mathewhe/aqua_rat huggingface dataset:
Question: Of the 20 members of a kitchen crew, 17 can use the meat-cutting machine, 18 can use the bread-slicing machine, and 15 can use both machines. If one member is chosen at random, what is the probability that the member chosen will be someone who cannot use either machine?
(A) 0
(B) 1/10
(C) 1/7
(D) 1/4
(E) 1/3
Rationale: You know how to solve for Total number of people who can use at least one machine:
Total = n(A) + n(B) - n(A and B)
Total people who can use at least one machine = 17 + 18 - 15 = 20
So all 20 people know how to use at least one machine. Hence, if you pick anyone, the probability is 0 that he wouldn't know how to use any machine.
Answer A
Answer: (A) 0
Question: A CAR HAS RUNS 10000 MILES USING 5 TYRES INTERCHANGABLY TO HAVE A EQUAL WORNOUT BY ALL TYRES HOW MANY MILES EACH TYRE SHOULD HAVE RUN?
(A) 7000 miles.
(B) 8000 miles.
(C) 9000 miles.
(D) 6000 miles.
(E) 5000 miles.
Rationale: Total distance traveled by all the tires is 4*10000= 40000 miles.(since only 4 tires can be active at a time.
To make an equal run, Distance traveled by each tire is 40000/5 = 8000 miles.
ANSWER:B
Answer: (B) 8000 miles.
Question: A person buys an article at Rs.800. At what price should he sell the article so as to make a profit of 35%?
(A) 600
(B) 277
(C) 269
(D) 261
(E) 1080
Rationale: Cost price = Rs.800
profit = 35% of 800 = Rs.280
Selling price = Cost price + Profit
= 800 + 280 = 1080
Answer: E
Answer: (E) 1080
Question: A train covers a distance at a speed of 240kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of?
(A) 516
(B) 840
(C) 560
(D) 720
(E) 920
Rationale: Distance = 240*5 = 1200km
Required speed = 1200*3/5 = 720 km/hr
Answer is D
Answer: (D) 720
Question: Calculate how many ways a woman who has 4 bags and 5 books can put the books in her bag?
(A) 1034
(B) 1025
(C) 1024
(D) 1025
(E) 1324
Rationale: First book can be put in 4 ways, similarly second, third ,forth and fifth books also can be put in 4 ways.
So total number of ways = 4 x 4 x 4 x 4 x 4 = 1024
C
Answer: (C) 1024
Question: Two pipes P and Q can fill a tank in 4 hours and 5 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?
(A) 4 hours 20 min
(B) 5 hours 49 min
(C) 3 hours 50 min
(D) 3 hours 22 min
(E) 2 hours 13 min
Rationale: Explanation:
Part filled by P in 1 hour = 1/4
Part filled by Q in 1 hour = 1/5
Part filled by (P + Q) in 1 hour = ( 1/4 + 1/5) = (9/20)
Time taken to fill the tank is (20/9) = 20/9*60 = 133 mins = 2 hrs 13 mins
ANSWER E
Answer: (E) 2 hours 13 min
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.74 km
(B) 5.78 km
(C) 5.76 km
(D) 5.79 km
(E) 5.29 km
Rationale: M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76
Answer:C
Answer: (C) 5.76 km
Question: What is the CP of Rs 100 stock at 5 discount, with 1/5% brokerage?
(A) 99.6
(B) 95.2
(C) 97.5
(D) 98.25
(E) None of these
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-5+1/5
95.2
Thus the CP is Rs 95.2.
ANSWER B
Answer: (B) 95.2
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 900 gm and 750 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?
(A) 3.84
(B) 1.75
(C) 3.36
(D) 2.72
(E) None of these
Rationale: Here's how I did it. My notes from reading the problem were:
1L A = 900 gm
1L B = 850 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Eachpartis 4/5 of a liter.
