mathewhe/aqua_rat huggingface dataset:
Question: Three business people who wish to invest in a new company. Each person is willing to pay one third of the total investment. . After careful calculation, they realize that each of them would pay $ 7000 less if they could find two more equal investors. How much is the total investment in the new business.
(A) a)	$ 64,000
(B) b)	$ 54,000
(C) c)	$ 21,000
(D) d)	$ 52,500
(E) e)	$3,600
Rationale: Initially each invest in x. Hence total investment is 3x.
Total investment is also 5(x-7000).
3x = 5(x-7000)
x= 5*7000/2 = 17500
3x = 52500 and the answer is D.
Answer: (D) d)	$ 52,500
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long W would it have taken for him to walk both ways.
(A) 8 h 45 min
(B) 7 h 45 min
(C) 6 h 45 min
(D) 5 h 30 min
(E) None of these
Rationale: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back W=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Answer: (A) 8 h 45 min
Question: A and B can do a work in 12 days and 36 days respectively. If they work on alternate days beginning with B, in how many days will the work be completed?
(A) 11
(B) 17
(C) 10
(D) 17
(E) 18
Rationale: The work done in the first two days = 1/12 + 1/36 = 1/9
so, 9 such two days are required to finish the work.
i.e., 18 days are required to finish the work.
Answer: E
Answer: (E) 18
Question: Can anyhow help me with an easy solution for this
3, 4, 81, 4, 5, 121, 6, 7, ?
(A) 144
(B) 121
(C) 256
(D) 225
(E) 376
Rationale: 3, 4, 81, 4, 5, 121, 6, 7, ?
3+4=7 and 7+2=9 and 9^2=81
4+5=9 and 9+2=11 and 11^2=121
6+7=13 and 13+2=15 and 15^2=225
ANSWER:D
Answer: (D) 225
Question: If the range E of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 	0
(B) 	2
(C) 	12
(D) 	13
(E) 	15
Rationale: The range E of a set is the difference between the largest and smallest elements of a set.
Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.
The the difference between the greatest possible value of x and least possible value of x is 15-2=13.
Answer: D.
Answer: (D) 	13
Question: 8 identical machines, working alone and at their constant rates, take 6 hours to complete a job lot. How long would it take for 5 such machines to perform the same job?
(A) 2.25 hours
(B) 8.75 hours
(C) 12 hours
(D) 14.25 hours
(E) 9.6 hours
Rationale: Let each machine do 1 unit of work for 1 hour
8 machines --> 8 units of work in 1 hour
For 6 hours = 8*6 = 48 Units of total work is done.
Now this 48 Units of total work must be done by 5 machines
5 units of work(5 machines) ---> 1 hour
for 48 Units of work
5*9.6 ---> 1*9.6 hours
E 9.6 hours
Answer: (E) 9.6 hours
Question: The mean of 50 observations is 200. But later he found that there is decrements of 47 from each observations. what is the the updated mean is ?
(A) 165
(B) 185
(C) 153
(D) 198
(E) 199
Rationale: 153
Answer is C
Answer: (C) 153
Question: Car R and Car Y traveled the same 80-mile route. If Car R took 2 hours and Car Y traveled at an average speed that was 50 percent faster than the average speed of Car R, how many hours did it take Car Y to travel the route?
(A)  2/3
(B)  1
(C)  4/3
(D)  8/5
(E)  3
Rationale: The speed of car R is (distance)/(time) = 80/2 = 40 miles per hour.
The speed of car Y = 3/2*40 = 60 miles per hour --> (time) = (distance)/(speed) = 80/60 = 4/3 hours.
Answer: C.
Or: to cover the same distance at 3/2 as fast rate 2/3 as much time is needed --> (time)*2/3 = 2*2/3 = 4/3 hours.
Answer: C.
