mathewhe/aqua_rat huggingface dataset:
Question: Anand and Deepak started a business investing Rs. 27,500 and Rs. 33,000 respectively. Out of a total profit of Rs. 15,000, Deepak's share is?
(A) Rs. 8181.81
(B) Rs. 8900
(C) Rs. 8400
(D) Rs. 3400
(E) Rs. 8440
Rationale: Ratio of their shares = 27500 : 33000 = 5 : 6
Deepak's share = 15000 * 6/11 = Rs. 8181.81
Answer:A
Answer: (A) Rs. 8181.81
Question: At a dinner party, 4 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
(A) 6
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: Soln: Since the arrangement is circular and 2 seating arrangements are considered different only when the positions of the people are different relative to each other, we can find the total number of possible seating arrangements, by fixing one person's position and arranging the others.
Thus if one person's position is fixed, the others can be arranged in 3! =6 ways.
Ans is A.
Answer: (A) 6
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 89
(B) 23
(C) 56
(D) 79.2
(E) 67
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer: Option D
Answer: (D) 79.2
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
(A) 4 litres, 8 litres
(B) 6 litres, 6 litres
(C) 5 litres, 7 litres
(D) 7 litres, 4 litres
(E) None
Rationale: Let the cost of 1 litre milk be Re. 1
Milk in 1 litre mix. in 1st can = 3/4 litre, C.P. of 1 litre mix. in 1st can Re. 3/4
Milk in 1 litre mix. in 2nd can = 1/2 litre, C.P. of 1 litre mix. in 2nd can Re. 1/2
Milk in 1 litre of final mix. = 5/8 litre, mean price = Re. 5/8.
Ratio of two mixtures = 1/8 : 1/8 = 1:1.
So, quantity of mixture taken from each can = (1/2 X 12) = 6 litres.
Answer B
Answer: (B) 6 litres, 6 litres
Question: what is the units digit of the expression 17^7-2?
(A) 1
(B) 2
(C) 3
(D) 7
(E) 9
Rationale: 7^1=7
7^2=49
7^3=343
7^4=1(last digit)
7^5=7(last digit) and the cycle repeats after every 4 powers
Therefore, last digit of 17^7=3
3-2=1
Answer A
Answer: (A) 1
Question: Which of the following points falls outside of the region defined by 2y≤6x−17?
(A) (5, 1)
(B) (3, -8)
(C) (2, 0)
(D) (1, -2)
(E) (0, -14)
Rationale: Equation given is 2y<=6x-12
Simplifying this; y<=3x-6
Plug in the values provided in the options,
A. 1<=11
B. -8<=3
C. 0<=0
D.-2<=-4
E. -14<=-12
Option D is the answer.
Answer: (D) (1, -2)
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
(A) 500
(B) 342
(C) 250
(D) 362
(E) 879
Rationale: Explanation:
400*(90/100)*(95/100) = 342
Answer:B
Answer: (B) 342
Question: How many Books each of Volume 100 meter cube can be packed into a crate of volume 4000 meter cube?
(A) 100
(B) 120
(C) cannot be determined
(D) 180
(E) 200
Rationale: Gud question with a simple concept.
In geo if we want to insert one shape into another we need to know the dimensions of the two shapes.
In above with volume given , we can come up with different shapes, so we cant know the answer
For ex :4000 m3 can be 400*10 or 40*100 or just 4000*1 we don't know , so we cant calculate
Answer : C
Answer: (C) cannot be determined
Question: 5years ago, the age of Anand was one-forth of the age of Bala at that time. The present age of Bala is 13 years more than the present age of Anand. Find the present age of Anand?
(A) 11
(B) 21
(C) 19
(D) 22
(E) 14
Rationale: Explanation:
Let the present ages of Anand and Bala be 'a' and 'b' respectively.
a - 5 = 1/3 (b - 5) --- (1)
b = a + 13
Substituting b = a + 8 in first equation,
a - 10 = 1/3 (a +8) => 3a - 30 = a + 8=> 2a = 38 => a = 19.
Answer: C
Answer: (C) 19
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 8 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18 hours
(B) 15/7 hours
(C) 80/13 hours
(D) 30/13 hours
(E) 30/43 hours
Rationale: Speed downstream = 20 + 8 = 28 kmph.
Time required to cover 60 km downstream
= d/s = 60/28
= 15/7 hours.
Answer: B
Answer: (B) 15/7 hours
Question: Simple interest on a sum at 2% per annum for 2 years is Rs.100. The C.I. on the same sum for the same period is?
