mathewhe/aqua_rat huggingface dataset:
Question: In a factory, there are 90% technicians and 10% non-technicians. If the 90% of the technicians and 10% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 62%
(B) 57%
(C) 52%
(D) 82%
(E) 42%
Rationale: Total = 100
T= 90 NT= 10
90*(10/100)=910*(90/100)=9
9 + 9 = 18=> 100 - 18 = 82%
Answer:D
Answer: (D) 82%
Question: A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?
(A) 40
(B) 48
(C) 52
(D) 56
(E) 70
Rationale: milk:water = 5:2
5x : 2x + 10 = 5 : 3
3[5x] = 5[2x + 10]
15x = 10x + 50
15x - 10x = 50
x = 10
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7x = 70
E
Answer: (E) 70
Question: At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 hr less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 hr less than the upstream 12 miles. What is the speed of the current in miles per hour?
(A) 7/3
(B) 4/3
(C) 5/3
(D) 8/3
(E) None of these
Rationale: Explanation :
Let x be rate of rahul , and y be the rate of current in mph.
=> [12/ (x-y)] - [12 / (x+y)] = 6.
=> y = ( x2 - y2 ) / 4. ..................(i)
When Rahul doubles his rowing rate, then we have :-
=> 12/( 2x-y) - 12/( 2x+y) = 1.
=> 2y / (4x2 - y2) = 1/12.
=> y = (4x2 - y2) / 24. ..................(ii)
Hence, from (i) and (ii), we have 2x2 = 5y2 .
Putting, x2 = 5y2 / 2 in (i), we get
=> y = (3/2)y2 / 4 .
=> y = 8/3.
Answer : D
Answer: (D) 8/3
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 2
(B) 4
(C) 8
(D) 4
(E) 7
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer:D
Answer: (D) 4
Question: The fraction 101 27/100000 in decimal for is:
(A) 101.27
(B) 101.00027
(C) 101.0027
(D) 101.027
(E) None of them
Rationale: 101 27/100000
= 101 + 27/ 100000
= 101 + .00027
= 101.00027
Answer is B.
Answer: (B) 101.00027
Question: If exactly 7 guests drank only one of the two types of drinks, how many guests drank both types of drinks?
(A) 5
(B) 6
(C) 7
(D) 4
(E) 2
Rationale: Say x guests drank both drinks.
(7 - x) + (4 - x) = 7 --> x = 2.
Answer: E.
Answer: (E) 2
Question: Sara is younger than Robert by 8 years. If their ages are in the respective ratio of 3:5, how old is Sara?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: Let Robert's age be x years
Then Sara's age = x-8 years
(x-8)/x = 3/5
x = 20
Sara's age = x-8 = 12 years
Answer is C
Answer: (C) 12
Question: A car covers a distance of 520 km in 4 hours. Find its speed?
(A) 104
(B) 130
(C) 298
(D) 269
(E) 213
Rationale: 520/4 = 130 kmph
Answer:B
Answer: (B) 130
Question: A student travels from his house to school at 10 km/hr and reaches school 2 hours late. The next day he travels 16 km/hr and reaches school 1 hour early. What is the distance between his house and the school?
(A) 70
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: Let x be the distance from his house to the school.
x/10 = x/16 + 3
8x = 5x + 240
3x = 240
x = 80 km
The answer is C.
Answer: (C) 80
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 5% p.a. in 5 years. What is the sum?
(A) 12021
(B) 14520
(C) 16065
(D) 18925
(E) 12887
Rationale: Principal = (100 * 4016.25) / (5 * 5)
= Rs.16065.
Answer:C
Answer: (C) 16065
Question: A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 504. What is the sum of the last 8 of the even integers?
(A) 608
(B) 614
(C) 620
(D) 626
(E) 632
Rationale: The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 504
The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) =
504 + 8(16) = 504 + 128 = 632
The answer is E.
Answer: (E) 632
Question: At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 2:1. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?
