mathewhe/aqua_rat huggingface dataset:
Question: If a car had traveled 40 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 120 km, at what speed did it travel?
(A) 50 kmh
(B) 60 kmh
(C) 70 kmh
(D) 80 kmh
(E) 90 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
120/x - 120/(x + 40) = 1/2
Substitute the value of x from the options. --> x = 80 --> 120/80 - 120/120 = 3/2 - 1 = 1/2
Answer: D
Answer: (D) 80 kmh
Question: There are 8 men and 4 chairs. In how many ways men can occupy the chairs?
(A) 1760
(B) 8400
(C) 1680
(D) 1740
(E) 1800
Rationale: total men = 8
total chairs = 4
1st chair can be occupy in 8ways
2nd chair can be occupy in 7ways
3rd chair can be occupy in 6ways
4th chair can be occupy in 5ways
total number of ways = 8*7*6*5 = 1680 ways
correct option is C
Answer: (C) 1680
Question: A new beverage, which is a mixture of grape juice and apple juice, is being tested. The test container of 800 milliliters is 15% grape juice. If the response to the beverage causes the maker to increase the percentage of grape juice in the container to 20%, how much grape juice will be added?
(A) 30
(B) 40
(C) 50
(D) 120
(E) 160
Rationale: So, (120+k)/(800+k)=20/100
Or, (120+k)/(800+k)=15
Or, 600+5k=800+k
Or, 4k=200
Or, k=50
Or, k=50k=50
So, 50 ml of Grape juice , must be added , answer must be (C)
Answer: (C) 50
Question: Of the 400 members at a health club, 260 use the weight room and 310 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
(A) 40 to 100
(B) 240 to 280
(C) 230 to 260
(D) 220 to 300
(E) 200 to 260
Rationale: W=260
P=310
ALL=400
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+310-BOTH+60=400
BOTH=230
now pay attention to the fact, that both at most can be 260, since W=260
C
Answer: (C) 230 to 260
Question: If each digit in the set A = {1, 2, 3, 4, 5} is used exactly once, in how many ways can the 5 digits be arranged?
(A) 6
(B) 24
(C) 72
(D) 96
(E) 120
Rationale: Use the slot method for all the possible arrangements:
we have 5 options for the 1st slot, 4 for the 2nd, 3 for 3rd , 2 for 4th and 1 for the 5th, giving the total number of
arrangements = 5*4*3*2*1 = 120,
E is the correct answer.
Answer: (E) 120
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 72 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
(A) 2000
(B) 2100
(C) 2200
(D) 2300
(E) 2400
Rationale: 1 percent for 3 years= 72
1 percent for 1 year = 24
=> 100 percent = 2400
ANSWER:E
Answer: (E) 2400
Question: The average age of 4 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
(A) 22
(B) 30
(C) 99
(D) 26
(E) 27
Rationale: total age increased = (8 * 2) years = 8 years.
Sum of ages of two new men = (21 + 23 + 8) years = 52 years
Average age of two new men = (52/2) years = 26 years.
Answer: D
Answer: (D) 26
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 12%. What was its profit on the items sold in February?
(A) 27.5%
(B) 32%
(C) 35%
(D) 37.5%
(E) 40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.88*150x = 132x
Hence total profit = 32%
Option B
Answer: (B) 32%
Question: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
(A) 15y/18
(B) 6y/5
(C) 18y/5
(D) 60y
(E) 3600000y
Rationale: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
We need to find an equation with y in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)
Speed = y/t
y meters/second
(3600) x meters/hour
Speed = x/t
x KM/hour
Speed = x(1000m)/hour
x(1000meters)/hour = (3600) x meters/hour
x(1000)/1hour = y(3600) / 1 hour
x(1000) = y(3600)
x = 3.6y
Answer: C. 18y/5
Answer: (C) 18y/5
Question: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every nine minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
(A) 150%
(B) 200%
(C) 250%
(D) 300%
(E) 350%
Rationale: Dolphin once in 3 min;
Beluga once in 9 min;
So, dolphin comes up 3 times frequently than beluga, which is 300% (9-3)/2*100.
Answer: D.
Answer: (D) 300%
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
(A) 16 kmph
(B) 19 kmph
(C) 14 kmph
(D) 11 kmph
(E) 13 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 42/3 = 14 kmph.
Answer: C
Answer: (C) 14 kmph
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 5^a and y = 4^b, which of the following is a possible units digit of xy?