So if we have 3 parts A, we have 900*3*(4/5) = 2160
If we have 2 parts B, we have 750*2*(4/5) = 1200
2160 + 1200 = 3360
Solving for units gives us 3.36
So the answer is C
Answer: (C) 3.36
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 16 km/hr
(B) 56 km/hr
(C) 43 km/hr
(D) 50 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man
= (125/10) m/sec
= (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45
==> x
= 50 km/hr.
Answer:D
Answer: (D) 50 km/hr
Question: If 5^k + 5^k = (5^9)^(5^9) - 5^k, then k = ?
(A)  5^11 - 1
(B)  11/2
(C)  242
(D)  3^10
(E)  3^11 - 1
Rationale: 5^k + 5^k = (5^9)^5^9 - 5^k
5*(5^k) = 5 ^ (25 * 5^9 ) = 5^(5^2 * 5^9) = 5^(5^11)
5^k+1 = 5^(5^11)
So k+1 = 5^11
So k = 5^11 -1
Answer is A
Answer: (A)  5^11 - 1
Question: The cash realised on selling a 14% stock is Rs.107.25, brokerage being 1/4% is?
(A) 366
(B) 107
(C) 102
(D) 192
(E) 122
Rationale: Cash realised= Rs. (107.25 - 0.25)
= Rs. 107.
Answer: B
Answer: (B) 107
Question: An employer pays Rs.20 for each day a worker works and for fests Rs.3 for each day is ideal at the end of sixty days a worker gets Rs.280 . for how many days did the worker remain ideal?
(A) 40
(B) 30
(C) 70
(D) 20
(E) 10
Rationale: Suppose a worker remained ideal for x days then he worked for 60-x days
20*(60-x)-3x=280
1200-23x=280
23x=920
x=40
Answer is A.
Answer: (A) 40
Question: A car covers a distance of 624 km in 6 Â½ hours. Find its speed?
(A) 104
(B) 140
(C) 200
(D) 150
(E) 250
Rationale: 624/6 = 104 kmph
ANSWER A
Answer: (A) 104
Question: The ages of two persons differ by 16 years. 6 years ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder person
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: Explanation:
Let's take the present age of the elder person = x
and the present age of the younger person = x – 16
(x – 6) = 3 (x-16-6)
=> x – 6 = 3x – 66
=> 2x = 60
=> x = 60/2 = 30
Answer: Option D
Answer: (D) 30
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/8 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
(A) 9.6
(B) 12.4
(C) 16.2
(D) 18.3
(E) 21.5
Rationale: Machine K works at a rate of 1/24 of the units per hour.
The rate of K + M together is 7/8 * 1/6 = 7/48 of the units per hour.
The rate of machine M is 7/48 - 2/48 = 5/48.
It would have taken machine M a total time of 9.6 hours.
The answer is A.
Answer: (A) 9.6
Question: The number 219 can be written as sum of the squares of 3 different positive integers. What is the sum of these 3 different integers?
(A) 20
(B) 21
(C) 19
(D) 17
(E) 15
Rationale: sum of the squares of 3 different positive integers = 219
13^2 + 7^2 + 1^2 = 219
now,
sum of these 3 different integers = 13 + 7 + 1 = 21
Ans - B
Answer: (B) 21
Question: Griffin has a bag of marbles that contains 7 black marbles and 5 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be black?
(A) 4/15
(B) 5/22
(C) 6/35
(D) 7/44
(E) 8/55
Rationale: P(3 black marbles) = 7/12*6/11*5/10 = 7/44
The answer is D.
Answer: (D) 7/44
Question: A train 100 m long is running at the speed of 30 km / hr. Find the time taken by it to pass a man standing near the railway line in seconds
(A) 5 sec
(B) 6 sec
(C) 7 sec
(D) 8 sec
(E) 9 sec
Rationale: Explanation:
Speed of the train = (60 x 5/18m / sec = 50/3 m/ sec.
Distance moved in passing the standing man = 100 m.