(A) 2/3
(B) 4/5
(C) 6/2
(D) 5/2
(E) 4/9
Rationale: Red: Blue = 2:1
Let Red = 2x and Blue = 1x
1/3 of Red are left handed => 1/3 * 2x = 2x/3 Red left handed
2/3 of Blue are left handed => 2/3 *1x = 2x/3 blue left handed
fraction of participants who are left handed = total left handed/ total participants = (red left handed + blue left handed)/total participants = (2x/3 + 2x/3)/(2x+1x) = 4/9
Answer : E
Answer: (E) 4/9
Question: If cement, gravel and sand are to be mixed in 7:10:13 and 11 tons of cement is available how many tons of mixture can be produced assuming that sufficient gravel and sand is readily available.
(A) 35 7/8
(B) 36
(C) 34 2/7
(D) 47 1/7
(E) 34 6/7
Rationale: Cement:Gravel:Sand = 7:10:13 --> total of 7+10+13 = 30 parts.
If we use 11 tons of cement, then we'll get 11/7*30 = 47 1/7 tons of mixture.
Answer: D.
Answer: (D) 47 1/7
Question: If a man crosses a 600 m long street in 5 minutes. What is his speed?
(A) 7 km/hr
(B) 7.1 km/hr
(C) 7.2 km/hr
(D) 8 km/hr
(E) 8.5 km/hr
Rationale: distance = 600 meter
time = 5 minutes = 5 x 60 seconds = 300 seconds
Speed = distancetime=600300=2m/s=2×185 km/hr=365 km/hr=7.2 km/hr
C
Answer: (C) 7.2 km/hr
Question: 3^7+3^7+3^7=?
(A) a) 81^2
(B) b) 81^4
(C) c) 81^5
(D) d) 81^6
(E) e) 81^15
Rationale: The correct answer is A 81^2
Answer: (A) a) 81^2
Question: Mohit sold an article for Rs . 18000. Had he offered a discount of 10% on the selling price, he would have earned a profit of 8%. What is the cost price of the article?
(A) Rs.15000
(B) 15002
(C) 26879
(D) 26992
(E) 12681
Rationale: Let the CP be Rs. x.
Had he offered 10% discount, profit = 8%
Profit = 8/100 x and hence his SP = x + 8/100 x
= Rs. 1.08x = 18000 - 10/100(18000)
= 18000 - 1800 = Rs. 16200
=> 1.08x = 16200
=> x = 15000
Answer: A
Answer: (A) Rs.15000
Question: Nr Books bought Nr of People
5 7
6 3
7 3
8 2
What is the median of books bought per person?
(A) a) 2
(B) b) 4
(C) c) 6
(D) d) 8
(E) e) 18
Rationale: 5,5,5,5,5,5,5,6,6,6,7,7,7,8,8
so you will observer that the median of the list is 6.
Ans C
Answer: (C) c) 6
Question: A customer bought a product at the shop. However, the shopkeeper increased the price of the product by 20% so that the customer could not buy the required amount of the product. The customer managed to buy only 80% of the required amount. What is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase?
(A) 10%
(B) 8%
(C) 6%
(D) 4%
(E) 2%
Rationale: Let x be the amount of money paid for the first purchase.
The second time, the customer paid 0.8(1.2x)=0.96x.
The difference is 4%.
The answer is D.
Answer: (D) 4%
Question: For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the standard deviation for the exam?
(A) 7
(B) 6
(C) 8
(D) 0
(E) 2
Rationale: Mean-2SD=58
Mean+3SD=98
By solving above equation we get,
SD (absolute value)=8
Ans. C
Answer: (C) 8
Question: A committee has 5 men and 5 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 127
(B) 100
(C) 882
(D) 272
(E) 323
Rationale: The number of ways to select two men and three women
= ⁵C₂ * 5C₃
= (5 *4 )/(2 * 1) * (5 * 4 * 3)/(3 * 2)
= 100
Answer: B
Answer: (B) 100
Question: The G.C.D of 1.08, 0.36 and 1.5 is
(A) 0.06
(B) 0.1
(C) 0.18
(D) 0.11
(E) 0.12
Rationale: Explanation:
Given numbers are 1.08 , 0.36 and 1.5
H.C.F of 108, 36 and 150 is 6[because G.C.D is nothing but H.C.F]
therefore H.C.F of given numbers = 0.06
Answer: A
Answer: (A) 0.06
Question: Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $155, $155, $199, $199, $219
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $219
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1408/11 =128
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $128, answer is 1 unit
Correct Answer - B
Answer: (B) 1
Question: The average of 2,7,6 and x is 5 and the average of 18,1,6,x and y is 10. What is the value of y ?
