mathewhe/aqua_rat huggingface dataset:
Question: To fill a tank, 200 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-fifths of its present ?
(A) 50
(B) 100
(C) 150
(D) 200
(E) 250
Rationale: Let the capacity of 1 bucket = x.
Then, the capacity of tank = 200x.
New capacity of bucket = 4/5 x
Therefore, Required number of buckets = (200x)/(4x/5)
= (200x) x 5/4x
= 1000/4
= 250
Answer is E.
Answer: (E) 250
Question: A photographer is to take group photographs of a class of students for the school magazine such that each photograph should have five students. If there are four girls and four boys in the class and each photograph must not have two girls or two boys standing together, how many different photographs can the photographer take?
(A) 80
(B) 288
(C) 44
(D) 576
(E) 288^2
Rationale: Case-1: 3 Boys and 2 Girls are taken
Selection of 3 boys and 2 girls can be done in 4C3 * 4C2
Arrangement will look like B G B G B and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways = 12 ways
No. of arrangement = 4C3 * 4C2 *3!*2! = 4*6*12 = 288
Case-2: 2 Boys and 3 Girls are taken
Selection of 2 boys and 3 girls can be done in 4C2 * 4C3
Arrangement will look like G B G B G and Such arrangement of 5 individual can be done in desired manner in 3!*2! ways = 12 ways
No. of arrangement = 4C2 * 4C3 *3!*2! = 4*6*12 = 288
Total Ways of Taking Photograph of 5 in desired manner = 288 + 288 = 576 ways
Answer: Option D
Answer: (D) 576
Question: Arabica coffee costs $0.6 per ounce while Robusta coffee costs $0.5 per ounce. If the blend of Arabica and Robusta costs $0.55 per ounce, what is the share of Arabica in this blend?
(A) 20%
(B) 24%
(C) 30%
(D) 50%
(E) 40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.6a + .5(1-a) = .55
.6a + .5 - .3a = .55
a= .5
therefore: .5/1 ounce = 50%. Therefore, the answer should be D
Answer: (D) 50%
Question: A rope of which a calf is tied is increased from 12 m to 23 m, how much additional grassy ground shall it graze?
(A) 1217
(B) 1219
(C) 1210
(D) 1212
(E) 1312
Rationale: π (232 – 122) = 1210
Answer:C
Answer: (C) 1210
Question: A local bank that has 18 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 18 codes?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Add one more integer: 5
55, 15, 51, 25, 52, 35, 53,54,45 = 9 Codes
Total = 25 Codes. Enough.
Answer: C
Answer: (C) 5
Question: Which of the following inequalities is equivalent to 40 + 6x > -3x - 11x + 20?
(A)  x < 1
(B)  x < -1
(C)  x < 3
(D)  x < -3
(E)  x < 4
Rationale: You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
40 + 6x > -3x - 11x + 20
40 + 20 > - 20x (Correct)
60 > - 20x (Correct)
-3 > x (Correct)
the correct option is D
Answer: (D)  x < -3
Question: Find the average of the first 21 natural numbers?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Average of the first 'n' natural numbers = (n + 1)/2
We get (21+ 1)/2 = 11
ANSWER:D
Answer: (D) 11
Question: For a finite sequence of non zero numbers, the number of variations in the sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The questions basically asks: how many pairs of consecutive terms are there in the sequence such that the product of these consecutive terms is negative.
1*(-3)=-3=negative;
-3*2=-6=negative;
5*(-6)=-30=negative.
So there are 3 pairs of consecutive terms.
Answer: C.
Answer: (C) 3
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How
many days will 5 women and 10 children take to complete the work?
(A) 6 days
(B) 7 days
(C) 8 days
(D) 9 days
(E) None of these
Rationale: Explanation:
1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work =
(570+10140)=17
So 5 women and 10 children will finish the work in 7 days
Answer: B
Answer: (B) 7 days
Question: Peter traveled the entire 50 miles trip. If he did the first 12 miles of at a constant rate 36 miles per hour and the remaining trip of at a constant rate 48 miles per hour, what is the his average speed, in miles per hour?
(A) 20mph
(B) 24mph
(C) 30mph
(D) 38mph
(E) 40mph
Rationale: Average speed=sum of distance/sum of time. If he travelled the first 12 miles at 36 miles/hr, it would take 0.3 hr. For the remaining trip, if he went at 48 miles/1hr, it would take 1 hour. Then, the average speed is 50miles/(0.3+1)hrs=38miles/1hr.
