mathewhe/aqua_rat huggingface dataset:
Question: There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
(A) 120
(B) 116
(C) 140
(D) 20
(E) 10
Rationale: Solution: The number of triangle can be formed by 10 points = 10C3.
Similarly, the number of triangle can be formed by 4 points when no one is collinear=4C3.
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3-4C3 = 120-4 = 116.
Answer B
Answer: (B) 116
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 5 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
(A) 6
(B) 20
(C) 24
(D) 35
(E) 36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7 = 10:35.
For every 5 fantasy books, there are 8 reference books:
F:R = 5:8 = 35:56
H:F:R = 10:35:56
After the changes, H:F:R = 20:35:56
There are fewer than 60 fantasy books, so there are 35 fantasy books.
The number of history books is 20.
The answer is B.
Answer: (B) 20
Question: A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 19%?
(A) 17 per kg
(B) 17.85 per kg
(C) 16.5 per kg
(D) 16 per kg
(E) None of these
Rationale: C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 119% of 3000 = (119⁄100 × 3000) = 3570
∴ Rate of S.P. of the mixture = (3570⁄200) per kg
= 17.85 per kg.
Answer B
Answer: (B) 17.85 per kg
Question: The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
(A) 61.4.
(B) 51.7
(C) 51.4
(D) 51.1
(E) 51.2
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 52 * 100
= 1600 + 775 + 55x = 5200
= 55x = 2825
= x = 565/11 =51.4.
Answer:C
Answer: (C) 51.4
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
(A) 16 2/5%
(B) 16 2/9%
(C) 16 5/3%
(D) 16 2/3%
(E) 16 3/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: (D) 16 2/3%
Question: In a certain game, you perform three tasks. You flip a quarter, and success would be tails. You roll a single die, and success would be a even number. You pick a card from a full playing-card deck, and success would be picking a ace card. If exactly one of these three tasks is successful, then you win the game. What is the probability of winning?
(A) 1/52
(B) 6/13
(C) 25/52
(D) 11/13
(E) 23/52
Rationale: Event(1): Probability of getting tail in a flip of coin = 1/2
Event(2): Probability of getting even number in a roll of dice = 3/6 = 1/2
Event(3): Probability of getting ace in a pack of card = 4/52 = 1/13
Probability of winning is having exactly one successful event is:
P(success 1)* P(Fail 2)* P(Fail 3) + P(Fail 1)* P(Success 2)* P(Fail 3) + P(Fail 1)* P(Fail 2)* P(Success 3)
= 1/2*1/2*12/13 +1/2*1/2*12/13 +1/2*1/2*1/13
=3/13 + 3/13 +1/52
=25/52
Answer :C
Answer: (C) 25/52
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 10 sec
(B) 30 sec
(C) 40 sec
(D) 20 sec
(E) 50 sec
Rationale: D
Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer: (D) 20 sec
Question: If r and s are positive integers, and r2 + r/s is an odd integer, which of the following cannot be even?
(A) 3r + 2s
(B) (r-1)(s+2)
(C) r^(s+1) + s^r
(D) D. r^3 +3
(E) s^4 +4
Rationale: r and s are positive integers.
r2+rsr2+rs is an odd integer. Since r2r2 is an integer, rsrs will also be an integer. So s is a factor of r.
To get an odd integer after adding two terms, one term must be odd and the other even.
Say r is even. Then r^2 is even. So r/s must be odd. This means that when we divide r by s, we are removing all the 2s that r has. So s must be even too. This is one possible case.
Say r is odd. Then r^2 is odd. So r/s must be even. But if you divide an odd integer by another integer, it will never become even because division takes away factors. It cannot introduce 2 as an additional factor. So r/s cannot be even. This case is not possible.
Hence, r and s both MUST BE EVEN.
In option (D), r^3 + 3 will be odd because Even + Odd = Odd. Hence option (D) can never be even.