(A) 5
(B) 10
(C) 20
(D) 30
(E) 40
Rationale: Answer C
Solution
We have :(2+7+6+X/4) = 5 or 15+x = 20 or x=5
Also, (18+1+6+X+Y/5) = 10 or 25+5+y = 50 or y=20. Answer C
Answer: (C) 20
Question: A bookseller has two display windows. She plans to display 4 new fiction books in the left window, and 5 new non-fiction books in the right window. Assuming she can put the five fiction books in any order, and separately, the three non-fiction books in any order, how many total configurations will there be for the two display windows?
(A) 2400
(B) 720
(C) 2880
(D) 336
(E) 420
Rationale: Two displays books could be arranged n! # of total arrangements are combinations multiplied together,
4!*5! =24*120=2880
Answer is C
Answer: (C) 2880
Question: The larger of two negative consecutive even integers 2t and 2(t-1) is multiplied by 6 and then added to the smaller of the two original integers. Which of the following represents this operation?
(A) 6t-2
(B) 8t-2
(C) 14t-2
(D) 3
(E) -2-4t^2
Rationale: larger of 2t-2, 2t (when they are negative) is 2t. the smallest of 2t and 2t-2 when they are positive is 2t-2.
therefore 6* 2t + 2t-2 = 14t-2.
option C.
Answer: (C) 14t-2
Question: Number of ways in which the letters of word PARTI can be arranged with vowels in alphabetical order, is
(A) 60
(B) 240
(C) 120
(D) 480
(E) None of these
Rationale: Solution
Order of vowels of fixed
âˆ´ required number of ways are 5!/2!.
Answer A
Answer: (A) 60
Question: Each shelf of a bookcase contained 11 books. If the librarian took out 33 books and rearranged the remaining books so that all shelves but the last one contained 7 books and that last shelf contained 2 books, how many shelves does the bookcase have?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
11x - 33 = 7(x-1) + 2
4x = 28
x = 7
The answer is C.
Answer: (C) 7
Question: If 60 percent of the members of a certain organization are women and 6/8 of the members of the organization are married men, which of the following statements concerning the membership must be true? I. The number of women in the organization is greater than the number of married men in the organization. II. The number of women in the organization is greater than the number of unmarried men in the organization. III. The number of married men in the organization is greater than the number of unmarried men in the organization.
(A) II
(B) III
(C) I, II
(D) I
(E) II, III
Rationale: 6/10 (60%) of the members are women and 6/8 of the members are married men. Let the total numbers of members is 80 (the LCM of 10 and 8). Then there are:
6/10*80 = 48 women;
80 - 48= 32 men;
6/8*32 = 24 married men;
32 - 24 = 8 unmarried men.
So, option I,II is true.
Answer: C
Answer: (C) I, II
Question: The price of pulses has fallen by 20%. How many quintals can be bought for the same amount which was sufficient to buy 18 quintals at the higher price?
(A) 20
(B) 22.5
(C) 25
(D) 30
(E) 32.5
Rationale: 80% of original price can buy = 18 quintals.
Therefore, he can buy ( 18 x 100 )/ 80 = 22.5 quintals at the lower price.
ANSWER:B
Answer: (B) 22.5
Question: There are 6 boxes numbered 1, 2,3,4,5 and 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball & the boxes containing green balls are consecutively numbered. The total no. of ways in which this can be done is?
(A) 18
(B) 19
(C) 21
(D) 23
(E) 25
Rationale: If only one of the boxes has a green ball, it can be any of the 6 boxes. So, this can be achieved in 6 ways.
If two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes. 12, 23, 34, 45, 56.
Similarly, if 3 of the boxes have green balls, there will be 4 options.
If 4 boxes have green balls, there will be 3 options.
If 5 boxes have green balls, then there will be 2 options.
