mathewhe/aqua_rat huggingface dataset:
Question: There are 4 red shoes & 4 green shoes . If two of red shoes are drawn what is the probability of getting red shoes
(A) 1/3
(B) 1/14
(C) 3/14
(D) 1/15
(E) 1/16
Rationale: taking 2 red shoe the probability is 4C2
from 8 shoes probability of taking 2 red shoes is 4C2/8C2=3/14
ANSWER:C
Answer: (C) 3/14
Question: The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the second largest sector?
(A) 1/72
(B) 1/36
(C) 1/18
(D) 1/12
(E) 7/36
Rationale: Its an AP question .... it is given clearly in the question .
Let the smallest angle be a
and the circle has 8 sectors and hence 8 angle with a common difference d
hence all the angles can be written in AP form with Cd as d ,
a, a+d, a+2d, a+3d ,a+4d, a+5d, a+6d ,a+7d,
given that a+7d = 80 --------1
also
a + a+d + a+2d + a+3d +
a+4d + a+5d + a+6d + a+7d = 360 ( as sum of all the angle is 360)
which is 8a + 28d = 360 --------2
solving 1 and 2
we get a=10
We are almost done ,
now the question ask what fraction of the wheel’s area is represented by the smallest sector ?
(70/360)( pie r*r)/ (pie r*r) = 70/360= 7/36
E ans ....
Answer: (E) 7/36
Question: 10 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played?
(A) 90
(B) 98
(C) 35
(D) 99
(E) 80
Rationale: Though 2*(10C2) is the correct approcah to do this, but for people like me who find Perm, Comb n Prob a nightmare, an easy approach can be used.
The first guy has to play 2 matches with the rest of 9, so he'll play 18 matches.
Similarly, second guy has to play with the rest of 8 as his 2 games with the first guy are already played. So he plays 16 matches.
This continues like this and the total matches are 18+16+14...+2
18+16+...+2 = 2(9+8+...+1) = 2((9*10)/2) = 9*10 = 90.
ANSWER:A
Answer: (A) 90
Question: A tennis championship is played on a knock-out basis, i.e., a player is out of the tournament when he loses a match.
(a) How many players participate in the tournament if 15 matches are totally played?
(b) How many matches are played in the tournament if 50 players totally participate?
(A) 15,49
(B) 16,49
(C) 16,48
(D) 16,47
(E) None of these
Rationale: (a) u don’t need to sum it up. since it’s a knock out only 1 person emerges winner finally. so15+1=16 is answer.because after15 matches finally we shud’ve 15 losers and 1winner.
(b) 49:its always one less than no of players as per the idea given above.so no need to check okay cos its always true.ans is 49
Answer B
Answer: (B) 16,49
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 90 m
Rationale: Explanation:
Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
ANSWER IS A
Answer: (A) 50 m
Question: A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit.
(A) 1260
(B) 1200
(C) 1300
(D) 1500
(E) 2000
Rationale: Let SP be x then
(100-loss)%(1st SP) =(100+gain%):(2nd SP)
=>(95/1140 = 105/x)
x=1260
ANSWER A
Answer: (A) 1260
Question: A man has Rs. 400 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) 90
(B) 75
(C) 50
(D) 80
(E) 60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 400
16x = 400
x = 25.
Hence, total number of notes = 3x = 75.
Answer is B.
Answer: (B) 75
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 5 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
(A) 168.
(B) 80.
(C) 56.
(D) 64.
(E) 16.
Rationale: ways to select one shelf = 2
ways to select one bed = 4
ways to select one of the following: a chair or a closet = 5+3 = 8
ways to select all of them together = 2*4*8 = 64
D
Answer: (D) 64.
Question: If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 315, what is the greatest possible profit that might be made in selling eight books ?
(A) 23267
(B) 2677
(C) 1800
(D) 2778
(E) 920
Rationale: Explanation:
Least Cost Price = Rs. (200 * 8) = Rs. 1600.
Greatest Selling Price = Rs. (315 * 8) = Rs. 2520.
Required profit = Rs. (2520 - 1600) = Rs. 920.
Answer: E) 920
Answer: (E) 920
Question: Carol is three times Kalice’s age but only twice as old as Betty. Alice is twelve years younger than Carol. How old is Betty?
(A) 6
(B) 9
(C) 12
(D) 18
(E) 24
Rationale: ans B..9..
given that C=3K=2B..AND K=C-12..
substituting the values K=6,C=18 AND B=9..
Answer: (B) 9
Question: A coin is tossed seven times. What is the probability that there is at the least one tail?