Answer: (C)  4/3
Question: A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:
(A) 10
(B) 6
(C) 5
(D) 4
(E) None of these
Rationale: Explanation:
Speed of the motor boat =15 km/hr
Let speed of the stream =v
Speed downstream =15+v km/hr
Speed upstream =15-v km/hr
Time taken downstream =30/15+v
Time taken upstream =30/15-v
Total time =30/15+v + 30/15-v
Given that total time is 4 hours 30 minutes
=4 1/2hour =9/2hour
ANSWER IS C
Answer: (C) 5
Question: Find the missing number in the series.
2 , 3 , 6 , 0 , 10, -3 , 14...
(A) -6
(B) 8
(C) 7
(D) 67
(E) 65
Rationale: Explanation:
There are two series in the question
1.	Add 4 : 2+3 = 6, 6+4 = 10
2.	Subtract 3 : 3-3 = 0, 0-3 - -3
Thus, following the series:
-3-3 = -6
ANSWER: A
Answer: (A) -6
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2+y-12=0
(A) If x>y
(B) If x>=y
(C) If x < y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X=4,3
Y=-4,3
So, X>=Y
B
Answer: (B) If x>=y
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 7 hours?
(A) 125 miles
(B) 225 miles
(C) 455 miles
(D) 425 miles
(E) 525 miles
Rationale: During each hour, the car travels 65 miles. For 7 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 + 65 = 7 × 65 = 455 miles
correct answer is C) 455 miles
Answer: (C) 455 miles
Question: Triangle ATriangle B are similar triangles with areas 1536 units square and 1734 units square respectively. The ratio of there corresponding height would be
(A) 9:10
(B) 17:19
(C) 23:27
(D) 16:17
(E) 15:23
Rationale: Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=1536/1734
(x^2/y^2)=(16*16*6)/(17*17*7)
(x^2/y^2)=16^2/17^2
x/y=16/17
Ans=D
Answer: (D) 16:17
Question: Kyle, David, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/3, 2/7 and 5/9, respectively, what is the probability that Kyle and Catherine, but not David will solve the problem?
(A) 35/189
(B) 33/129
(C) 25/189
(D) 24/113
(E) 20/189
Rationale: P(Kyle will solve)=1/3
P(David will not solve)= 1 - 2/7 = 5/7
P(Catherine will solve) = 5/9
P= (1/3)*(5/7)*(5/9) = 25/189
Answer:C
Answer: (C) 25/189
Question: A and B invests Rs.5000 and Rs.6000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 2:3
(B) 82:31
(C) 32:45
(D) 34:89
(E) 35:21
Rationale: A : B
(5000*4)+(2500*8) : (6000*6)+(4000*6)
40000 : 60000
2 : 3
Answer:A
Answer: (A) 2:3
Question: A car traveled from San Diego to San Francisco at an average speed of 63 miles per hour. If the journey back took twice as long, what was the average speed of the trip?
(A) 24.
(B) 32.
(C) 36.
(D) 42.
(E) 44.
Rationale: Let the time taken be = x
One way distance = 63x
Total distance traveled = 2 * 63x = 126x
Total time taken = x + 2x = 3x
Average speed = 126x/3x = 42
Answer: D
Answer: (D) 42.
Question: If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?
(A) Rs. (xd/y)
(B) Rs. xd
(C) Rs. (yd/x)
(D) Rs. yd
(E) None of these
Rationale: Explanation :
cost of x metres of wire = Rs. d
cost of 1 metre of wire = Rs.(d/x)
cost of y metre of wire = Rs.(y × (d/x)) = Rs. (yd/x).. Answer : Option C
Answer: (C) Rs. (yd/x)
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 14 miles, how many miles was Mike's ride?
(A) 28
(B) 30
(C) 32
(D) 34
(E) 36
Rationale: The cost of Annie's ride was 2.5+5+(0.25*14) = $11
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 11
0.25*x = 8.5
x = 34 miles
The answer is D.
Answer: (D) 34
Question: The rowing athletes in a rowing conference voted for coach of the year. Each rower who voted chose exactly 3 coaches to vote for among the 36 coaches in the conference. If each of the 36 coaches received exactly 5 votes (a 36 way tie), how many rowers voted for coach of the year?