Therefore, the answer is D.
Answer: (D) 38mph
Question: During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons. If Kim purchased 15 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount?
(A) 80%
(B) 100%
(C) 116.7%
(D) 120%
(E) 180%
Rationale: Kim purchased 15 gallons of gas. She paid for 10 + 0.9*5 = 14.5 gallons, so the overall discount she got was 0.5/15 = 3.33%.
Isabella purchased 25 gallons of gas. She paid for 10 + 0.9*15 = 23.5 gallons, so the overall discount she got was 1.5/25 = 6%.
6 is 6/3.33*100 = 180% of 3.33.
Answer: E.
Answer: (E) 180%
Question: What is the least number of squares tiles required to pave the floor of a room 6 m 75 cm long and 4 m 5 cm broad?
(A) 15
(B) 20
(C) 40
(D) 44
(E) 54
Rationale: Length of largest tile = H.C.F. of 675 cm and 405 cm = 135 cm.
Area of each tile = (135 x 135) cm2.
Required number of tiles =675 x 405/(135^2)= 15
ANSWER:A
Answer: (A) 15
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2354
(B) 2644
(C) 2645
(D) 4577
(E) 5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) 5184
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 36 hours respectively. The ratio of their speeds is?
(A) 3:6
(B) 6:3
(C) 4:9
(D) 4:4
(E) 4:2
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= âˆšb : âˆša = âˆš36 : âˆš9 = 6:3.Answer: B
Answer: (B) 6:3
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 62.5
(B) 69.5
(C) 62.3
(D) 62.1
(E) 62.4
Rationale: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer:A
Answer: (A) 62.5
Question: The retirement plan for a company allows employees to invest in 10 different mutual funds. Six of the 10 funds grew by at least 10% over the last year. If Sam randomly selected 4 of the 10 funds, what is the probability that 3 of Sam’s 4 funds grew by at least 10% over last year?
(A) 6C3 / 10C4
(B) 6C3 * 4C1 / 10C4
(C) 6C3 * 4C1 / 10P4
(D) 6P3 * 4P1 / 10C4
(E) 6P3 * 4P1 / 10P4
Rationale: Total funds = 10
>10% = 6
<10% = 4
Question: Prob to pick 4 funds (3>10% and 1> 10%)
Option 1: Pick 3 out of 6 = 6C3 = 20
Option 2: Pick 1 out of 4 = 4C1 = 4
Total # = 4C10 = 210
Probability = Option1∗Option2/Total
or "B"
Answer: (B) 6C3 * 4C1 / 10C4
Question: A person buys an article at $200. At what price should he sell the article so as to make a profit of 10%?
(A) 240
(B) 260
(C) 220
(D) 300
(E) 360
Rationale: C
220
Cost price = $200
profit = 10% of 200 = $20
Selling price = Cost price + Profit
= 200 + 20 = 220
Answer: (C) 220
Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
(A) 2x2 – 3xy + y2
(B) (2x + y)(x – y)
(C) (x – y)2 + x(x – y)
(D) (2x – y)2 – x(2x – y)
(E) (2x – y)2 – 2x2 + xy
Rationale: Other parts are equal to
2x2 + y2 – 3xy.
Answer B
Answer: (B) (2x + y)(x – y)
Question: A retailer buys a radio for Rs 225. His overhead expenses are Rs 30. He sellis the radio for Rs 300. The profit percent of the retailer is
(A) 10%
(B) 50%
(C) 25%
(D) 17.6%
(E) None of these
Rationale: Explanation:
cost price = (225 + 30) = 255 sell price = 300
gain = (45/255)*100 = 17.6%. Answer: D
Answer: (D) 17.6%
Question: what is the sum of the first 10 odd natural numbers
(A) 300
(B) 400
(C) 500
(D) 600
(E) 100
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 10 odd natural numbers=(10)^2=100
ans 100
ANSWER:E
Answer: (E) 100
Question: Albert borrowed a total of $ 6000 from Brian and Charlie. He paid simple interest at the rate of 7 % Per yr and 9 % per yr respectively.At the end of three years he paid $ 1400 as total interest. What is the interest paid to Brian at the end of three years?
(A) 825
(B) 790
(C) 795
(D) 785
(E) 770
Rationale: Let x be the amount borrowed form Brian. So amount borrowed form Charlie = 6000-x.
1400 = 21/100x + 27/100(6000-x)
=>x = 22000/6.
Interest paid = 3*7/100*22000/6 = 770.
E
Answer: (E) 770
Question: A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ?
