The range of the other 8 numbers is 175-80 = 95, so x must be either the smallest number or the largest number in the set.
Then x = 175-105 = 70 or x = 80+105 = 185
The answer is D.
Answer: (D) 70
Question: The cost of 3 pens and 5 pencils is Rs.260. Also the cost of one pen and one pencil is in the ratio of 5:1 respectively. What is the cost of one dozen pens?
(A) Rs.200
(B) Rs.250
(C) Rs.300
(D) Rs.780
(E) None of these
Rationale: Explanation:
Let the cost of one pen is ‘5x’ and pencil is ‘x’
3 X 5x + 5x = Rs.260
15x + 5x = Rs.260
X = 260/20 = 13
:. Cost of 1 pen = 5x = 5 x 13 = 65
:. Cost of 12 pens, i.e. (one dozen) = 65 x 12 = Rs.780
Answer: Option D
Answer: (D) Rs.780
Question: In 10 years, P will be as old as Q is now. Fifteen years ago, Q was twice as old as P was then. How old is P now?
(A) 17
(B) 18
(C) 21
(D) 25
(E) 30
Rationale: Q = P+10
Q-15 = 2(P-15)
P-5 = 2P-30
P = 25
The answer is D.
Answer: (D) 25
Question: A man can row downstream at the rate of 16 Km/hr and upstream at 8 Km/hr. Find man's rate in still water and the rate of current?
(A) 12,4
(B) 6,3
(C) 9,3
(D) 6,6
(E) None of these
Rationale: Explanation:
Rate of still water = 1/2 (16 + 8) = 12 Km/hr
Rate of current = 1/2 (16-8) = 4 Km/hr
Answer: Option A
Answer: (A) 12,4
Question: Harkamal purchased 8kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
(A) 1055
(B) 1065
(C) 1070
(D) 1075
(E) 1080
Rationale: Cost of 8 kg grapes = 70 × 8 = 560.
Cost of 9 kg of mangoes = 55 × 9 = 490.
Total cost he has to pay = 560 + 490 = 1055
A
Answer: (A) 1055
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
(A) 200 m
(B) 178 m
(C) 186 m
(D) 168 m
(E) 150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 12
= 200 m
Answer:A
Answer: (A) 200 m
Question: Pipe A can fill a tank in 60 min . There is a second pipe in the bottom of the cistern to empty it. If all the two pipes are simultaneously opened, then the cistern is full in 180 min. In how much time, the second pipe alone can empty the cistern?
(A) 60 min
(B) 45 min
(C) 90 min
(D) 70 min
(E) 30 min
Rationale: Work done by the third pipe in 1 min = 1/180 - (1/60) = - 1/45.
[-ve sign means emptying]
The third pipe alone can empty the cistern in 45 min.
ANSWER:B
Answer: (B) 45 min
Question: What is the dividend. divisor 15, the quotient is 9 and the remainder is 5?
(A) A)140
(B) B)134
(C) C)148
(D) D)158
(E) E)160
Rationale: D = d * Q + R
D = 15 * 9 + 5
D = 135 + 5
D = 140
Answer A
Answer: (A) A)140
Question: What is the Mode of the following data set M- {5,4,5,5,6,6,5,7,8,9}
(A) 5
(B) 4
(C) 6
(D) 7
(E) 9
Rationale: Mode of a set is the data point that is repeated the most number of times. In the set given,5 is repeated
Answer: A
Answer: (A) 5
Question: A train running at the speed of 60 km/hr crosses a pole in 21 sec. What is the length of the train?
(A) 350 m
(B) 490 m
(C) 115 m
(D) 210 m
(E) 150 m
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 21 = 350 m
Answer: A
Answer: (A) 350 m
Question: ABCE is an isosceles trapezoid and ACDE is a rectangle.AB=10 and EC=20.What is the length of AE.
(A) 5
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: As ABCE is an isosceles trapezoid and EC is twice times AB, we can consider the given trapezoid as half of a regular hexagon(as length of diagonal in regular hexagon is always double the side).
Thus, sides AB=AE=BC. => AE = 10.
ANSWER:B
Answer: (B) 10
Question: The length of the bridge, which a train 160 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 876 m
(B) 157 m
(C) 215 m
(D) 156 m
(E) 167 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (160 + x)/30 = 25/2
=> 2(160 + x) = 750 => x
= 215 m.
Answer: C
Answer: (C) 215 m
Question: What is the dividend. divisor 17, the quotient is 9 and the remainder is 5
(A) 134
(B) 136
(C) 140
(D) 158
(E) 160
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: (D) 158
Question: A company bought for its 7 offices 2 computers of brand N and 3 computers of brand M. In how many ways could computers be distributed among the offices if each office can have only 1 computer.
(A) 196
(B) 210
(C) 256
(D) 292
(E) 312
Rationale: I solved it in a slightly different way. I would love feedback on the logic.