(A) 60
(B) 70
(C) 75
(D) 84
(E) 90
Rationale: There were 36*5 = 180 total votes made. If each voter picked 3 coaches, there were 180/3 = 60 voters. A
Answer: (A) 60
Question: A seller uses 900 gm in place of one kg to sell his goods. Find
his actual % profit or loss When he sells his articles at 5 % profit
on cost price ?
(A) 15.5 %
(B) 16.5 %
(C) 16.67 %
(D) 17 %
(E) None of these
Rationale: Explanation :
=[100-x]*z/y-100
=[100+5]1000/900-100=16.67 %
Answer : C
Answer: (C) 16.67 %
Question: Due to 10% decrease in the price of sugar and John can buy 5kg more sugar in Rs100 , then find the CP of sugar?
(A) Rs. 1(2/7)
(B) Rs. 2(1/9)
(C) Rs. 3(2/11)
(D) Rs. 2(2/13)
(E) Rs. 2(2/7)
Rationale: Here r = 10 % ,x = 100 and A = 5 kg
Actual price of sugar = 10*100/((100-10 )*5) = Rs. 2(2/9)
B
Answer: (B) Rs. 2(1/9)
Question: By selling an shirt for $300, a shop keeper gains 20% . During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is:
(A) 2
(B) 14
(C) 8%
(D) 12
(E) 10
Rationale: C
8%
Marked price = $300
C.P. = 100/120 * 300 = $250
Sale price = 90% of $300 = $270
Required gain % = 20/250 * 100 = 8%.
Answer: (C) 8%
Question: The probability that A will not tell truth is 75% and the probability that B will tell truth is 60%.what is the probability that an incident described by them is true?
(A) 10%
(B) 12%
(C) 15%
(D) 17%
(E) 19%
Rationale: A truth....> 25%
B truth.....> 60%
a&b truth...> 0.25*0.6=0.15=15%
ANSWER:C
Answer: (C) 15%
Question: A and B Started a business with Rs.15000 and 12000 respectively. After 6 months B puts Rs.1000 more in his capital while after 8 months A puts Rs.5000 more in his capital. If there is a profit of Rs.35,000 after one year then B will get
(A) Rs.15,000
(B) Rs.18,000
(C) Rs.16,000
(D) Rs.20,000
(E) Rs.22,000
Rationale: Ratio of A and B
=15000*8+20,000*4 : 12000*6+1300*6
= 4 :3
Then B will get
= 3/7*35,000
=15,000
ANSWER:A
Answer: (A) Rs.15,000
Question: How long does a train 130 m long running at the speed of 65 km/hr takes to cross a bridge 150 m length?
(A) 15.7 sec
(B) 15.1 sec
(C) 15.5 sec
(D) 17.1 sec
(E) 16.7 sec
Rationale: Speed = 65 * 5/18
= 18.1 m/sec
Total distance covered
= 130 + 150 = 280 m.
Required time = 280/18.1 '
= 15.5 sec.
Answer:C
Answer: (C) 15.5 sec
Question: What is the next number in the sequence below? 1 4 9 16 25 36 49 64 81 100 121 __ ?
(A) 45
(B) 64
(C) 81
(D) 136
(E) 144
Rationale: as the series of numbers are squares of numbers
1^2=1
2^2=4
3^2=9
and so on
therefore 12^2=144
ANSWER:E
Answer: (E) 144
Question: Find the value of 72519 x 9999 = m?
(A) 723437481
(B) 725465481
(C) 625117481
(D) 725117481
(E) 725118081
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: In how many ways can 4 rings be arranged in 5 finger (no finger has more than 1 ring)?
(A) 5C4
(B) 5P4
(C) (5C4)4!
(D) B and C
(E) NONE OF THE ABOVE
Rationale: No. of ways of selecting 4 fingers from 5(considering a non-mutant) = 5C4.
No. of ways of arranging the 4 rings= 4!
Answer: (5C4).4!
ANSWER:C
Answer: (C) (5C4)4!
Question: In 20 years, A will be twice as old as B was 20 years ago. If A is now 10 years older than B, the present age of B is?