If all 6 boxes have green balls, then there will be just 1 options.
Total number of options = 6 + 5 + 4 + 3 + 2 + 1 = 21
C
Answer: (C) 21
Question: A, B and C enter into a partnership by investing $11000, $15000 and $23000 respectively. At the end of 8 months, B receives $3315 as his share. Find the share of A.
(A) $1865
(B) $2087
(C) $2217
(D) $2431
(E) $2662
Rationale: The ratio of capital of A, B and C = 11000 : 15000 : 23000 = 11 : 15 : 23
A's share = (11/15)*3315 = $2431
The answer is D.
Answer: (D) $2431
Question: A cubical tank is filled with water to a level of 2 feet. If the water in the tank occupies 50 cubic feet, to what fraction of its capacity is the tank filled with water?
(A) 1/3
(B) 2/3
(C) 3/4
(D) 2/5
(E) 5/6
Rationale: The volume of water in the tank is H*L*B = 50 cubic feet.
Since H = 2, then L*B = 25 and L = B = 5.
Since the tank is cubical, the capacity of the tank is 5*5*5 = 125.
The ratio of the water in the tank to the capacity is 50/125 = 2/5
The answer is D.
Answer: (D) 2/5
Question: 5 is added to a certain number, the sum is multiplied by 7, the product is divided by 5 and 5 is subtracted from the quotient. The remainder left is half of 66. What is the number?
(A) 21
(B) 20
(C) 22
(D) 30
(E) 45
Rationale: Let number is X.
When 5 added to it,
= (X+5)
7 multiplied to sum,
= 7 *(X +5)
Now,
= [{7 *(X +5)} /5]
And,
= [{7 *(X +5)} /5] - 5
According to question,
[{7 *(X +10)} /5] - 5 = half of 66
[(7X + 35) /5) = 33 +5
7X + 35 = 38 *5
X = 155/7
X = 22.14=22
So, required number is: 22.
ANSWER : C
Answer: (C) 22
Question: In the accounting branch of a commercial institute, the percentage of male and female workers is 48% and 52% respectively. In this branch, 40% of males and 20% of females are age 25 or older. If one of the workers is selected at random, what is the probability Y that the worker is under 25 years old?
(A)  0.30
(B)  0.25
(C)  0.45
(D)  0.70
(E)  0.90
Rationale: Percentage of male worker = 48
Percentage of female worker = 52
Let total number of workers = 1000
number of male workers= 480
number of female workers = 520
Number of male age 25 or older = (4/10)*480 = 192
Number of female age 25 or older =(2/10)*520 = 104
Total number of workers 25 or older = 192+104 = 296
Total number of workers under 25 = 1000 - 296 = 704
Probability that a worker randomly selected is under 25 years old = 704/1000 = .704
Alternatively , since the answer options are not close , we can use estimation here .
Percentage of male worker 25 or older = (4/10)*48 = 20 % approx
Percentage of female worker 25 or older = (2/10)*52 = 10 % approx
Percentage of total worker 25 or older = 30 %
Percentage of total worker under 25 = 70 %
Probability that a worker randomly selected is under 25 years old Y= .7
Answer D
Answer: (D)  0.70
Question: The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
(A) 9000
(B) 9400
(C) 9600
(D) 9800
(E) 7500
Rationale: Explanation:
Greatest number of 4-digits is 9999.
L.C.M. of 15, 25, 40 and 75 is 600.
On dividing 9999 by 600, the remainder is 399.
Required number (9999 - 399) = 9600.
ANSWER IS C
Answer: (C) 9600
Question: In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 5), and (a, b+1) are three points on the line, where a and b are unknown, then k = ?
(A)  1/2
(B)  1
(C)  3/4
(D)  2
(E)  5/2
Rationale: b=4k+1...(1)
b+1=ak+1...(2)
5=ak+1...(3)
Taking (2) and (3)
5=b+1
b=4
Taking (1)
4=4k+1
k=3/4
Answer :C
Answer: (C)  3/4
Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B’s money was used?
(A) 4 months
(B) 6 months
(C) 8 months
(D) 10 months
(E) None
Rationale: Sol.