Again, this is a comb problem. So I though of it as follows.
From the seven offices, there will be 5 'winners' (of PCs) and 2'losers'. The number of ways they could be winners and losers is 7!/(5!2!) = 21
For the five winners, the 5 computers can be distributed in 5!/(2!3!) ways = 10.
If you have trouble seeing this, think of anagrams NNMMM (so 5! ways of ordering them but divide by 2! because 2 Ns are similar and 3! because 3 'M's are similar.)
The number of different combinations is then 21*10 = 210 -> B.
Answer: (B) 210
Question: In how many ways can the letters in mmmnnnppqq can be arranged with two n's together?
(A) 15120 ways
(B) 16120 ways
(C) 14120 ways
(D) 13120 ways
(E) 12120 ways
Rationale: MMMN(NN)PPQQ so taking two N's together we can get =9!/(3!*2!*2!) arrangements
bow this NN can be arranged in =2!/2!=1 ways
so total arrangements=9!/(3!*2!*2!)=15120 ways
ANSWER:A
Answer: (A) 15120 ways
Question: The product of two numbers is 168 and the sum of these two numbers is 26. What is the largest of these two numbers?
(A) 22
(B) 77
(C) 88
(D) 12
(E) 62
Rationale: Let the numbers be x and (26 – x).
Therefore, x (26 – x) = 168
x2 – 26x + 168 = 0
(x – 14) (x – 12) = 0
x = 14 or x = 12
So, the numbers are 14 and 12.
ANSWER: D
Answer: (D) 12
Question: A rectangular grass field is 70 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 1350
(B) 1971
(C) 9676
(D) 1300
(E) 2691
Rationale: Area = (l + b +2d) 2d
= (70 + 55 +2.5 * 2) 2*2.5 => 650
650 * 2 = Rs.1300
Answer:D
Answer: (D) 1300
Question: Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?
(A) 27 sec
(B) 87 sec
(C) 67 sec
(D) 47 sec
(E) 36 sec
Rationale: Explanation:
Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 400 / (20 + 20)5/18 = 400 x 18 / 40 x 5 = 36 seconds.
Answer: E
Answer: (E) 36 sec
Question: A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ?
(A) 3
(B) 10
(C) 20
(D) 39
(E) None of these
Rationale: 3 socks must be taken out to be sure that he has a matching pair .
ANSWER:A
Answer: (A) 3
Question: If the number 52,1n7, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
(A) 7
(B) 5
(C) 2
(D) 1
(E) 0
Rationale: The sum of the digits 5 + 2 + 1 + n + 7 must be a multiple of 3
15 + n must be a multiple of 3
substituting the numbers n must = 0
Aswer E
Answer: (E) 0
Question: For any number Z, Z* is defined as the greatest positive even integer less than or equal to y. What is the value of 6.15 – 6.15*?
(A) 1.5
(B) 0.15
(C) 6.25
(D) 0.25
(E) 6.0
Rationale: Since Z* is defined as the greatest positive even integer less than or equal to Z, then 6.15* =6 (the greatest positive even integer less than or equal to 6.15 is 6).
Hence, 6.15 – 6.15* = 6.15 - 6 = 0.15
Answer: B.
Answer: (B) 0.15
Question: The first doughnut is priced at $1 and then if you purchase additional doughnuts as dozens then the price is $6/dozen. What is the total number of doughnuts purchased if you paid $26?
(A) 50
(B) 52
(C) 54
(D) 56
(E) 58
Rationale: $26 = 4 * $6 + $2
The number of doughnuts is 4*12 + 2 = 50
The answer is A.
Answer: (A) 50
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 50 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
(A) 160
(B) 275
(C) 360
(D) 440
(E) 560
Rationale: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 50.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*50 = 225.
Total area = 50 + 225 = 275.
Answer: B.
Answer: (B) 275
Question: The ratio of the present ages of a man and his wife is 4 : 3. Which of the following can't be a possible ratio of their ages 30 years ago?
(A) 2: 4
(B) 3: 4
(C) 4:4
(D) 5: 4
(E) 6: 4
Rationale: 4x-30/3x-30 = 5/4
Therefore x=-30
Age cannot be negative.
Answer: D
Answer: (D) 5: 4
Question: A can do a piece of work in 5 hours; B and C together can do it in 4 hours, while A and C together can do it in 3 hours. How long will B alone take to do it?
(A) 60/7 hours
(B) 70/6 hours
(C) 35/2 hours
(D) 90.8 hours
(E) none of the above
Rationale: A's 1 hour's work = 1/5 ;
(B + C)'s 1 hour's work = 1/4 ;
(B + C)'s 1 hour's work = 1/3
(A + B + C)'s 1 hour's work = (1/5 + 1/4) = 9/20
B's 1 hour's work = (9/20 - 1/3) = 7/60
B alone will take 60/7 hours to do the work.