(A) 35yrs
(B) 40yrs
(C) 50yrs
(D) 60yrs
(E) 70yrs
Rationale: Let B's present age = x years
Then A's present age = x+10 years
x+10+20 = 2(x-20)
x + 30 = 2x - 40
x = 70years
Answer is E
Answer: (E) 70yrs
Question: In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 9 feet between each tree. How many trees can be planted if the road is 151 feet long?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 16
Rationale: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T
To maximize the number of trees, the number of 14 feet spaces between trees should be 1 less than total number of trees.
For example, If there are 3 trees, then there should be 2 spaces between them.
So the number of 9 feet spaces will be T-1. Then, the length of sidewalk required for 9 feet spaces will be 9*(T-1)
It is given that total lenght of sidewalk is 151 feet.
or 9(T-1)+T = 151
or 9T-9+T = 151
or 10T = 160
or T=16
Answer:- E
Answer: (E) 16
Question: If the number 517*326 is completely divisible by 7, then the smallest whole number in the place of * will be:
(A) 3
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 6) = (24 + x), which must be divisible by 7.
x = 4.
D
Answer: (D) 4
Question: What approximate value should come in place of question mark (?) in the following equation?
of 857 of 14% – 5.6 × 12.128 = ?
(A) 48
(B) 36
(C) 60
(D) 52
(E) 46
Rationale: ? = 857 of 14% – 5.6 × 12.128
≈ 857 of 14% – 5.6 × 12 ≈ 120 – 67 ≈ 52
Answer D
Answer: (D) 52
Question: How many numbers greater than 5000 can be formed with four of the digits 3, 4, 5, 6, 7 where no digit can be repeated.
(A) 62
(B) 72
(C) 82
(D) 90
(E) 95
Rationale: 3*4*3*2=72
ANSWER:B
Answer: (B) 72
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 32 cm?
(A) 276 sq.cm
(B) 268 sq.cm
(C) 640 sq.cm
(D) 297 sq.cm
(E) 600 sq.cm
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225)
= √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus
= 1/2 * d1d2
= 1/2 * 40 * 32
= 640 sq.cm.
Answer:C
Answer: (C) 640 sq.cm
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 31 km/hr.
(B) 32 km/hr.
(C) 34 km/hr.
(D) 35 km/hr.
(E) 36 km/hr.
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12
2x = 20
x = 10.
Speed of each train = 10 m/sec = 10 x 18/5 km/hr = 36 km/hr.
answer :E
Answer: (E) 36 km/hr.
Question: By selling a bat for Rs.450/- a man loses 10% what is that bat cost price
(A) s.600/-
(B) s.500/-
(C) s.700/-
(D) s.780/-
(E) s.800/-
Rationale: 90 % ------> 450 (90 * 5 = 450)
100 % ------>500 (100 * 5 = 500)
Cost price = Rs.500/-
B)
Answer: (B) s.500/-
Question: The sum of the first 40 positive even integers is 1,640. What is the sum of the first 40 odd integers?
(A) 1500
(B) 1600
(C) 1400
(D) 1200
(E) 1000
Rationale: Sum of first n even numbers = n(n+1) =1640
Sum of first n odd numbers = n^2 = 40*40 = 1600 (here n=40)
Answer : B
Answer: (B) 1600
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 42, the dividend is:
(A) 5330
(B) 5336
(C) 5343
(D) 4452
(E) 5350
Rationale: Divisor = (5 * 42) = 210
= 10 * Quotient = Divisor
=> Quotient = 210/10 = 21
Dividend = (Divisor * Quotient) + Remainder
Dividend = (210 * 21) + 42 = 4452.
D
Answer: (D) 4452
Question: If a = (1/2)b and c = 8a, then which of the following represents the average (arithmetic mean) of a, b, and c, in terms of a ?
(A)  a + 4
(B)  (11/3)a
(C)  4a
(D)  (4 1/7)a
(E)  (7 1/4)a
Rationale: Official Answer: B
The average of the three variables isa + b + c/3. However, we need to solve in terms of a, which means we must convert b and c into something in terms of a.