(A) 127/128
(B) 31/37
(C) 31/18
(D) 31/10
(E) 31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed seven times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/128; P(T) = 1 - 1/128= 127/128
Answer: A
Answer: (A) 127/128
Question: The price of lunch for 15 people was $206.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
(A)  $11.73
(B)  $12.48
(C)  $13.80
(D)  $14.00
(E)  $15.87
Rationale: Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 206 is for 115 then we have to calculate for 100
for 115 206
for 100 x
so by cross multiplication we get 115x=100*206 => x=100*206/110 by simplifying we get x as 187.27 which is the price of lunch before gratuity so the gratuity is 18.73 so
as the question ask the average price person excluding gratuity is 187.27/15=12.48 so our answer is B)
Answer: (B)  $12.48
Question: Last year a certain bond price with a face value of 5000 yielded 9% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
(A) 4063
(B) 5325
(C) 5351
(D) 6000
(E) 6923
Rationale: Interest = 0.09*5000 = 0.065*selling price --> selling price = 0.09*5000/0.065 --> selling price = ~6,923
Answer: E.
Answer: (E) 6923
Question: If the remainder is 11 when positive integer n is divided by 18, what is the remainder when n is divided by 9?
(A) 0
(B) 2
(C) 1
(D) 3
(E) 4
Rationale: Assume x is quotient here,
n=18x+11 ----------(1)
and n=9x+ ?
We can also write equation (1) as:
n=(18x+9)+2.
ie 9(2x+1)+2 ie the first term is perfectly divisible by 6.
So,the remainder left is 2.
So,answer (B) is right choice.
Answer: (B) 2
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
(A) 22
(B) 27
(C) 12
(D) 71
(E) 53
Rationale: Explanation:
T = 9/45 * 60 = 12
Answer: Option C
Answer: (C) 12
Question: The difference of 2 digit no. & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 14
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: 3 ltr of water is added with 11 ltr of a solution containing 42%of alcohol in the water. The %of alcohol in the new mixture is?
(A) 23%
(B) 35%
(C) 33%
(D) 40%
(E) 45%
Rationale: We have a 11 litre solution containing 42% of alcohol in the water.
=> Quantity of alcohol in the solution
=11×42/ 100
Now 3 litre of water is added to the solution.
=> Total quantity of the new solution = 11 + 3 = 14
Percentage of alcohol in the new solution
=11×42/100
14
×
100
=11×4210014×100
=11×3/100
=33%
C
Answer: (C) 33%
Question: Which of these expressions has the greatest value?
(A) 1345211/1345215
(B) 1892345/1862348
(C) 1215768/1215769
(D) 1532672/1532675
(E) 1214651/1214651
Rationale: Using elimination method on options
1892345/1862348 = 1.01610708632...
ANSWER:B
Answer: (B) 1892345/1862348
Question: There are different 10 circles. What is the number of the greatest possible points with which the circles intersect?
(A) 90
(B) 100
(C) 110
(D) 180
(E) 200
Rationale: Maximum points of intersection between n different circles = n*(n - 1) = 10*9 = 90
Answer: A
Answer: (A) 90
Question: If 15% of A is the same as 25% of B, then A : B is :
(A) 5:3
(B) 4:3
(C) 7:16
(D) 12:17
(E) 11:13
Rationale: Expl : 15% of A I= 25 % of B =15A/100 = 25B/100 = 5/3 = 5:3
Answer:A
Answer: (A) 5:3
Question: A card is drawn from a pack of 250 card numberd 1 to 200.what is the probability that drawing a no.which is perfect cube?
(A) 1/40
(B) 1/20
(C) 1/30
(D) 3/40
(E) 5/40
Rationale: 6^3 is 216 so only 1to 5 is a perfect cube with in 200
therefore 5c1/200c1
=1/40
ANSWER:A
Answer: (A) 1/40
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are picked at random, what is the probability that they are all blue?
(A) 1/455
(B) 1/439
(C) 1/429
(D) 1/409
(E) 1/420
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that all the three marbles picked at random are blue = ³C₃/¹⁵C₃ = (1 * 3 * 2 * 1)/(15 * 14 * 13)
= 1/455
Answer:A
Answer: (A) 1/455
Question: Following an increase in prices, the price of a candy box was 10 pounds and the price of a can of soda was 9 pounds. If the price of a candy box was raised by 25%, and the price of a can of soda was raised by 50%. What was the price of a box of candy plus a can of soda before prices were raised?
(A) 11.
(B) 12.
(C) 13.
(D) 14.