Let the total profit be Rs. z. Then,
B’ share = Rs. 2z/3, A’s share = Rs. [z - 2z/3] = Rs. z/3
∴ A : B = z/3 : 2z/3 = 1 : 2.
Let the total capital be Rs. x and suppose B’s money was used for x months. Then,
[1/4 x * 15] / [3/4 x * y] = 1/2 ⇔ y = [15 * 2 / 3] = 10.
Thus, B’s money was used for 10 months.
Answer D
Answer: (D) 10 months
Question: A searchlight on top of the watchtower makes 2 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 6 seconds?
(A) 5/6
(B) 4/5
(C) 3/4
(D) 2/3
(E) 1/2
Rationale: The searchlight completes one revolution every 30 seconds.
The probability that the man's area will be lit up is 6/30=1/5.
The probability that he will stay in the dark is 1-1/5=4/5
The answer is B.
Answer: (B) 4/5
Question: Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(A) lost 4 cents
(B) broke even
(C) gained 4 cents
(D) lost 10 cents
(E) gained 10 cents
Rationale: B
broke even
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
Answer: (B) broke even
Question: what is the probability of always having x+y>0 ,where y<0
(A) 1/2
(B) 1/8
(C) 3/4
(D) 1/4
(E) none
Rationale: total value of X can be : 1. X < 0 ; 2. X = 0 ; 3. X > 0 but less than Y in magnitude 4. X > 0 as well as |Y|
so probability of having X + Y > 0 would be 1/4
ANSWER:D
Answer: (D) 1/4
Question: According to the 2001 census,the population growth rate of Lucknow is going to be an increasing AP with first year's rate as 5% and common difference as 5% but simultaneously the migration,rate is an increasing GP with first term as 1% and common ratio of 2.If the population on 31 december 2000 is 1 million,thn find in which year will Lucknow witness its first fall in population?
(A) 2006
(B) 2007
(C) 2005
(D) 2008
(E) 2009
Rationale: population growth rate according to the problem
year 1 = 5%
year 2 = 10%
year 3 = 15%
year 4 = 20%
year 5 = 25%
year 6 = 30%
population decrease due to migration
year 1 = 1%
year 2 = 2%
year 3 = 4%
year 4 = 8%
year 5 = 16%
year 6 = 32%
Thus, the first fall would happen in year 2006
ANSWER:A
Answer: (A) 2006
Question: In a game of billiards, A can give B 20 points in 60 and he can give C 30 points in 60. How many points can B give C in a game of 100?
(A) 43
(B) 54
(C) 25
(D) 86
(E) 23
Rationale: A scores 60 while B score 40 and C scores 30.
The number of points that C scores when B scores 100
= (100 * 30)/40 = 25 * 3 = 75.
In a game of 100 points, B gives (100 - 75)
= 25 points to C.
Answer: C
Answer: (C) 25
Question: For any two numbers X and Y , define X#Y=X+Y -XY . If X,Y>0.5, then X#X < Y#Y if
i. 1>X>Y
ii. 1>Y>X
iii. Y>X>1
(A) i only
(B) option ii only
(C) i and ii only
(D) ii and iii only
(E) i and ii only
Rationale: X#X = 2X-X^2 and Y#Y=2Y-Y^2
X#X <Y#X
=> 2X - X^2 < 2Y - Y^2
=> 2(X-Y) < (X-Y)(X+Y)
=> X+Y>2 and X-Y>0 or X+Y<2 and X-Y<0
=> X+Y>2 and X>Y or X+Y<2 and X<Y
Using (i), if 1>X>Y, then the first case applies but X+Y>2 is not satisfied. False.
Using (ii), if 1>Y>X, then the second case applies and X+Y<2 is satisfied. True.
Using (iii), if Y>X>1, then the second case applies but X+Y<2 is not satisfied. False.
Therefore only (ii) is true, and choice (B) is correct.
Answer: (B) option ii only
Question: Car Z travels 50 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour, but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour. How many miles does car Z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour?
(A) 320
(B) 375.2
(C) 400
(D) 408.3
(E) 440
Rationale: The question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour. We therefore first calculate the fuel efficiency at that speed.