Were told that a =1/2b, which is equivalent to b = 2a. We can plug that in and simplify the average to:a + 2a + c/3
We also know that c = 8a, which we can plug directly into the average expression:
a + 2a + 8a/3
= 11a/3=(11/3)a , choiceB.
Answer: (B)  (11/3)a
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 33 1/9%
(B) 33 1/2%
(C) 33 1/3%
(D) 33 5/3%
(E) 35 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: 5358 x 56 = ?
(A) 272258
(B) 272358
(C) 300048
(D) 274258
(E) 274358
Rationale: 5358 x 51	= 5358 x (50 + 6)
= 5358 x 50 + 5358 x 6
= 267900 + 32148
= 300048.
C)
Answer: (C) 300048
Question: If @ is a binary operation defined as the difference between an integer n and the product of n and 5, then what is the largest positive integer n such that the outcome of the binary operation of n is less than 10?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: the product of n and 5 =5n..
the difference between an integer n and the product of n and 5=5n-n=4n..
the outcome of the binary operation of n is less than 10?
so 4n<10...
max value that n can take as an integer is 2
ANSWER:B
Answer: (B) 2
Question: If 5x = 3y and xy ≠ 0, what is the ratio of 1/5*x to 1/6*y ?
(A)  25/6
(B)  36/25
(C)  18/25
(D)  5/6
(E)  25/36
Rationale: 5x = 3y => x/y = 3/5
1/5*x to 1/6*y = x/y * 6/5 =(3/5)* (6/5)=18/25
Ans: C
Answer: (C)  18/25
Question: In a group of cows and chickes, the number of legs was 14 more than twice the number of heads . the number of cows was:
(A) 7
(B) 5
(C) 11
(D) 12
(E) 14
Rationale: no of cows x and their legs 4x, no of chicke y and their legs 2y, total no of legs= 4x + 2y, total nof heads = x + y, the no of legs was 14 mor than twice the number of heads. 2x + 2y +14 = 4x + 2y, 14= 4x-2x+ 2y -2y, therefore, 14 = 2x , x = 7, correct answer : (A)
Answer: (A) 7
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles.
(A) 3566
(B) 5467
(C) 4132
(D) 3526
(E) 3782
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer: Option C
Answer: (C) 4132
Question: Arun obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Chemistry, Biology and Physics. What is his average mark?
(A) 53
(B) 54
(C) 72
(D) 75
(E) 78
Rationale: Explanation:
Average mark = 76+65+82+67+85/5=375/5=75
Answer: Option D
Answer: (D) 75
Question: How many 6 digit number contain number 4 ?
(A) 317608
(B) 327608
(C) 337608
(D) 427608
(E) 357608
Rationale: total 6 digit no. = 9*10*10*10*10*10 = 900000
not containing 4 = 8*9*9*9*9*9 = 472392
total 6 digit number contain 4 = 900000 - 472392 = 427608
ANSWER:D
Answer: (D) 427608
Question: Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability w that the World Series will consist of fewer than 7 games?
(A)  12.5%
(B)  25%
(C)  31.25%
(D)  68.75%
(E)  75%
Rationale: In order to determine the probability that the World Series will last less than 7 games, we can first determine the probability w that the World Series WILL last exactly 7 games and then subtract this value from 1.
In order for the World Series to last exactly 7 games, the first 6 games of the series must results in 3 wins and 3 losses for each team.
Let's analyze one way this could happen for Team 1:
Game 1 Game 2 Game 3 Game 4 Game 5 Game 6
T1 Wins T1 Wins T1 Wins T1 Loses T1 Loses T1 Loses
There are many other ways this could happen for Team 1. Using the permutation formula, there are 6!/(3!)(3!) = 20 ways for Team 1 to win 3 games and lose 3 games in the first 6 games.
Logically, there are also 20 ways for Team 2 to win 3 games and lose 3 games in the first 6 games.
Thus, there are a total of 40 ways for the World Series to last the full 7 games.
The probability that any one of these 40 ways occurs can be calculated from the fact that the probability of a team winning a game equals the probability of a team losing a game = 1/2.