(A) 1
(B) 4
(C) 5
(D) 7
(E) 0
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=5
a=2; X=25
a=3; X=125........ Units digit repeat in a cycle of 5......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=4
b=2; Y= 16
b=3; Y= 64....... Units digit repeat in cycle of 4,6,4....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=5 and Y=4: Units digit of XY = 20
When X=5 and Y=6: Units digit of XY = 30
Only one possibility for Units digit of XY i.e. 0.
therefore answer is E
Answer: (E) 0
Question: Two dice are rolled. What is the probability the sum will be greater than 11?
(A) 1/9.
(B) 1/12.
(C) 1/36.
(D) 1/6.
(E) 1/5.
Rationale: Combinations possible: (6,6) = 1
Total combinations possible: 6*6=36
Answer = 1/36 Option C.
Answer: (C) 1/36.
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3500, A will get:
(A) Rs.1200
(B) Rs.1500
(C) Rs. 2100
(D) Rs.2000
(E) None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3500/25 = 140
So, A’s amount = 120 × 15 = Rs.2100.
Answer: Option C
Answer: (C) Rs. 2100
Question: A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 8 sec
(C) 10 sec
(D) 12 sec
(E) 14 sec
Rationale: Speed of the train relative to man = (59 + 7) kmph
= 66 *5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec
= (220 *3/55) sec = 12 sec
Answer : D.
Answer: (D) 12 sec
Question: An investment of $5000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $5000 increased to $20000 by earning interest. In how many years after the initial investment was made the $5000 have increased to $40000 by earning interest at that rate?
(A) 16
(B) 12
(C) 20
(D) 24
(E) 18
Rationale: In 12 years the investment quadrupled (from $5,000 to $40,000).
Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $20,000 to $40,000).
Therefore, 12+6=18 years are needed $5,000 to increase to $40,000.
Answer: E.
Answer: (E) 18
Question: All factors of a positive integer B are multiplied and the product obtained is B^3. If B is greater than 1, how many factors does B have?
(A) 2
(B) 3
(C) 6
(D) 7
(E) 8
Rationale: The question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.
For example,
Factors of 6: 1, 2, 3, 6
1 has a complementary factor 6 such that 1*6 = 6 (the original number)
2 has a complementary factor 3 such that 2*3 = 6 (the original number)
So if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).
So if you know that the product of all factors is B^3, it means there must have been twice the number of factors i.e. 3*2 = 6 factors.
C)
Answer: (C) 6
Question: he average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
(A) 37
(B) 74
(C) 30
(D) 34
(E) 35
Rationale: 20 + 24 + 8 * 2
= 60/2
= 30
Answer:C
Answer: (C) 30
Question: How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?
(A) 29
(B) 28
(C) 27
(D) 25
(E) 23
Rationale: Any odd number can be expressed as 2k+1 or 2k+(3-2) or 2(K-1)+3.
Thus, with the prime number 3,
we can express all the odd numbers.
Since, 1 i is the only number that cannot be expressed,
answer is numbers <30 =29-1.
ANSWER:B
Answer: (B) 28
Question: How many six-digit numbers that do not contain the digits 5 or 8 are there?
(A) 483224
(B) 156444
(C) 229376
(D) 816416
(E) 316544
Rationale: We can have 7 digits ( 1,2,3,4,6,7,9) for the first place ( hundred thousand's place).
and similarly 8 digits for ten thousands, thousands, hundred's, tenth's and unit digit. ( 0,1,2,3,4,6,7,9)
So in total 7*8*8*8*8*8= 229376
Hence C
Answer: (C) 229376
Question: A train covers a distance of 12 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
(A) 200
(B) 288
(C) 120
(D) 776
(E) 991
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 10
= 200 m.
Answer:A
Answer: (A) 200
Question: he number of sequences in which 9 players can throw a ball, so that the youngest player may not be the last is?
(A) 432881
(B) 322560
(C) 432020
(D) 288212
(E) 278212
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 8 players. The first 8 players can throw the ball in 8p8 ways.
The required number of ways = 8(8!) = 322560
Answer:B
Answer: (B) 322560
Question: In a sports club with 55 members, 23 play badminton and 29 play tennis and 7 do not play either. How many members play both badminton and tennis?