Required time taken = 100/(50/3) = (100 ×(3/50)) sec =6 sec
Answer: Option B
Answer: (B) 6 sec
Question: A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 181 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
(A) 6564
(B) 7372
(C) 8281
(D) 9331
(E) can not be determined
Rationale: Let the side for growing cabbages this year be X ft. Thus the area is X^2.
Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2.
The area would have increased by 181 sq ft as each cabbage takes 1 sq ft space.
X^2 - Y^2 = 181
(X + Y)(X - Y) = 181
181 is a prime number and thus it will be (91+90)*(91-90).
Thus X = 91 and Y = 90
X^2 = 91^2 = 8281
The answer is C.
Answer: (C) 8281
Question: Given that 2x + 15 > 5 and 5x - 13 < 7, all values of x must be between which of the following pairs of integers?
(A) -4 and -1
(B) -5 and 4
(C) -4 and 1
(D) -2 and 5
(E) 2 and 5
Rationale: 2x + 15 > 5
i.e 2x >5-15
i.e. 2x > -10
i.e. x > -5
Also, 5x - 13 < 7
i.e. 5x <7+13
i.e 5x < 20
i.e x < 4
i.e. -5 < x < 4
Answer: Option B
Answer: (B) -5 and 4
Question: Difference between the length &breadth of a rectangle is 15 m. If its perimeter is 90 m, then its area is??
(A) 2000 m^2
(B) 2340 m^2
(C) 450 m^2
(D) 2556 m^2
(E) 2534 m^2
Rationale: We have: (l - b) = 15 and 2(l + b) = 90 or (l + b) = 45
so 2 l = 60 = > l = 30 & b = 15
Area = 30 * 15 = 450 m^2
Answer : C
Answer: (C) 450 m^2
Question: During a Thanksgiving weekend, a car rental company rented seven-tenths of the vehicles with it including three fifths of the 4WDs that it had. If 60% of the vehicles are 4WDs, then what percent of the vehicles that were not rented were not 4WDs?
(A) 20%
(B) 30%
(C) 40%
(D) 60%
(E) 25%
Rationale: 60% of the vehicles are 4WDs:
60 are 4WDs and 40 are not.
Seven-tenths (70%) of the vehicles were rented:
70 rented and 30 not.
Three fifths of the 4WDs were rented:
3/5*60 = 36 4WDs were rented and 24 not.
So, out of 30 vehicles that were not rented 24 were 4WDs and 6 not: 6/30 = 20%.
Answer: A.
Answer: (A) 20%
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 93, what is the value of x?
(A) 95
(B) 91
(C) 102
(D) 101
(E) 85
Rationale: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 93
x = 91
Answer : B
Answer: (B) 91
Question: Find the missing number. 1, 4, 9, 16, 25, 36, 49, (....)
(A) 80
(B) 67
(C) 64
(D) 85
(E) 96
Rationale: The series is 1^2, 2^2, 3^2, 4^2, 5^2, 6^2, 7^2, ...
Hence, next term = 8^2 = 64
Answer is C
Answer: (C) 64
Question: A rectangular courty 3.78 metres long and 5.25 metres wide is to be paved exactly with square tiles, all of the same size. What is the largest size of the tile which could be used for the purpose ?
(A) 14 cms
(B) 21 cms
(C) 42 cms
(D) None of these
(E) Cannot be determined
Rationale: Solution
Largest size of the tile .
H.C.F of 378 cm and 525 cm = 21 cms.
Answer B
Answer: (B) 21 cms
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 22
(B) 28
(C) 25
(D) 82
(E) 34
Rationale: M = 20
S = 5
DS = 20 + 5 = 20.Answer:C
Answer: (C) 25
Question: A University library checks out books for a 5-week period, but allows them to be renewed up to 6 times. What is the Maximum no.of Weeks the library will allow a book to be checked out?