Given that 7 distinct events must happen in any 7 game series, and that each of these events has a probability of 1/2, the probability that any one particular 7 game series occurs is.
Since there are 40 possible different 7 game series, the probability that the World Series will last exactly 7 games is:
Thus the probability that the World Series will last less than 7 games is 100% - 31.25% = 68.75%.
The correct answer is D.
Answer: (D)  68.75%
Question: A mixture of 70 liters of wine and water contains 10% water. How much water must be added to make water 12 ½% of the total mixture?
(A) 6 liters
(B) 8 liters
(C) 4 liters
(D) 2 liters
(E) 1 liters
Rationale: 70 * (10/100) = 7
Wine Water
87 1/2% 12 1/2%
87 1/2% ------- 63
12 1/2% -------? => 9-7=2
Answer: D
Answer: (D) 2 liters
Question: If x^2+(1/x^2)=7, x^4+(1/x^4)=?
(A) 10
(B) 47
(C) 12
(D) 14
(E) 15
Rationale: -> x^4+(1/x^4)=(x^2)^2+(1/x^2)^2=(x^2+1/x^2)^2-2x^2(1/x^2)=7^2-2=47.
Thus, the answer is B.
Answer: (B) 47
Question: A man ordered 4 pairs of black socks and some pair of brown socks. The price of a black socks is double that of a brown pair, while preparing the bill the clerk interchanged the number of black and brown pairs by mistake which increased the bill by 50%.The ratio of the number of black and brown pairs of socks in the original order was
(A) 1:4
(B) 1:2
(C) 1:3
(D) 1:5
(E) 1:7
Rationale: Let the price of a pair of brown socks=x, then price of a pair of black socks=2x
If in original order there are 'a' pairs of brown socks, then total price= 4*2x + a*x
With interchanging number of black and brown pairs, new price=a*2x + 4*x
Given new price is 50% more than the original, So a*2x+4*x= (150/100)(4*2x+a*x)
=> 2ax+4x= (3/2)(8x+ax)
=> 4ax - 3ax= 16x
=> a=16 = original number of pairs of brown socks
So ratio of number of black and brown pairs of socks in original order= 4:16 =1:4
ANSWER:A
Answer: (A) 1:4
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 15
Rationale: C= 1/2-1/4-1/5
=1/20
=20days
ANSWER B
Answer: (B) 20
Question: A alone can complete a work in 16 days and B alone can complete in 12 days. Starting with A they work on alternate days. The total work will be completed in?
(A) 12
(B) 13
(C) 13 5/7
(D) 13 ¾
(E) None of these
Rationale: Explanation:
(A+B)’s 2 day work = 1/16 + 1/12 = 7/18
work done in 6 pairs of days=7/48 x 6 = 7/8
remaining work = 1/8
work done by A on 13th day =1/16 remaining work = 1/16
on 14th day its B turn 1/12 work is done by B in 1 day 1/16 work is done by B in 12 x 1/16 = 3/4 day
total time taken =13 ¾ days
Answer: Option D
Answer: (D) 13 ¾
Question: Of a group of people, 10 play piano, 11 play guitar, 14 play violin, 3 play all the instruments, 20 play only one instrument. How many play 2 instruments?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: Let single piano players = p
Let single guitar players = g
Let single violin players = v
Given, p + g + v + 3 + 20 = 10 + 11 + 14.
Hence, p + g + v = 35 - 23 = 12
ANSWER:D
Answer: (D) 12
Question: Jaya invests in a new mutual fund. The fund averages 10% growth annually for the first three years, but it loses 30% of its value in the fourth year. At the end of four years, the value of the mutual fund is approximately what percent of the amount Jaya originally paid?
(A) 93%
(B) 90%
(C) 88%
(D) 85%
(E) 80%
Rationale: Let the initial amount be 100.
Since it grew on constant basis as 10% for three years = 100*1.1^3 = 11*11*1.1 = 132 [Taking 1.1 as 1]
It eroded by 30% = 132 * .7 = 92.something approximated to 93%
So, The correct answer will be (A) 93%
Answer: (A) 93%