(E) 14.5
Rationale: Price of candy before price increase= 10/1.25= 8
Price of soda before price increase= 9/1.5= 6
Total price = 8+6= 14
D is the answer
Answer: (D) 14.
Question: After decreasing 25% in the price of an article costs Rs.1500. Find the actual cost of an article?
(A) 1400
(B) 1300
(C) 1200
(D) 2000
(E) 1500
Rationale: CP* (75/100) = 1500
CP= 20* 100 => CP = 2000
ANSWER:D
Answer: (D) 2000
Question: 850 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
(A) a) 162
(B) b) 138
(C) c) 60
(D) d) 17
(E) e) 12
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 850 = 17
Answer: D
Answer: (D) d) 17
Question: A certain auto manufacturer sold 3% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,00, did the manufacturer sell in 2007?
(A) 63,000
(B) 2,000,000
(C) 2,030,000
(D) 204,000
(E) 2,300,000
Rationale: Let's assume in 2006 he has sold X. Therefore in 2007 he should have sold 97/100×X.
97/100×2100=2037
-->2,037,000 sold in 2007. When rounded to the nearest 10,000 :
204,000
D
Answer: (D) 204,000
Question: With # andeach representing different digits in the problem below, the difference between #and ## is 534. What is the value of?
#
-##
____
534
(A) 7
(B) 8
(C) 9
(D) 6
(E) 10
Rationale: 100x
-(10x +x)
-----------
89 x= 534
x = 6
D
Answer: (D) 6
Question: How many seconds will a train 140 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 28 sec
(B) 29 sec
(C) 24 sec
(D) 25 sec
(E) 26 sec
Rationale: D = 140 + 150 = 290
S = 36 * 5/18 = 10 mps
T = 290/10 = 29 sec
B
Answer: (B) 29 sec
Question: A student finds the average of nine positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say pq for qp. Due to this, the average becomes 1 less than the previous one. What was the difference of the two digits p and q?
(A) 8
(B) 6
(C) 1
(D) 4
(E) 2
Rationale: Explanation :
Let the original number be pq i.e., (10p + q).
After interchanging the digits, the new number becomes qp i.e., (10q + p).
The question states that the average of 9 numbers has become 1 less than the original average.
Therefore, the sum of the original 9 numbers will be 9*1 more than the sum of the 9 numbers with the digits interchanged.
i.e., 10p + q = 10q + p + 9
=> 9a - 9b = 9
=> a - b = 1.
Answer : C
Answer: (C) 1
Question: If x is 12 percent greater than 70, then x =
(A) 78.4
(B) 91.0
(C) 88.0
(D) 70.4
(E) 71.2
Rationale: 12% of 70 = (70*0.11) = 8.4
12% greater than 70 = 70 + 8.4 = 78.4
Answer is clearly A.
Answer: (A) 78.4
Question: 3 years ago, the avg age of a family of 5 individuals was 17. A kid have been born the avg age of family is an exact today? What is the age of the kid?
(A) 2 years
(B) 5 years
(C) 6 years
(D) 4 years
(E) 7 years
Rationale: A
2 years
Current age of 5 individuals is,
=5 x 17 + 3 x 5 = 100 years
Also, current ages of 5 persons + Age of the kid
= 6 x 17 = 102 years
Therefore, Age of the Kid = 102 – 100 = 2 years.
Answer: (A) 2 years
Question: select the no. which is different from series
13,16,19,22,24,28
(A) 24
(B) 28
(C) 19
(D) 13
(E) 22
Rationale: 13. 16. 19. 22. 24. 28
every step it increase by 3 but from 22 it should 25 but it is 24so,24 is different
answer A
Answer: (A) 24
Question: The moon revolves around the earth at a speed of approximately 1.05 kilometers per second. This approximate speed is how many kilometers per hour?
(A) 60
(B) 61.2
(C) 62.5
(D) 3,780
(E) 3,672
Rationale: moon revolves around the earth at a speed of 1.02kilometers per second.
one hour equal to 60 minutes.
one minute equals to 60 seconds. so one hour equals to 3600seconds.
so one hour, speed= 1.05*3600=3780kilometers per hour.
Option D is correct
Answer: (D) 3,780
Question: In what time will a train 150 metres long cross an electric pole, if its speed be 122 km/hr?
(A) 2.42
(B) 6.42
(C) 5.42
(D) 4.42
(E) 3.42
Rationale: Solution
Speed	= (122 x 5 /18) m/sec
= 33.88m / sec
Time taken	= (150 /33.88) sec
= 4.42 sec.
Answer D
Answer: (D) 4.42
Question: What is the units digit of the expression 14^7−16^4?