(A) 140 meter
(B) 145 meter
(C) 150 meter
(D) 155 meter
(E) 160 meter
Rationale: Explanation:
Let the length of the train is x meter and Speed of the train is y meter/second
Then x/y = 15 [because distance/speed = time]
=> y = 15/x
x+100/25 =x/15
x=150 meters
So length of the train is 150 meters
ANSWER IS C
Answer: (C) 150 meter
Question: A starts business with Rs.3500 and after 10 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Bâ€™s contribution in the Capital ?
(A) 24887
(B) 20778
(C) 23788
(D) 31500
(E) 2811
Rationale: Explanation:
A invested Rs.3500 for 12 months.
Let B joined with investment x. And he invested for 12 - 10 = 2 months.
So there profit ratio = (3500 Ã— 12) : (2x) = 2 : 3
â‡’ x = 31500
Answer: D
Answer: (D) 31500
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 6 employees to 2 different offices?
(A) 64
(B) 65
(C) 44
(D) 43
(E) 56
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 2*2*2*2*2*2=2^6=64.
Answer: A.
Answer: (A) 64
Question: The average age of M boys is ‘b’ years and of ‘n’ girls ‘c’ years. The average age of all together is?
(A) (mb + nc)/ (m + m) years
(B) (mb + nc)/ (n + n) years
(C) (mb + nc)/ (m + n) years
(D) (mb + nn)/ (m + n) years
(E) (mn + nc)/ (m + n) years
Rationale: (mb + nc) / (m+ n)
Answer:C
Answer: (C) (mb + nc)/ (m + n) years
Question: From the sale of sleeping bags, a retailer made a gross profit of 17% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
(A) 3.0
(B) 3.36
(C) 23.93
(D) 25.0
(E) 31.36
Rationale: Cost price * 1.17 = Selling price --> Cost price * 1.17= $28 --> Cost price = $23.93.
Answer: C.
Answer: (C) 23.93
Question: Ronika deposited Rs.7000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much ?
(A) 9850
(B) 9500
(C) 9620
(D) 9760
(E) 9100
Rationale: Explanation:
As the interest rate increases by 2%
=> (7000x3x2)/100 = 420
9200
--------
9620
ANSWER IS C
Answer: (C) 9620
Question: A train speeds past a pole in 50 seconds and a platform 500 m long in 100 seconds. Its length is:
(A) 550 m.
(B) 300 m.
(C) 600 m.
(D) 400 m.
(E) 500 m.
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 50 => y = x/50
x + 500 / 100 = x / 50
x = 500 m.
Answer: Option E
Answer: (E) 500 m.
Question: Raman,Lakshmi and Muthu enter into partnership. Raman invests some money at the beginning, Lakshmi invests double the amount after 6 months, and Muthu invests thrice the amount after 8 months. If the annual gain be Rs.36000. Lakshmi's share is?
(A) 12000
(B) 14000
(C) 8000
(D) 5000
(E) 3000
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 36000 = 12000
Answer: A
Answer: (A) 12000
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 25
(B) 28
(C) 20
(D) 21
(E) 18
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer:C
Answer: (C) 20
Question: A man can do a piece of work in 8days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone?
(A) 5
(B) 5 1/2
(C) 4 4/5
(D) 6
(E) 9 1/2
Rationale: Son's 1day work = 1/3 - 1/8 = 5/24
Son alone can do the work in 24/5days = 4 4/5 days
Answer is C
Answer: (C) 4 4/5
Question: If f > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - f) =
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4
(E) 1
Rationale: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have f-x=2t. So y-x=-t, y-f=-3t. ---> (y - x)/(y - f) = 1/3.
The answer is (B).
Answer: (B) 1/3
Question: A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son (in years) is
(A) 12
(B) 15
(C) 18
(D) 20
(E) 22
Rationale: Explanation:
Let son's age be x years. Then, father's age = (3x) years.
Five years ago, father's age = (3x - 5) years and son's age = (x - 5) years.
So, 3x - 5 = 4 (x - 5) 3x - 5 = 4x - 20 x = 15.
Answer: B
Answer: (B) 15
Question: Two trains each 260 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively. In what time will they cross each other completely?