ANSWER:D
Answer: (D) D. r^3 +3
Question: Shekar scored 76, 65, 82, 47 and 85 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
(A) 71
(B) 69
(C) 75
(D) 85
(E) 90
Rationale: Explanation :
Average= (76+65+82+47+85)/5 = 355/5 =71
Hence average=71
Answer : A
Answer: (A) 71
Question: An assembly line produces 15 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the overall average output, in cogs per hour, for the assembly line during this whole time?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 28
Rationale: The time to produce the first 60 cogs is 60/15 = 4 hours.
The time to produce the next 60 cogs is 60/60 = 1 hour.
The average output is 120 cogs / 5 hours = 24 cogs per hour.
The answer is C.
Answer: (C) 24
Question: Matt and Peter can do together a piece of work in 20 days. After they have worked together for 10 days Matt stops and Peter completes the remaining work in 10 days. In how many days Peter complete the work separately.
(A) 21
(B) 20
(C) 22
(D) 23
(E) 24
Rationale: Together they complete the job in 20 days means they complete 10/20 of the job after 10 days.
Peter completes the remaining (10/20) of the job in 10 days which means that the whole job(1) can be completed in X days.
<=> 8/20->10 <=> X=10/(10/20)=20
B
Answer: (B) 20
Question: If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
(A) 120
(B) 30
(C) 24
(D) 11
(E) 7
Rationale: Soln. Since combinations within the group not matter, and since all boys go together. We can group all 5 boys into 1 group. The 6 girls and the 1 group of boys can be arranged in 7 ways.
Ans is E
Answer: (E) 7
Question: Train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 20 seconds. The length of train K is three-fourths the length of train L. What is the ratio of the speed of train K to that of train L
(A) 1 : 2
(B) 3 : 1
(C) 2 : 1
(D) 1 : 3
(E) 2 : 3
Rationale: Given that train K crosses a pole in 30 seconds and train L crosses the same pole in one minute and 15 seconds.
Let the length of train K be Lk and that of train L be Ll
given that Lk = 3/4 Ll
As the train K and L crosses the pole in 30 seconds and 80 seconds respectively,
=> Speed of train K = sk = Lk/30
Speed of train L = sl = Ll/80
Lk = 3/4 Ll
=> sk = 3/4 Ll/(30) = Ll/40
Ratio of their speeds = sk : sl
= Ll/40 : Ll/80
=> 1/40 : 1/80 = 2 : 1
Answer : C
Answer: (C) 2 : 1
Question: At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:40 a.m., how long Q will the conference last if there are a total of 6 seminars that day?
(A) 5 hours and 15 minutes
(B) 5 hours and 20 minutes
(C) 5 hours and 25 minutes
(D) 5 hours and 30 minutes
(E) 5 hours and 35 minutes
Rationale: Shouldnt the answer be 5 hours 20 mins?
Break = b
Seminar= 10b
9am to 11:40am= 160mins
3s+b=160
30b+b=160
b=160/31
6 seminar will take
6s+2b
=60b+2b
=62b
=62*160/31
=320
Q=5 hours 20 mins.B
Answer: (B) 5 hours and 20 minutes
Question: In 10 years, P will be as old as Q is now. Ten years ago, Q was three times as old as P was then. How old is P now?
(A) 11
(B) 12
(C) 15
(D) 18
(E) 21
Rationale: Q = P+10
Q-10 = 3(P-10)
P = 3P-30
2P = 30
P = 15
The answer is C.
Answer: (C) 15
Question: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
(A) A.10%
(B) B.20%
(C) C.25%
(D) D.41%
(E) E.50%
Rationale: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.D
Answer: (D) D.41%
Question: If x ≠ 0 and 1/x - (2+ x^2)/x = y/x, then y =
(A) x^2+1
(B) x^2-2
(C) -(x^2+1)
(D) x^2+2
(E) 2x^2+1
Rationale: 1/x - (2+ x^2)/x = y/x
1-2-x^2/x = y/x
y = -(x^2+1)
Answer : C
Answer: (C) -(x^2+1)
Question: In a friendship gang Andrew has 8 gang, in how many ways can he invite one or more of the gang to his house?