(A) 101.8
(B) 101.4
(C) 101.2
(D) 100
(E) 110.2
Rationale: SI = 50 + 50
CI = 50 + 50 + 1.8 = 101.8
Answer: A
Answer: (A) 101.8
Question: Which of the following expressions CAN be equal to 0 when x^2 −16= 0 ?
(A) x^2 − 6x + 9
(B) x^2 − 4x + 3
(C) x^2 − x − 2
(D) x^2 − 7x + 6
(E) x^2 − 5x + 4
Rationale: x^2 − 16 = 0
x=-4 or x=4
Onle one choice results in a possibility of 0 when you plug in -4 or 4 for x except rest of all
x^2 − 5x + 4
Answer is E
Answer: (E) x^2 − 5x + 4
Question: If 100% of j is equal to 25% of k, 150% of k is equal to 50% of l, and 125% of l is equal to 75% of m, then 20% of m is equal to what percent of 200% of j ?
(A) 0.35
(B) 3.5
(C) 350
(D) 35
(E) 3500
Rationale: IMO answer should be 350...
consider j=10, then k=50, l=150 and m=350....
20% of 350, comes out to be 70....
200% of 10 is 20....
(70*100)/20=350....
Ans : C
Answer: (C) 350
Question: W and B are integers. The expression (W+1)(B+1) is even. What can be said about W and B?
(A) They are both even numbers.
(B) At least one of them is even.
(C) At least one of them is odd.
(D) They are both odd.
(E) Nothing can be said surly on W and B
Rationale: Odd x Odd = Odd
Odd x Even = Even
Even x Even = Even
To fulfill condition Either (W+1) or (B+1) needs to be Even
So either W or B needs to be odd
Or At least one of them is odd.
At least one of them is odd=C
Answer: (C) At least one of them is odd.
Question: Two friends want to buy a snack. They combine their money and find they have $4.15, consisting of quarters, dimes, and nickels. If they have 37 coins and the number of quarters is half the number of nickels, how many quarters do they have?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
Rationale: Let x be the number of quarters. Then 2x is the number of nickels.
(1) 25x + 10x + 10D = 415. Then 7x + 2D = 83
(2) 3x + D = 37. Then 6x + 2D = 74
Let's subtract equation (2) from equation (1).
x = 9
The answer is A.
Answer: (A) 9
Question: Bobby bought 2 shares, and which he sold for $96 each. If he had a profit of 25% on the sale of one of the shares but a loss of 28% on the sale of the other share, then on the sale of both shares Bobby had...
(A) a profit of 10
(B) a profit of 8
(C) a loss of 8
(D) a loss of 18
(E) neither a profit nor a loss
Rationale: Cost of the first stock: 96/1.25=76.8, so profit from it 96-76.8=19.2
Cost of the second stock: 96/0.72=133.33, so loss from it 96-133.33=-37.33
Overall loss 19.2 - 37.33=-18.13
Answer: D.
Answer: (D) a loss of 18
Question: Average monthly income of a family of 4 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 590. The income of the deceased was?
(A) Rs. 692.80
(B) Rs. 820
(C) Rs. 1170
(D) Rs. 1385
(E) None
Rationale: Answer
Income of the deceased = Total income of 4 members - total income of remaining 3 members.
= 735 x 4 - 590 x 3 Rs.
= 1170 Rs.
Correct Option: C
Answer: (C) Rs. 1170
Question: There are 14 cans in the refrigerator. 7 of them are red and 7 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
(A) 460
(B) 490
(C) 493
(D) 455
(E) 445
Rationale: Answer: C.
Answer: (C) 493
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses W at the restaurant? (Assume that all boxes are filled to capacity.)
(A) 96
(B) 240
(C) W=256
(D) W=384
(E) W=480
Rationale: Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
We're told that there are 2 types of boxes: those that hold 12 glasses and those that hold 16 glasses. Since the AVERAGE number of boxes is 15, we know that there MUST be at least some of each. We're also told that that there are 16 MORE of the larger boxes.
This means, at the minimum, we have...
1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can justadd 28suntil we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:
E
Answer: (E) W=480
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 7 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
(A) 2
(B) 4
(C) 5
(D) 40
(E) 160
Rationale: Actual miles/gallon is = 480/40 = 12 miles/gallon.
Current engine miles/gallon is 7 miles/gallon.
Additional 5 miles/gallon is required to match the actual mileage.
IMO option C.