(A)  0
(B)  3
(C)  8
(D)  6
(E)  4
Rationale: I think answer on this one should be C too. Since we know that 14^7>16^4, as Will said one should always check if the number is positive.
Answer: (C)  8
Question: Find the average of all numbers between 4 and 41 which are divisible by 5
(A) 22.5
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Average=(5+10+15+20+25+30+35+40)/8=180/8=22.5
Answer: Option A
Answer: (A) 22.5
Question: A and B began business with Rs.2000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of B.
(A) 240
(B) 288
(C) 277
(D) 455
(E) 361
Rationale: (2*8 + 1*4):(4*8 + 5*4)
5:13
13/18 * 630 = 455
Answer: D
Answer: (D) 455
Question: A gambler rolls three fair six-sided dice. What is the probability that two of the dice show the same number, but the third shows a different number?
(A) 1/36
(B) 5/36
(C) 10/36
(D) 15/36
(E) 20/36
Rationale: First off, we want to find the probability of rolling a pair of any number. There are six
pairs and a total of 36 different ways to roll a pair of dices: 6/36 = 1/6.
Next, we want to account for the third die - it cannot be the same as the first two,
so it can be any of five numbers out of 6: 5/6.
Therefore probability is 5/6 x 1/6 = 5/36.
It is tempting here to think that we have solved the problem. But if we read carefully, the
question does not say that the first two dice have to be the same and the third die has
to be different.
the question says a gambler rolls 3 dice. So the first two do not have to be pairs.
As long as 2 of the 3 dice are pairs and the last die is a different number. To find the
number of way this can occur, we use combinations formula: 3!/2!1! = 3.
We multiply this to the numerator to give us 3 x 5/36 = 15/36.
ANSWER:D
Answer: (D) 15/36
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 15 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 5 days?
(A) 3
(B) 5
(C) 6
(D) 9
(E) 12
Rationale: Explanation: If six computers require 15 days to process the data, thats
a total of 90 computer-days the product of 6 and 15. If you change the number
of computers or the number of days, 90 will have to remain the product, whether
that means 90 days of one computer or one day with 90 computers.
In 5 days, the number of computers is:
5c = 90
c = 18
18 computers is 12 more than the 6 that it took to do the job in 15 days, so
the correct choice is (E).
Answer: (E) 12
Question: In a business, three friends X,Y and Z shared the profit in the ratio 5:7:8. X invested his amount for 14 months, Y for 8 months and Z for 7 months respectively. Find the ratio of their investments?
(A) 19:49:64
(B) 20:49:64
(C) 20:49:65
(D) 20:50:64
(E) None
Rationale: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively Then, 14x : 8y : 7z = 5 : 7 : 8 Now, 14x/8y = 5/7 => y = (49/20)x 14x/7z = 5/8 => z = (16/5)x => x : y : z = x : (49/20)x : (16/5)x => x : y : z = 20 : 49 : 64
Answer B
Answer: (B) 20:49:64
Question: In Town X, 90 percent of the population are employed, and 20 percent of the population are employed males. What percent of the employed people in Town X are females?
(A) 16%
(B) 66%
(C) 77%
(D) 88%
(E) 52%
Rationale: Total employed people 90%, out of which 20 are employed males, hence 70% are employed females.
(employed females)/(total employed people)=70/90=7/9=77%
Answer: C.
Answer: (C) 77%
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Explanation:
63 + 83 + 103 = a3 => a = 12
A)
Answer: (A) 12
Question: Insert the missing number
3, -9, 27, -81, 243, (....)
(A) 0
(B) -739
(C) 729
(D) 739
(E) -729
Rationale: 3*-3=-9
-9*-3=27
27*-3=-81
-81*-3=243
243*-3=-729
ANSWER:E
Answer: (E) -729
Question: A certain mixture of nuts consists of 5 parts almonds to 1 parts walnuts, by weight. What is the number of pounds of almonds in 140 pounds of the mixture ?
(A)  116
(B)  84
(C)  40
(D)  28
(E)  20
Rationale: Almonds : Walnuts = 5 : 1
Total mixture has 6 parts
In a 140 pound mixture, Almonds are 5/6 (total mixture)
= 5/6 * 140 = 116 pounds
Answer (A)
Answer: (A)  116
Question: In a can, there is a mixture of milk and water in the ratio 8 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 12 : 5. Find the capacity of the can?
(A) 40
(B) 18.4
(C) 48
(D) 50
(E) 56
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 8/13 (T - 8)
After adding milk, quantity of milk in the mixture = 12/17 T.