(A) 35
(B) 36
(C) 37
(D) 39
(E) 41
Rationale: Library checkout is 5 week period and can be renewed 6 times. So he can keep for a maximum of 8 weeks.
when he is allotted the book
0-5 weeks (1st renew)
5-10 weeks (2nd renew)
10-15 weeks (3rd renew)
15-20 weeks (4th renew)
20-25 weeks (5th renew)
25-30 weeks (6th renew)- maximum renew
after that,
30-35 (submission)
So 35 weeks is maximum.
ANSWER:A
Answer: (A) 35
Question: Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many Q hours does it currently take Anne to clean the house on her own?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 14
Rationale: Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to Q=1/3 (As the work is completed in Q=3 hours)
Solving these 2 equations we can find B as 12
So, D
Answer: (D) 12
Question: An bus covers a certain distance at aspeed of 100 kmph in 5 hours. To cover the same distance in 1hr, it must travel at a speed of?
(A) 560 km/h
(B) 567 km/h
(C) 300 km/h
(D) 723 km/h
(E) 720 km/h
Rationale: Distance = (100 x 5) = 500 km.
Speed = Distance/Time
Speed = 500/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 500 x 3/5 km/hr = 300 km/hr.
C
Answer: (C) 300 km/h
Question: In a simultaneous throw of two coins, the probability of getting atleast one headis:
(A) 1/2
(B) 1/3
(C) 2/3
(D) 3/4
(E) 1/4
Rationale: n(S)=4
E = even getting at least one head
N(E)=3
P(E)=3/4
ANSWER D 3/4
Answer: (D) 3/4
Question: A right circular cylinder has a height of 22 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
(A) 500(π – 3)
(B) 500(π – 2.5)
(C) 500(π – 2)
(D) 550(π – 1.5)
(E) 500(π – 1)
Rationale: [quote=Bunuel]A right circular cylinder has a height of 20 and a radius of 5. A rectangular solid with a height of 15 and a square base, is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. What is the volume of the liquid?
The square base has sides of sqrt(50) due to the 45-45-90 triangle
22*25*pi - 15*sqrt(50)^2
=550(π – 1.5)
D. 500(π – 1.5)
Answer: (D) 550(π – 1.5)
Question: A table is bought for Rs.1000/- and sold at Rs.1500/- find gain or loss percentage
(A) 25% gain
(B) 35% gain
(C) 45% loss
(D) 50% gain
(E) None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (1500 - 1000)/1000 = 50% gain
D
Answer: (D) 50% gain
Question: 7^6n -1^ 6n When n is an integer > 0 is divisible by
(A) 112
(B) 127
(C) 145
(D) 187
(E) 185
Rationale: 127
B
Answer: (B) 127
Question: The sum of three consecutive integers is 93. What are the integers?
(A) 20,21,22
(B) 10,11,12
(C) 30,31,32
(D) 40,41,42
(E) 30,31,32
Rationale: First x Make the first number x
Second x+1 To get the next numberwe go up one or+1
Third x+2 Add another 1(2 total) to get the third
F +S +T =93 First (F) plus Second (S) plusThird (T) equals 93
(x)+(x+1)+(x+2)=93 Replace F with x, S with x+1, and T with x+2
x+x+1+x+2=93 Here the parenthesis aren′t needed.
3x+3=93 Combine like terms x+x+x and 2+1
−3 −3 Add 3 to both sides
3x=90 The variable ismultiplied by 3
3 3 Divide both sides by 3
x=30 Our solution for x
First 30 Replace x in our origional listwith 30
Second (30)+1=31 The numbers are 30, 31, and 32
Third (30)+2=32
correct answer E
Answer: (E) 30,31,32
Question: A rectangular plot measuring 60 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart. How many poles will be needed?