Answer: (C) 5
Question: John has taken four (4) tests that have an average of 85. In order to bring his course grade up to a ‘B’, he will need to have a final average of 89. What will he need to average on his final two tests to achieve this grade?
(A) 87
(B) 90
(C) 92
(D) 97
(E) 98
Rationale: Traditional Method:
Total scored till now 85*4=340
Total score to avg 89 in 6 tests = 89*6=534
Total to be scored on 2 tests = 534-340=194
Avg on 2 tests = 194/2 = 97
Answer: D
Answer: (D) 97
Question: If the price of an article went up by 25%, then by what percent should it be brought down to bring it back to its original price?
(A) 20%
(B) 16 4/3%
(C) 16 7/3%
(D) 16 6/3%
(E) 16 2/3%
Rationale: Let the price of the article be Rs. 100.
25% of 100 = 25.
New price
= 100 + 25 = Rs. 125
Required percentage
= (125 - 100)/125 * 100
= 25/125 * 100
= 20%
Answer:A
Answer: (A) 20%
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 Q 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 Q=> 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: A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 33
(B) 38
(C) 37
(D) 90
(E) 28
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
⇒ 16x = 480
∴ x = 30.
Hence, total number of notes = 3x = 90
Answer:D
Answer: (D) 90
Question: The length of a room is 9 m and width is 4.75 m. What is the cost of paying the floor by slabs at the rate of Rs. 900 per sq. metre.
(A) 25650
(B) 25750
(C) 26550
(D) 30750
(E) 38475
Rationale: Area = 9 × 4.75 sq. metre.
Cost for 1 sq. metre. = Rs. 900
Hence total cost = 9 × 4.75 × 900
= 9 × 4275 = Rs. 38475
Answer is E.
Answer: (E) 38475
Question: The average runs scored by a batsman in 22 matches is 28. In the next 13 matches the batsman scored an average of 15 runs. Find his average in all the 35 matches?
(A) 31.23
(B) 25.12
(C) 36.25
(D) 23.17
(E) 27.66
Rationale: Total score of the batsman in 22 matches = 616.Total score of the batsman in the next 13 matches = 195.Total score of the batsman in the 35 matches = 811.Average score of the batsman = 811/35 = 23.17.Answer: D
Answer: (D) 23.17
Question: Praveen starts business with Rs.3920 and after 5 months, Hari joins with Praveen as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Hari’s contribution in the capital?
(A) s.10080
(B) s.8000
(C) s.8500
(D) s.9000
(E) s.6000
Rationale: Let Hari’s capital be Rs. x. Then, 3920 * 12/7x = 2/3
=> 14x = 141120
=> x = 10080.
ANSWER:A
Answer: (A) s.10080
Question: A company organized a recruiting process for 3 vacant positions of assistant manager for its product launches. The company's efforts yielded 12 eligible candidates. How many sets of 3 candidates can the company choose to fill the 3 assistant manager positions?
(A) 2,060
(B) 1,320
(C) 545
(D) 315
(E) 220
Rationale: t will be 12C3: 12!9!3!12!9!3!
12∗11∗10/6 = 220
E is the answer.
Answer: (E) 220
Question: Which one of the following numbers is completely divisible by 45?
(A) 202860
(B) 331145
(C) 1254186
(D) 2534164
(E) 8756241
Rationale: 45 = 5 x 9, where 5 and 9 are co-primes.
Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.
ANSWER A
Answer: (A) 202860
Question: How many digits are required to number a book containing 300 pages?
(A) 792
(B) 684
(C) 492
(D) 372
(E) 340
Rationale: 9 pages from 1 to 9 will require 9 digits.
90 pages from 10 to 99 will require 90*2=180 digits.
300-(90+9)=201 pages will require 201*3=603 digits.
The total number of digits is 9+180+603=792.
The answer is A.
Answer: (A) 792
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a trolley that is running with a speed of 12 km/hr in the direction opposite to that in which the train is going?
(A) 4.31
(B) 6.75
(C) 7.92
(D) 5.5
(E) 6.5
Rationale: Speed of train relative to trolley = 60 + 12 = 72 km/hr.
= 72 * 5/18 = 20 m/sec.
Time taken to pass the trolley = 110 * 1/20
= 5.5 sec.
Answer: D
Answer: (D) 5.5
Question: Two trains of length 100 m and 220 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 18 sec
(B) 70 sec
(C) 21 sec
(D) 20 sec
(E) 16 sec
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5
= 20 mps.
Distance covered in passing each other
= 100 + 220= 320 m.