(A) 3
(B) 5
(C) 4
(D) 7
(E) 8
Rationale: 23+29=52
but where as total number is 55-7=48
therefore answer is 52-48=4
Hence Answer is C
Answer: (C) 4
Question: A certain basketball team that has played 2/3 of its games has a record of 15 wins and 5 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
(A)  7
(B)  6
(C)  5
(D)  4
(E)  2
Rationale: 15 wins, 3 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30
3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 5 games so it can lose another 2 at most.
Answer (E)
Answer: (E)  2
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) Rs.3178
(B) Rs.3120
(C) Rs.3127
(D) Rs.3121
(E) Rs.3122
Rationale: Explanation:
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: (B) Rs.3120
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/9%
(B) 33 8/3%
(C) 33 1/3%
(D) 33 2/3%
(E) 33 1/2%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: (C) 33 1/3%
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability M that the sum of the two integers will equal 9 ?
(A)  0.15
(B)  0.20
(C)  0.25
(D)  0.30
(E)  0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20.M=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: M=1*1/5.
Answer: B.
Answer: (B)  0.20
Question: A number when divided by 342 gives a remainder 47. When the same number ift divided by 19, what would be the remainder ?
(A) 7
(B) 8
(C) 9
(D) 21
(E) 14
Rationale: Sol. On dividing the given number by 342, let k be the quotient and 47 as remainder.
Then, number – 342k + 47 = (19 x 18k + 19 x 2 + 9) = 19 (18k + 2) + 9.
The given number when divided by 19, gives (18k + 2) as quotient and 9 as remainder.
Option C
Answer: (C) 9
Question: All of the citizens of a country have a six-character or seven-character national identification code that is created using the 26 letters of the alphabet and the 10 digits from 0 to 9. What is the maximum number of citizens who can be designated with these codes?
(A) 36^13
(B) 35(36^7)
(C) 37(36^6)
(D) 35(36^6)
(E) 37(36^7)
Rationale: The number of possible 6-digit codes is 36^6.
The number of possible 7-digit codes is 36^7.
The total sum is 36^6 + 36^7 = 36^6(1+36) = 37(36^6)
The answer is C.
Answer: (C) 37(36^6)
Question: A man can row a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18
(B) 30/21
(C) 30/11
(D) 30/7
(E) 30/8
Rationale: Speed downstream = 10 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 60/16
= 30/8 hours.
Answer:E
Answer: (E) 30/8
Question: 72519 x 9999 = ?
(A) 728727481
(B) 725117481
(C) 725189201
(D) 725173920
(E) 722928481
Rationale: B
725117481
72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481.
Answer: (B) 725117481
Question: If 2x +3y = 30 and (x+y)/y = 11/8, then find the value of 5y + 6x
(A) 76
(B) 58
(C) 99
(D) 26
(E) 17
Rationale: Explanation:
The given equations are :
2x + 3y = 30 --------- (i)
and, (x+y)/y = 11/8
8x + 8y = 11y
8x – 3y =0 ----(ii)
Adding (i) & (ii), we get : 10 x = 30 or x = 3.
Put x = 3 in (i), we get : y = 8
Therefore, 5y + 6x = (5 * 8 + 6 * 3) = 40 + 18 = 58.
ANSWER: B
Answer: (B) 58
Question: 30 men can do a work in 40 days. When should 15 men leave the work so that the entire work is completed in 40 days after they leave the work?
(A) 87 days
(B) 10 days
(C) 15 days
(D) 44 days
(E) 22 days
Rationale: Total work to be done = 30 * 40 = 1200
Let 15 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (15 * 40) = 1200
40P = 600 => P = 15 days
Answer:C
Answer: (C) 15 days
Question: Rajesh spends 40% of his monthly salary on food, 20% of the medicines and saves 60% of the remaining amount. If his monthly salary is Rs.15,000, how much money does he save every month ?
(A) Rs.1000
(B) Rs.2596
(C) Rs.4320
(D) Rs.6489
(E) Rs.4789
Rationale: Explanation:
Ramesh's monthly income = Rs.15,000
He spends 40% on food.
The total money spent on food = 40/100 * 15000 = Rs. 6000
Now, his monthly remaining income = Rs.15000 – Rs.6000 = Rs. 9000
Out of Rs. 9000, he spends 20% on medicines.
The total money spent on medicines = 20/100 * 9000 = Rs.1800
Now, his monthly remaining income = Rs.9000 – Rs.1800 = Rs. 7200
Out of Rs. 7200, he saves 600%.