(A) 44m
(B) 66m
(C) 26m
(D) 56m
(E) 25m
Rationale: Perimeter of the plot = 2(60+50) = 220m
no of poles =220/5 =44m
Answer: A
Answer: (A) 44m
Question: A straight fence is to be constructed from posts 6 inches wide and separated by lengths of chain 10 feet long. If a certain fence begins and ends with a post, which of the following could not be the length of the fence in feet? (12 inches = 1 foot)
(A) 32
(B) 53
(C) 74
(D) 86
(E) 95
Rationale: There is one post for each length of chain, plus one final post at the end.
The length of the fence in feet is 10.5x + 0.5, where each is the number of chain lengths.
The length of the fence is an integer when x = 1,3,5,7,...
The length of the fence could be 11, 32, 53, 74, 95,...
The answer is D.
Answer: (D) 86
Question: A train 1600 m long can cross a pole in 40 sec and then find the speed of the train?
(A) 140
(B) 142
(C) 144
(D) 146
(E) 148
Rationale: Length = Speed * time
Speed = L/T
S = 1600/40
S = 40 M/Sec
Speed= 40*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 144 Kmph
Answer:C
Answer: (C) 144
Question: 2 trains starting at the same time from 2 stations 200km apart and going in opposite direction cross each other at a distance of 110km from one of the stations.what is the ratio of their speeds ?
(A) 11:9
(B) 11:2
(C) 91:9
(D) 11:1
(E) 11:5
Rationale: In same time ,they cover 110km & 90 km respectively so ratio of their speed =110:90
= 11:9
Answer:A
Answer: (A) 11:9
Question: A person jogged 10 times along the perimeter of a rectangular field at the rate of 12 kilometers per hour for 30 minutes. If field has a length that is twice its width, find the area of the field in square meters.
(A) 20,000 square meters.
(B) 40,000 square meters.
(C) 60,000 square meters.
(D) 80,000 square meters.
(E) 100,000 square meters.
Rationale: Let us first find the distance d jogged
distance = rate ? time = (12 km / hr) ? 30 minutes
= (12 km/hr) ? 0.5 hr = 6 km
The distance of 6 km corresponds to 10 perimeters and therefore 1 perimeter is equal to
6 km / 10 = 0.6 km = 0.6 ? 1000 meters = 600 meters
Let L and W be the length and width of the field. The length is twice the width. Hence
L = 2 W
The perimeter is 600 meters and is given by
2 (L + W) = 600
Substitute L by 2 W
2 (2 W + W) = 600
Simplify and solve for W
4 W + 2 W = 600
6 W = 600
W = 100
Find L
L = 2 W = 200
Find the area A of the rectangle
A = L * W = 200 * 100 = 20,000 square meters
correct answer A
Answer: (A) 20,000 square meters.
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 35 cm2
(B) 37 cm2
(C) 87 cm2
(D) 16 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2
=35 cm2
Answer: E
Answer: (E) 35 cm2
Question: If the complement of a certain angle is one time the measure of that certain angle, then what is the measure of that certain angle?
(A) 45°
(B) 30°
(C) 22.5°
(D) 18°
(E) 15°
Rationale: Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example.
The original angle is x, so the complement is x, and together, these add up to 90 degrees.
x + x = 90
2x = 90
x =45°
Answer = (A)
Answer: (A) 45°
Question: A train , having a length of 165 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
(A) 9 sec
(B) 8 sec
(C) 6 sec
(D) 4 sec
(E) 2 sec
Rationale: Explanation:
Distance = 165 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 165/(110/6) = 9 s
Answer: Option A
Answer: (A) 9 sec
Question: A sum of Rs. 1360 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B's share is:
(A) 240
(B) 120
(C) 190
(D) 200
(E) 250
Rationale: Let C's share = Rs. x
Then, B's share = Rs. x/4, A's share = Rs. (2/3 x (x/4))= Rs. x/6
Therefore, x/6 + x/4 + x = 1360
=17x/12 = 1360
x = 1360 x 12/17= Rs. 960
Hence, B's share = Rs. (960/4)= Rs. 240.
Answer is A.