The time required = d/s
= 320/20
= 16 sec.
Answer: E
Answer: (E) 16 sec
Question: A football field is 9600 square yards. If 800 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?
(A) 450
(B) 600
(C) 750
(D) 2400
(E) 300
Rationale: Answer E) 9600 yards need 1200 lbs
1 Yard will need 800/9600 = 1/12 lbs
3600 Yards will need 1/12* 3600 Yards = 300lbs
Answer: (E) 300
Question: What is the least number which when divided by 12,21,35 will leave in each case the same reminder 6?
(A) 210
(B) 420
(C) 414
(D) 426
(E) 454
Rationale: Here least number means LCM
Hence LCM of 12,35,21 = 2^2 x 7 x 3 x 5
= 420
Therefore required number is 420 + 6 = 426
Ans - D
Answer: (D) 426
Question: (x + 3) is a factor in x^2 - mx - 15. What is the value of m?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: I solved the second degree equation and found it like this:
x^2 - mx - 15 = 0
(x-5)(x+3) = 0
x=5 or x= -3
Substituting both values for x in the equation we find:
x^2 - mx -15
=> (-3)^2 - m(-3) = 15
=> 9+ 3m= 15
=> 3m = 15-9=6
=> m = 2
And with 5, using a similar process we end up with:
(5)^2 - m(5) =15
-5m = 15-25= -10
m=2
Ao,ANS B
Answer: (B) 2
Question: If each digit in the set of A = (2,3,4,5) is exactly used once, in how many ways can the digits be arranged such that the 3 and 4 are not adjacent?
(A) 12
(B) 15
(C) 18
(D) 22
(E) 24
Rationale: The answer should be = total arrangements - arrangements when 2 and 5 are together.
= 4! - 3! * 2! = 24 -12 = 12
take 2,5,(3,4) here there are 3 entities whose number of arrangements are 3! and 2! is the arrangement between 3 and 4
Answer is A
Answer: (A) 12
Question: Mary’s annual income is $15,000 and John’s annual income is $18,000. By how much must Mary’s annual income increase so that it constitutes 60% of Mary and John’s combined income?
(A)  $3,000
(B)  $4,000
(C)  $7,000
(D)  $12,000
(E)  $25,000
Rationale: Let Mary's income increase by x, then the equation will be
15,000 + x= (60/100)* (15,000 + x + 18000 )
15,000 + x = (3/5) * (33,000 + x)
75,000 + 5x = 3x + 99,000
2x = 24,000
x = 12,000
So, Answer will be D
Answer: (D)  $12,000
Question: The manager at a health foods store mixes a unique superfruit juice cocktail that costs $1399.45 per litre to make. The cocktail includes mixed fruit juice and açai berry juice, which cost $262.85 per litre and $3104.35 per litre, respectively. The manager has already opened 36 litres of the mixed fruit juice. How many litres of the açai berry juice does he need to add?
(A) 17 litres
(B) 24 litres
(C) 11 litres
(D) 07 litres
(E) 38 litres
Rationale: 262.85(36)+3,104.35x = 1,399.45(36 + x)
Solve the equation.
262.85(36)+3,104.35x = 1,399.45(36 + x)
9,462.6 + 3,104.35x = 50,380.2+ 1,399.45x
9,462.6 + 1,704.9x = 50,380.2
1,704.9x = 40,917.6
x = 24
Answer is B.
Answer: (B) 24 litres
Question: The diagonals of two squares are in the ratio of 2 : 5. Find the ratio of their areas.
(A) 5:20
(B) 5:25
(C) 4:25
(D) 3:15
(E) 3:20
Rationale: Let the diagonals of the squares be 2x and 5x respectively.
Ratio of their areas = (1/2)*(2x) 2:(1/2)*(5x) 2= 4x2: 25x2= 4 : 25.
Option C
Answer: (C) 4:25
Question: A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 200 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
(A) 2989
(B) 2765
(C) 6110
(D) 2989
(E) 9772
Rationale: Total production of salt by the company in that year
= 5000 + 5200 + 5400 + .... + 7200 = 73400.
Average monthly production of salt for that year
= 73400/12
= 6116.