12T/17 - 8 = 8/13(T - 8)
20T = 1456 - 1088 => T = 18.4.
Answer:B
Answer: (B) 18.4
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C
(A) Rs. 300
(B) Rs. 400
(C) Rs. 500
(D) Rs. 600
(E) None of these
Rationale: Explanation:
C's 1 day's work =
1/3−(1/6+1/8)
=(1/3−7/24)
=1/24
A:B:C=1/6:1/8:1/24
=4:3:1
C′sShare=1/8∗3200=400
Option B
Answer: (B) Rs. 400
Question: For how many integers n is 1^n+3 = (n+3)^1?
(A) None of these
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: If n=0
1^0+3= (0+3)^1
1^3 = 1 ; 3^1 =1 not ok
If n=1
1^1+3 =1 ; (1+3)^1=3^1=3 not OK
So, Answer : A
Answer: (A) None of these
Question: one men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?
(A) 4 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: 1M + 3W ----- 35 h
4M + 4W ------- 21 h
7M -------? d
35M + 105W = 84M +84M
21W = 49M
4 * 35 = 7 * x => x = 20 hours
20/4 = 5 days
ANSWER:B
Answer: (B) 5 days
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
(A) 887
(B) 400
(C) 187
(D) 278
(E) 191
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages
1/6 : 1/8 : 1/24 = 4:3:1
C's share = 1/8 * 3200 = Rs. 400
Answer:B
Answer: (B) 400
Question: One woman and one man can build a wall together in one hour, but the woman would need the help of two girls in order to complete the same job in the same amount of time. If one man and one girl worked together, it would take them two hours to build the wall. Assuming that rates for men, women and girls remain constant, how many hours would it take one woman, one man, and one girl, working together, to build the wall?
(A) 5/7
(B) 6/7
(C) 10/7
(D) 12/7
(E) 22/7
Rationale: Solution:Let work done by man, women and girl per hour be m,w,g respectively.
Then, m+w = 1/1-->(1) , w + 2g = 1/1-->(2) and m + g =1/2-->(3).
No. of hours it would take forone woman, one man, and one girl, working together, to build the wall,n = 1/m+w+g
From (1) and (2), m=2g and from (3) g=1/6,m=1/3 and w=2/3.
So, n = 1/(7/6) = 6/7
Option, B
Answer: (B) 6/7
Question: A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is four times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is quartered by water evaporation. At that time, what is the ratio of water to salt in the solution?
(A) 12:8
(B) 8:16
(C) 9:16
(D) 8 :12
(E) 16:9
Rationale: Water:soap = 3:2
Soap:Salt=12:8
=> For 12 soap, salt = 8
=> For 2 Soap, salt = (8/12)*2 = 16/12=4/3
So, water:soap:salt = 3:2:4/3 = 9:6:4
After open container, water:soap:salt = 2.25:6:4
So, water:salt = 2.25:4 = 9:16
ANSWER:C
Answer: (C) 9:16
Question: Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter?
(A) Rs.932
(B) Rs.132
(C) Rs.108
(D) Rs.109
(E) Rs.131
Rationale: 2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer: B
Answer: (B) Rs.132
Question: A = {2,0, 1, -3, 6, -8}
B = {-1, 2, -4, 7,-6,20}
If a is a number that is randomly selected from Set A, and b is a number that is randomly selected from Set B, what is the probability that ab > 0?
(A) 1/4
(B) 1/3
(C) 5/12
(D) 4/9
(E) 1/2
Rationale: For the product of 2 numbers to be positive either both of them must be positive or both of them must be negative:
P(positive, positive) = 3/6*3/6 = 9/36;
P(negative, negative) = 2/6*3/6 = 6/36.
P = 9/36 + 6/36
= 15/36
= 5/12.
Answer: C.
Answer: (C) 5/12
Question: When a=x+(3/x) and b=x-(3/x), (2^a^2)/(2^b^2)=?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 4096
Rationale: --> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=6/x and a+b=2x, 2^(a-b)(a+b)=2^(6/x)(2x)=2^12=4096
Therefore, the answer is E
Answer: (E) 4096
Question: A person travels equal distances with speeds of 5 km/hr, 6 km/hr and 7 km/hr and takes a total time of 47 minutes. The total distance is?
(A) 5 km
(B) 3 km
(C) 7 km
(D) 9 km
(E) 2 km
Rationale: Let the total distance be 3x km.
Then, x/5 + x/6 + x/7 = 27/53
27x/53 = 47/60 => x = 1.54
Total distance = 3 * 1.54 = 4.61 km.
Answer:A
Answer: (A) 5 km