The stem tells us that at 50 miles/hour, the car will run 40 miles/gallon and at 60 miles/hour, that distance decreases by 20%. We can therefore conclude that the car will travel 40 miles/gallon at a constant speed of 60 miles/gallon. With 10 gallons of fuel, the car can therefore travel 40 miles/gallon * 10 gallons = 400 miles.
Answer C.
Answer: (C) 400
Question: How many positive integers will divide evenly into 310?
(A) 4
(B) 6
(C) 8
(D) 12
(E) 16
Rationale: The question is asking how many factors 310 has.
310 = 2*5*31
The number of factors is 2^3 = 8
The answer is C.
Answer: (C) 8
Question: 3,7,12,..............4th terms
(A) 43
(B) 53
(C) 18
(D) 65
(E) 78
Rationale: 3+4=7
7+5=12
12+6=18
ANSWER:C
Answer: (C) 18
Question: Divide Rs. 1700 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
(A) 346
(B) 425
(C) 375
(D) 337
(E) 639
Rationale: A+B+C = 1700
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1700 => 425
Answer:B
Answer: (B) 425
Question: A person traveled from his house to office at 30 kmph; then he was late to his office by 5 minutes. If he increases his speed by 10 kmph he would be early by 15 minutes to his office. What should be his speed so that he reaches his office on time ?
(A) 36 kmph
(B) 32 kmph
(C) 34 kmph
(D) 35 kmph
(E) 37 kmph
Rationale: Let the distance between house and office be x km
(x/30) – (x/40) = 20/40; x/120 = 1/3 x = 40 km
Travlling at 40 kmph, he reaches office in 1 hour i.e. 15 minutes early
So required speed = 40/ 5/4 = 40 * 4/5
= 160/5
= 32 kmph
ANSWER:B
Answer: (B) 32 kmph
Question: Which of the options below is the lowest interger divisible by all the numbers below: 1,2,3,4,5,6,7,8,9,10
(A) 234
(B) 1222
(C) 2520
(D) 2894
(E) 1430
Rationale: To get the least positive integer that can be divided by each of these numbers 1,2,3,4,5,6,7,8,9,10 you calculate the lowest common denominator of all the numbers. Express each number as a product of their prime factors and multiply the set of prime numbers from each set with the highest exponent value.
LCM=2^3*3^2*5*7
The answer is C)
Answer: (C) 2520
Question: If two numbers, a and b, are to be chosen from a set of 4 consecutive integers starting with 1 and a set of three consecutive even integers starting with 12, respectively, what is the probability that b/a will not be an integer?
(A) 2/12
(B) 3/12
(C) 4/12
(D) 1/2
(E) 2/3
Rationale: a is from the following set {1,2,3,4}
b is from the following set {12,14,16}
The total number of ways of choosing 2 integers, one from each set is 4*3 = 12 ways.
The possibilities where b/a is not an integer is for the following outcomes:
{b,a} = {14,3},{14,4},{16,3} = 3 ways
Thus the probability is 3/12 = 1/4
The answer is B.
Answer: (B) 3/12
Question: If def < 0 and ef > 0, which of the following must be positive?
(A)  xy
(B)  xz
(C)  (d^2)ef
(D)  d(e^2)f
(E)  xy(z^2)
Rationale: Given that ef is positive and def is negative, you can say that a MUST be negative. As for e and f either they are both positive or both negative.
Option (C) has d^2 which is positive and ef which is positive. So (C) must be positive.
Answer: (C)  (d^2)ef
Question: Jim bought edging to go around a circular garden with a radius of 10 feet. Later he decided to
double the diameter of the garden. How many more feet of edging must he buy?
(A) 28.84' additional edging
(B) 48.84' additional edging
(C) 38.84' additional edging
(D) 62.80' additional edging
(E) 58.84' additional edging
Rationale: circumference of small garden = 2 x 3.14 x 10 = 62.80'
double of the circumference of small garden = 2 x 62.80' = 125.60'
More feet to be buy =125.60 - 62.80 = 62.80
Answer :D
Answer: (D) 62.80' additional edging