Amount saved = 60/100 * 7200 = RS.4320
ANSWER:C
Answer: (C) Rs.4320
Question: There are 4 books on fairy tales, 5 novels and 3 plays. In how many ways can you arrange these so that books on fairy tales are together, novels are together and plays are together and in the order, books on fairy tales, novels and plays.
(A) 17280
(B) 1900
(C) 21548
(D) 36554
(E) None of these
Rationale: There are 4 books on fairy tales and they have to be put together. They can be arranged in 4! ways. Similarly, there are 5 novels. They can be arranged in 5! ways. And there are 3 plays. They can be arranged in 3! ways. So, by the counting principle all of them together can be arranged in 4!*5!*3!= 17280 ways
Answer A
Answer: (A) 17280
Question: A lady bought five books namely A,B,C,D,E to distribute her 2 children. How many ways she can distribute books?
(A) 3^3
(B) 3^4
(C) 2^5
(D) 3^6
(E) 3^2
Rationale: 2*2*2*2*2
2^5
ANSWER:C
Answer: (C) 2^5
Question: A man's speed with the current is 18 km/hr and the speed of the current is 3.4 km/hr. The man's speed against the current is
(A) 9
(B) 10.4
(C) 11.2
(D) 12.5
(E) 13
Rationale: Man's rate in still water = (18 - 3.4) km/hr = 14.6 km/hr.
Man's rate against the current = (14.6 - 3.4) km/hr = 11.2 km/hr.
Answer:C
Answer: (C) 11.2
Question: A trade analyst announced 15% reduction in the unit price of bike. As a result, the sales volume went up by 15%. What was the net effect on the sales revenue?
(A) no change
(B) decreases by 6.5%
(C) increases by 6.5%
(D) increases by 5.6%
(E) None of these
Rationale: Explanation :
Reduction of price = (100 -15)% = 85% = 0.85
Increase of sale = (100+15)% = 115% = 1.15
Total effect = 0.85 X 1.15 = 93.5%, Decreases by 6.5%
Answer :B
Answer: (B) decreases by 6.5%
Question: A train 350 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?
(A) 5 sec
(B) 9 sec
(C) 12 sec
(D) 21 sec
(E) 18 sec
Rationale: Speed of the train relative to man = (68 - 8) kmph
= (60* 5/18) m/sec = (50/3)m/sec
Time taken by the train to cross the man
= Time taken by It to cover 350 m at 50/3 m / sec
= 350 *3/ 50 sec = 21sec
Answer : D
Answer: (D) 21 sec
Question: An alloy of copper and zinc contains copper and zinc in the ratio 5 : 3. Another alloy of copper and zinc contains copper and zinc in the ratio 1 : 7. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?
(A) 1 : 5
(B) 7 : 3
(C) 5 : 3
(D) 3 : 1
(E) 4 : 3
Rationale: Alloy-1: Copper: Zinc = 5:3, Let Quantity = x
i.e. Copper in Alloy-1 = [5/(5+3)]*x = (5/8)x
and Zinc in Alloy-1 = [3/(5+3)]*x = (3/8)x
Alloy-2: Copper: Zinc = 1:7, Let Quantity = y
i.e. Copper in Alloy-2 = [1/(1+7)]*y = (1/8)y
and Zinc in Alloy-1 = [7/(1+7)]*y = (7/8)y
After Combining the two alloys
Copper = (5/8)x + (1/8)y
Zinc = (3/8)x + (7/8)y
Now, (5x + y)/8 = (3x + 7y)/8
i.e. 2x = 6y
i.e. x = 3y
i.e. x/y = 3/1
Answer: option D
Answer: (D) 3 : 1
Question: In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 16% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 6
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Use the forumla ;
Total = Group1 + Group2 + Group3 - (sum of 2-group overlaps) - 2*(all three) + Neither
100 = 50 + 30 + 16 - ( sum of 2) -2(5) +15
100 = 101-( sum of 2)
1 = sum of 2
so more than 1 = 6
A
Answer: (A) 6
Question: A sum of Rs. 125000 amounts to Rs. 17500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 10%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: S.I. = (17500 - 12500) = Rs. 5000\
Rate = (100 * 5000) / (12500 * 4) = 10%
ANSWER:A
Answer: (A) 10%
Question: Find the compound interest on $1200 for 1year at 20% p.a. if CI is component yearly?