(A) 15 sec
(B) 19 sec
(C) 12.48 sec
(D) 10 sec
(E) 11 sec
Rationale: Explanation:
D = 260 m + 260 m = 520 m
RS = 80 + 70 = 150 * 5/18 = 125/3
T = 520 * 3/125 = 12.48 sec
Answer: Option C
Answer: (C) 12.48 sec
Question: We have boxes colored either red or blue. In each blue box there is a fixed number of blueberries. In each red box there is a fixed number of strawberries. If we dispose of one blue box for one additional red box, the total number of berries would increase by 12, and the difference between the total number of strawberries and the total number of blueberries would increase by 76. Each blue box contains how many blueberries?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Let x be the number of blueberries in each blue box.
Then there are x+12 strawberries in each red box.
x+(x+12)=76
x = 32
The answer is D.
Answer: (D) 32
Question: The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
(A) 277
(B) 665
(C) 287
(D) 208
(E) 268
Rationale: 8 * 84 = 672 – 7
= 665
Answer:B
Answer: (B) 665
Question: What is the normal price of an article sold at $108 after two successive discounts of 10% and 20%?
(A) $130
(B) $140
(C) $150
(D) $160
(E) $170
Rationale: 0.8*0.9*cost price = $108
cost price = $150
The answer is C.
Answer: (C) $150
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
(A) 25
(B) 31
(C) 27
(D) 29
(E) 39
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
=> 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39
Answer is E.
Answer: (E) 39
Question: How many seconds will a 450 metre long train take to cross a man running with a speed of 6 km/hr in the direction of the moving train if the speed of the train is 60 km/hr?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 60
Rationale: Explanation :
Speed of train relatively to man = ( 60 - 6)km/hr
= 54 km /hr
= (54 x 5 / 18)m/sec
= 15 m/sec
Time taken to pass the man = (450 / 15)sec = 30 sec.
Answer : B
Answer: (B) 30
Question: A bakery orders a shipment of apples and uses them all to make 150 apple pies. On slow days it takes 6 hours to sell all 150 apple pies. On busy days they sell 200 pies in 6 hours. Calculate how many hours one shipment of apples will last on a busy day.
(A) 6.2
(B) 5
(C) 4.5
(D) 4.2
(E) 3.8
Rationale: First set up a ratio with all the relevant values and also the unknown variable:
150*6 = 200*x
Now solve by multiplying 150 by 6 and then dividing that product by 200:
150*6 = 900
900/200 = x
x = 4.5 hours
Answer: C
Answer: (C) 4.5
Question: If 13 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) 143 days.
(C) 149 days.
(D) 148 days.
(E) 67 days.
Rationale: B
143 days.
From the above formula i.e (m1*t1/w1) = (m2*t2/w2)
so (13*6*88/1) = (6*8*d/1)
on solving, d = 143 days.
Answer: (B) 143 days.
Question: A’s speed is 22/19 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
(A) 1/22
(B) 1/19
(C) 3/19
(D) 2/19
(E) 3/22
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 22 meters, B covers 19 meters in that time. So if the race is 22 meters long, when A reaches the finish line, B would be 3 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 3 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 22 meters) would be the same as the time required by B (to cover 19 meters) to reach the finish line.
So B should get a head start of 3/22th of the race.
Answer (E)
Answer: (E) 3/22
Question: On a business trip, 30 percent of 60 sales representatives will be given accommodations at Hotel XYZ and the remaining 70 percent will be given accommodations at Hotel ABC. However, 55 percent of the sales representatives prefer to stay at Hotel XYZ and 45 percent prefer to stay at Hotel ABC. What is the highest possible number of sales representatives NOT given accommodations at the hotel they prefer?
(A) 72
(B) 52
(C) 66
(D) 90
(E) 51
Rationale: We were asked to find number of maximum possible people who were accommodated at hotels they dont prefer,
So for 18 XYZ accommodations , we can choose 18 ABC preferring people (so xyz is filled up) Here 18 were given to people who don't prefer XYZ
for 42 ABC accommodations, we can choose 33 ABC preferring people and rest to ABC. Here 33 were given to people who don't prefer ABC.
So total people who were accommodated at hotel they don't prefer = 18+33 = 51
Answer: E
Answer: (E) 51
Question: A can do a job in 16 days and B can do it in 30 days. A and B working together will finish twice the amount of work in ------- days?