Answer = A
Answer: (A) 60/7 hours
Question: A contractor undertakes to built a walls in 50 days. He employs 70 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time?
(A) 105
(B) 30
(C) 35
(D) 20
(E) None of these
Rationale: 70 men complete 0.4 work in 25 days.
Applying the work rule, m1 × d1 × w2 = m2 × d2 × w1
we have,
70 × 25 × 0.6 = m2 × 25 × 0.4
or m2 = 70×25×0.6/25×0.4 = 105 men
AnswerA
Answer: (A) 105
Question: 8 x 2.4 - 5 x 1.4/1.5 = ?
(A) 9.46
(B) 2.03
(C) 50.4
(D) 14.65
(E) 12.85
Rationale: Given Expression
= (19.2- 5 X 1.4)/1.5
= 14.2/1.5
= 14.2/1.5
= 9.46
Answer is A
Answer: (A) 9.46
Question: A certain kind of necklace is made from 9 blue, 6 red, and 3 pink beads. What is the maximum number of these necklaces that can be made from 54 beads of each color ?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Atleast 9 blue breads are needed to make a necklace, so irrespective of the combinations of red and pink beads, the number of necklaces that can be formed will be
54/9 =6
Answer:- B
Answer: (B) 6
Question: A bag contains 3 red, 5 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?
(A) 9/16
(B) 7/18
(C) 12/55
(D) 14/67
(E) 19/87
Rationale: Total number of balls = 3+5+4 = 12
n(S) = 12C3 = 12*11*10 / 3*2 = 220
n(E) = 4C2* 8C1 = 6*8 = 48
Probability = 48/220 = 12/55
Answer is C
Answer: (C) 12/55
Question: George can do a piece of work in 8 hours. Paul can do the same work in 10 hours, Hari can do the same work in 12 hours. George, paul and hari start the same work at 9 am, while george stops at 11 am, the remaining two complete the work. What time will the work complete?
(A) 12:00 Pm
(B) 1:00 Pm
(C) 2:00 Pm
(D) 3:00 Pm
(E) 4:00 Pm
Rationale: ((1/8)+(1/10)+(1/12))2+((1/10)+(1/12))(x-2)=1
x=4 hrs
work started at 9 am..
takes 4 hrs to complete 9am + 4hrs =1:00 Pm
ANSWER:B
Answer: (B) 1:00 Pm
Question: A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230 m
(B) 240 m
(C) 260 m
(D) 320 m
(E) 330 m
Rationale: Relative speed = (120 + 80) km/hr
=	(200 x(5/18))m/sec
=	(500/9)m/sec.
Let the length of the other train be x metres.
Then,	(x + 270)/9 = 500/9
x + 270 = 500
x = 230.
A
Answer: (A) 230 m
Question: If A lends Rs.2800 to B at 15% per annum and B lends the same sum to C at 18.5% per annum then the gain of B in a period of 3 years is?
(A) 294
(B) 289
(C) 240
(D) 233
(E) 200
Rationale: (2800*3.5*3)/100
=> 294
Answer: A
Answer: (A) 294
Question: The number of meters in QB is equal to the square root of the number of centimeters in QB. What is the length of QB (1 meter=100 centimeters)?
(A) 100 meters
(B) 10 meters
(C) 100 centimeters
(D) 10 centimeter
(E) 1 centimeter
Rationale: I'd plug in the options for this question.
Check option A: if the number of meters in QB is 100, then the number of centimeters is 100*100. The square root of 100*100 is 100: 100 = 100.
Answer: A.
Answer: (A) 100 meters
Question: From the integer n, if n*n*n*n*n is odd, then what is true from below options?
(A) n*n is odd
(B) n is odd and n*n*n is even
(C) n is even
(D) n is odd
(E) n*n is even
Rationale: n is odd and n*n is even
Option B
Answer: (B) n is odd and n*n*n is even
Question: The smallest prime number in the list:
(A) 5
(B) 7
(C) 10
(D) 14
(E) 18
Rationale: A
5
Answer: (A) 5
Question: A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(A) 4%
(B) 6%
(C) 6.4%
(D) 7%
(E) 8.2%
Rationale: C
6.4%
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (C) 6.4%
Question: The areas, in kilometers squared, of some countries are given below. USA: 9,629,091, Russia: 17,098,242, China: 9,598,094, Canada: 9,984,670, the UK: 242,400 and India: 3,287,263.
What is the difference between the areas of Russia and China?
(A) 5,500,148 kilometers squared
(B) 8,500,148 kilometers squared
(C) 7,500,148 kilometers squared
(D) 6,500,148 kilometers squared
(E) 3,500,148 kilometers squared
Rationale: he difference between the areas of Russia and China is given by
17,098,242 - 9,598,094 = 7,500,148 kilometers squared
correct answer C
Answer: (C) 7,500,148 kilometers squared