Answer: (A) 240
Question: Mazy bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
(A) $10
(B) $11
(C) $12
(D) $13
(E) $14
Rationale: From the given information,we can conclude that Mazy bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Answer: (B) $11
Question: A bag contains 5 white marbles and 5 red marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?
(A) 1/6
(B) 1/35
(C) 1/3
(D) 1/462
(E) 1/126
Rationale: first, total ways to select for all boys and girls, i.e 10!/(5!*5!) = 252
then there are one two way girls can have all same colors, either white or red.
The number of ways in which 5 girls can select 5 white balls = 5C5 = 1
The number of ways in which 5 girls can select 5 red balls = 5C5 = 1
Therefore, total favorable outcomes/total outcomes = 2/252= 1/126
E
Answer: (E) 1/126
Question: If xy not equal 0 and x^2*y^2 -xy = 6, which of the following could be y in terms of x?
I. 1/2x
II. -2/x
III. 3/x
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) II and III
Rationale: (xy)^2-xy-6=0
(xy-3)(xy+2)=0
so either xy=3 i.e. y=3/x
or xy=-2 i.e. y=-2/x
so E is the ans
Answer: (E) II and III
Question: During the break of a football match, the coach will make 3 substitutions. If the team consists of 14 players among which there are 2 forwards, what is the probability that none of the forwards will be substituted?
(A)  21/55
(B)  18/44
(C)  21/99
(D)  28/44
(E)  36/55
Rationale: Required probability = no. of favorable outcome/ total no. of outcomes
out of 14 players any 3 can be selected in 14C3 ways
after removing 2 forwards any 3 players can be selected from the remaining 9 players in 9C3 ways
thus required probability = 9C3/14C3 =21/99
Answer: (C)  21/99
Question: In the equation 2x – cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 3 ?
(A) −9/2
(B) -4
(C) -3
(D) 4
(E) 9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=3, c=-3, x=
x=9/2
ANSWER:E
Answer: (E) 9/2
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 25% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 976374
(B) 979923
(C) 980241
(D) 1178125
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 25/100)(1 - 35/100)(1 + 45/100)
= 1178125
D
Answer: (D) 1178125
Question: A sum fetched a total simple interest of Rs. 929.20 at the rate of 8 p.c.p.a. in 5 years. What is the sum?
(A) 2323
(B) 1223
(C) 2563
(D) 1853
(E) 2353
Rationale: Explanation :
SI = Rs.929.20
P = ?
T = 5 years
R = 8%
P = 100×SI/RT
=100×929.20/8×5
= Rs.2323
Answer : Option A
Answer: (A) 2323
Question: A toy store regularly sells all stock at a discount of 20 percent to 40 percent. If an additional 25 percent were deducted from the discount price during a special sale, what would be the lowest possible price of a toy costing $16 before any discount?
(A) $5.60
(B) $7.20
(C) $8.80
(D) $9.60
(E) $15.20
Rationale: Cost price is $16. Lowest possible price is when max discount is applied.
So Discount of 40% first and then 25%.
Final price = 16 * (1-40/100) * (1- 25/100) = 16 * 60/100 * 75/100 = 7.2
Ans B
Answer: (B) $7.20
Question: Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 8 hours to paint a wall with dimensions a and c. He takes 4 hours to paint a wall with dimensions b and c and 12 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 12, then what is the volume of the room?
(A) 218 cubic meters
(B) 224 cubic meters
(C) 230 cubic meters
(D) 288 cubic meters
(E) It can’t be determined.
Rationale: Time to paint each wall as given in problem:
AC = 8 hours
BC = 4 hours
AB = 12 hours
Since he works at constant rate and it takes him twice as long to paint AC compared to BC
AC=2BC
Plug in 6 for A and you find that B=6
Since painting AB takes 3 times as long compared to BC,
AB=3BC
Plug in 6 for A and 3 for B and you find that C=4
A*B*C=12*6*4=288 cubic meters
Answer: D
Answer: (D) 288 cubic meters