(A) 28 4/5 days
(B) 25 4/5 days
(C) 22 4/5 days
(D) 20 4/5 days
(E) 21 4/5 days
Rationale: 1/16 + 1/30 = 46/480 =23/240
240/23=11 2/5 *2 = 22 4/5 days
ANSWER:C
Answer: (C) 22 4/5 days
Question: Evaluate: |4 - 8(3 - 12)| - |5 - 11| =
(A) 49
(B) 55
(C) 69
(D) 70
(E) 82
Rationale: According to order of operations, inner brackets first. Hence
|4 - 8(3 - 12)| - |5 - 11| = |4 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |4 + 72| - |5 - 11|
= |76| - |-6|
= 76 - 6 = 70
correct answer D)70
Answer: (D) 70
Question: If 18 percent of the students at a certain school went to a camping trip and took more than $100, and 75 percent of the students who went to the camping trip did not take more than $100, what percentage of the students at the school went to the camping trip?
(A) 95
(B) 90
(C) 85
(D) 78
(E) 72
Rationale: Let x be the number of students in the school. 0.18x students went to the trip and took more than 100$. They compose (100-75)=25% of all students who went to the trip. Therefore the toal of 0.18x/0.25=0.72x students went to the camping which is 72%.
The answer is E
Answer: (E) 72
Question: A shipment of 8 television sets contains 2 black-and-white sets and 6 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set?
A.
B.
C.
D.
E. 13/28
(A) 1/7
(B) 1/4
(C) 5/14
(D) 11/28
(E) 13/28
Rationale: Total cases 8C2 - Selecting 2 from set of 8
Atleast one b/w means 1 b/w and 1 color or both b/w
(2C1*6C1 + 2C2)/8C2 = 13/28
the answer choices are correct E!!
Answer: (E) 13/28
Question: Two train each 500 m long, are running in opposite directions on parallel tracks. If their speeds are 45 km/hr and 30 km/hr respectively, the time taken by the slower train to pass the driver of the faster one is?
(A) 20s
(B) 24s
(C) 22s
(D) 23s
(E) 21s
Rationale: Relative speed = 45+30 = 75 km/hr = 750/36 m/s = 125/6 m/s
We are calculating the time taken by the slower train to pass the driver of the faster one
.Hence the distance = length of the smaller train = 500 m
Time = distance/speed = 500/(125/6) = 24 s
Answer is B.
Answer: (B) 24s
Question: There are 4 red shoes, 3 green shoes. If one draw randomly a shoe what is the probability of getting a red shoe
(A) 1/9
(B) 2/9
(C) 4/7
(D) 4/9
(E) 2/3
Rationale: total 7 from take one.
7c1=7
red 4 from one
4c1=4
4/7
ANSWER:C
Answer: (C) 4/7
Question: A speed of 7 metres per second is the same as :
(A) 28.64 km/hr
(B) 22 km/hr
(C) 30 km/hr
(D) 25.2 km/hr
(E) None
Rationale: Sol.
7 m/sec = [7 * 18/5] km/hr = 25.2 km/hr.
Answer D
Answer: (D) 25.2 km/hr
Question: If A:B is 3:4 and B:C is 4:5 then A:C is equal to
(A) 1:3
(B) 3:5
(C) 3:4
(D) 3:7
(E) 1:5
Rationale: The two ratios given are having the same number 4 for B in both the ratios.
Hence- A:B = 3:4 B:C = 4:5
=> A:C = 3:5
Answer B
Answer: (B) 3:5
Question: A bicyclist's wheel has a circumference of 2 meters. if the bicyclist covers 20 meters in 5 hours at a constant speed, how many rotations does the wheel make per hour at that speed?
(A) 2
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: The bicyclist covers y meters in t hrs. So he covers y/t meters in one hour.
To cover y/t meters, the bicycle's wheel went round and round that is, multiple times, the wheel completed one circumference on the road. How many times did it complete one full rotation. Since the circumference is x, the number of times it completes the circumference is y/xt.
given : x=2; y=20 and t=5
hence y/xt =20/2*5=2
Answer (A)
Answer: (A) 2
Question: A train travels from New York to Chicago, a distance of approximately 480 miles, at an average rate of 60 miles per hour and arrives in Chicago at 5:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
(A) 10:00
(B) 4:00
(C) 5:00
(D) 6:00
(E) 7:00
Rationale: 5:00 in evening in Chicago = 6:00 in evening in New York. So, the train was in Chicago 6:00 in the evening, New York time.
The trip took T=D/R=480/60=8 hours. Therefore, the train depart from New York at 6:00 - 8 hours = 10:00 in the morning, New York time.
Answer: A.
Answer: (A) 10:00
Question: Sohan ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class ?
(A) 43
(B) 31
(C) 32
(D) 37
(E) 35
Rationale: C
32
Clearly, number of students in the class
= (6 + 1 + 25) = 32
Answer: (C) 32