Answer:C
Answer: (C) 6110
Question: The labeled price of a table is Rs. 7,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
(A) Rs. 5758
(B) Rs. 6195
(C) Rs. 6425
(D) Rs. 7200
(E) None of these
Rationale: Explanation:
Labeled price = Rs. 7,500
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 7500 = Rs. 7125
By earning 15% profit on the selling of price Rs. 7125 the cost price is
= 100 / 115 * 7125 = Rs. 6195.65
Therefore, approximate cost is 6195.65 (ANSWER ROUNDED OFF: Rs.6195)
ANSWER IS B
Answer: (B) Rs. 6195
Question: A bag contains 6black pens and 8 white pens. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 4/7
(B) 2/3
(C) 5/8
(D) 1/4
(E) 4/9
Rationale: total number of pens = 14
number of white pens = 8
drawing a white pens= 8/14 = 4/7
Answer is A
Answer: (A) 4/7
Question: In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?
(A) 2
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Let the speed of Arun = x kmph
and the speed of Anil = y kmph
distance = 30 km
We know that distancespeed=timeHence30x−30y=2...........(Equation1)30y−302x=1...........(Equation2)Equation1 + Equation2⇒30x−302x=3⇒302x=3⇒15x=3⇒5x=1⇒x=5Hence Arun's speed = 5 kmph
Answer : B
Answer: (B) 5
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?
(A) 126
(B) 1386
(C) 3108
(D) 308
(E) thirteen thousand nine hundred and eighty six (13986)
Rationale: This can also be solved by using a formula
Sum of N numbers
With repetition = N ^ ( N - 1 ) * Sum of the Numbers * 111..... N no. of times
With out repetition = ( N - 1 ) ! * Sum of the Numbers * 111.... N no. of times.
Here repetition is allowed, therefore N is 3 ( No. of digits given ) and sum of No is 14.
3^2 * 14 * 111 = 13986. ans:E
Answer: (E) thirteen thousand nine hundred and eighty six (13986)
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 8.30 a.m. ?
(A) 7
(B) 2
(C) 9
(D) 2
(E) 8
Rationale: B
2
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 2 times before 8.30 a.m.
Answer: (B) 2
Question: x and y are positive integers. When x is divided by 6, the remainder is 3, and when x is divided by 16, the remainder is 5. When y is divided by 9, the remainder is 5, and when y is divided by 7, the remainder is 4. What is the least possible value of x / y?
(A) 2.5
(B) 3
(C) 2
(D) 1.3
(E) 1.5
Rationale: When x is divided by 6, the remainder is 3: So, the possible values of x are: 3, 9, 15, 21, etc.
When x is divided by 16, the remainder is 5: So, the possible values of x are: 5,21... STOP. Since both lists include 21, the smallest possible value of x is 21.
When y is divided by 9, the remainder is 5: So, the possible values of y are: 5, 14, 23,32 etc.
When y is divided by 7, the remainder is 4: So, the possible values of y are: 6, 14, ...STOP. Since both lists include 14, the smallest possible value of y is 14
Since the smallest possible values of x and y are 21 and 14 respectively, the smallest possible value of x / y is 1.5. So,E is the correct answer to the original question.
Answer: (E) 1.5
Question: Rahul can do a work in 3 days while Rajesh can do the same work in 2days. Both of them finish the work together and get $2250. What is the share of Rahul?
(A) $50
(B) $40
(C) $60
(D) $100
(E) $900
Rationale: Rahul's wages: Rajesh's wages = 1/3 : 1/2 = 2:3
Rahul's share = 2250*2/5 = $900
Answer is E
Answer: (E) $900
Question: Working alone, pump A can empty a pool in 6 hours. Working alone, pump B can empty the same pool in 9 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?
(A) 192
(B) 200
(C) 208
(D) 216
(E) 224
Rationale: Pump A can empty (1/6) of the pool per hour.
Pump B can empty (1/9) of the pool per hour.
Together the pumps can empty 1/6+1/9=5/18 of the pool per hour.
1 pool / (5/18) pool per hour = 18/5 hours = 216 minutes.
The answer is D.
Answer: (D) 216
Question: How many ways can the letters of the word, ‘MACHINE’ be arranged so that the vowels may occupy only the odd positions?
(A) 210
(B) 576
(C) 144
(D) 456
(E) 356
Rationale: In the word ‘MACHINE’ 3 vowels and 4 consonants.
v v v v
__ _ __ _ __ _ __
Now, 3 vowels can be placed at any of 3 places, out of which 4 marked 1,3,5,7.
Number of ways arranging the vowels= 4P3 = (4*3*2) =24
Also, 4 consonants at the remaining 4 positions may be arranged in = 4P4 = 4!= 24 ways.
Therefore, Required number of ways= (24*24) =576.
ANSWER:B
Answer: (B) 576