(A) $120
(B) $150
(C) $240
(D) $250
(E) $300
Rationale: A = P(1 + R/100)^T
= 1200(1 + 20/100)^1
= 1200*6/5
=$1440
CI = A-P = 1440-1200 = $240
Answer is C
Answer: (C) $240
Question: If GAVE is coded as 5137 and BAT is coded as 924. How is GATE coded?
(A) 5147
(B) 5247
(C) 6584
(D) 7489
(E) 9487
Rationale: g-5 a-1 e-7 from the code gate
t - 4 from bat
ANSWER:A
Answer: (A) 5147
Question: 6!/(6-3)!=?
(A) 120
(B) 346
(C) 356
(D) 366
(E) 396
Rationale: 6!/6-3)!=6!/3!=6*5*4=120. Hence, the correct answer is A.
Answer: (A) 120
Question: The monthly rent of a shop of dimension 20feet × 15feet is Rs.3600. What is the annual rent per square foot of the shop?
(A) 43
(B) 144
(C) 68
(D) 87
(E) 92
Rationale: Sol. Monthly rent per square feet = 3600/(20*15) = 12
& Annual rent per square feet
=12*12=144
Answer : B
Answer: (B) 144
Question: Diane find 3 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
(A) 5
(B) 17 and a half
(C) 10
(D) 12 and a half
(E) 15
Rationale: She will need 7 cans to paint the rest of this room and 10 1/2 for the next room for a total of 17 1/2 cans.
B
Answer: (B) 17 and a half
Question: What is the product of the prime factors of 27 and the prime factors of 121?
(A) 3676
(B) 3762
(C) 3627
(D) 3267
(E) 3257
Rationale: The prime factors of 27 are 3*3*3
The prime factors of 121 are 11*11
3*3*3*11*11 =27*121= 3267. D is the correct answer
Answer: (D) 3267
Question: A dice has one of the first 8 prime number on each its six sides ,with no two sides having the same number .the dice is rolled 10 times and the results added.the addition is most likely to be closet to
(A) 41
(B) 48
(C) 96
(D) 90
(E) 70
Rationale: if die is rolled then avg score = (2+3+5+7+11+13+17+19 )/8 = 77/8
so, most likely sum for 10 times = 77/8 * 10 = 96
ANSWER:C
Answer: (C) 96
Question: By approximately what percent is x greater than 4/5 if (4/5)(x) = 1?
(A) 73%
(B) 56%
(C) 41%
(D) 37%
(E) 29%
Rationale: 4/5= 80%, 5/4=125% increase by 45 percentage points 45/80=56% , hence B
Answer: (B) 56%
Question: The cash realised on selling a 14% stock is Rs.108.25, brokerage being 1/4% is
(A) 123
(B) 106
(C) 108
(D) 156
(E) 240
Rationale: Explanation:
Cash realised= Rs. (108.25 - 0.25)
= Rs. 108.
Answer: C
Answer: (C) 108
Question: If the number obtained on interchanging the digits of a two digit number is 18 more than the original number and the sum of the digits is 8, then what is the original number?
(A) 25
(B) 30
(C) 35
(D) 40
(E) 45
Rationale: Sol.
Let ten's digit = x.
Then, unit's digit = (8-x).
∴ [10 (8-x)+x] - [10x + (8-x)] = 18
⇔ 18x = 54
⇔x = 3
So, ten's digit = 3 and units digit = 5.
Hence, original number = 35.
Answer C
Answer: (C) 35
Question: If y = q/6 + r/6^2 + s/2^5, where q, r, and r are each equal to 1 or 0, then y could be any of the values below EXCEPT:
(A) 9/8
(B) 7/32
(C) 1/4
(D) 5/16
(E) 21/16
Rationale: y = q/6 + r/6^2 + s/2^5
= q/6 + r/36 + s/32
= (36q + 6r + s ) /32
Depending on whether q, r and r take 0 or 1 :
substitute 0 or 1 for the different values of q, r and r.
Answer D
Answer: (D) 5/16
Question: 2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in
(A) 05
(B) 21
(C) 51
(D) 11
(E) 41
Rationale: (2x14)men+(7x14)boys=(3x11)men+(8x11)boys
5 men= 10 boys 1man= 2 boys
Therefore (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys
( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.
Let the required number of days be x.
More boys , Less days (Indirect proportion)
More work , More days (Direct proportion)
Boys 22:11 and Work 1:3=:14:x
Therefore, (22x1x)=(11x3x14)
x=462/22=21
Hence, the required number of days = 21
Answer is B.
Answer: (B) 21