(A) 234
(B) 255
(C) 265
(D) 270
(E) 272
Rationale: Andrew can select one or more than one of his 8 gang.
=> Required number of ways = 28 – 1= 255.
B
Answer: (B) 255
Question: P and Q invested in a business. The profit earned was divided in the ratio 4 : 6. If P invested Rs 60000, the amount invested by Q is
(A) 30000
(B) 50000
(C) 90000
(D) 20000
(E) 60000
Rationale: Let the amount invested by Q = q
60000:q=4:6
⇒60000×6=4q
⇒q=(60000×6)/4=90000
Answer is C.
Answer: (C) 90000
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
(A) 879
(B) 278
(C) 999
(D) 167
(E) 218
Rationale: a2 = 3136 => a = 56
56 * 4 * 3
= 672 – 6
= 666 * 1.5
= 999
Answer: C
Answer: (C) 999
Question: For 1rs 4p interest
wat will be for 1000rs?
(A) 45Rs
(B) 50Rs
(C) 40Rs
(D) 30Rs
(E) 48Rs
Rationale: For 1rs , 4p interest
for 1000rs, x
x= 1000/1 * 4p ==> 4000 paise
To express in rs, 4000/100 = 40rs
ANSWER:C
Answer: (C) 40Rs
Question: If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:
(A) Rs. 768
(B) Rs. 968
(C) Rs. 1960
(D) Rs. 2400
(E) Rs. 2800
Rationale: td=pw*r*t/100 so 168=pw*14*2/100 so pw=600
sum=pw+td..
sum=600+168=768
ANSWER:A
Answer: (A) Rs. 768
Question: In the next World cup of cricket there will be 12 teams, divided equally in two groups. Teams of each group will play a match against each other. From each group 3 top teams will qualify for the next round. In this round each team will play against each others once. Four top teams of this round will qualify for the semifinal round, where they play the best of three matches. The Minimum number of matches in the next World cup will be:
(A) 54
(B) 53
(C) 38
(D) 43
(E) None of these
Rationale: Solution: The number of matches in first round,
= 6C2 +6C2;
Number of matches in next round,
= 6C2;
Number of matches in semifinals,
= 4C2;
Total number of matches,
= 6C2 +6C2+6C2+4C2+2.
= 53.
Answer: Option B
Answer: (B) 53
Question: If 0.75: x :: 5:12, then x is equal to:
(A) 1.12
(B) 1.16
(C) 1.8
(D) 1.3
(E) None of these
Rationale: Explanation:
(x * 5) = (0.75 *12)
X=9/5 = 1.80
Answer: C
Answer: (C) 1.8
Question: If R persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job?
(A) z
(B) x
(C) x/y
(D) z/x
(E) y/z
Rationale: the Q doesn't seem to be having the any correct answer as a choice..
since we are looking for days, lets keep days in end and work out a solution..
R person can do z jobs in y days..
so R person can do 1 job in y/z days..
and 1 person can do 1 job in y^2/z days..
so y person can complete 1 job in y^2/zy=y/z..
so the answer should be y/z=E
Answer: (E) y/z
Question: If log10 2 = 0.3010, the value of log10 80 is:
(A) 1.602
(B) 1.903
(C) 3.903
(D) 4.5231
(E) None of these
Rationale: Explanation:
log10 80	= log10 (8 x 10)
= log10 8 + log10 10
= log10 (23 ) + 1
= 3 log10 2 + 1
= (3 x 0.3010) + 1
= 1.9030.
ANSWER IS B
Answer: (B) 1.903
Question: 5 ltr of water is added with 15 ltr of a solution containing 26%of alcohol in the water. The %of alcohol in the new mixture is?
(A) 17.25%
(B) 19
(C) 19.5%
(D) 21.5%
(E) 22%
Rationale: We have a 15 litre solution containing 26% alcohol in water.
=> Quantity of alcohol in the solution
=15Ã—26/100
Now 5 litre of water is added to the solution.
=> Total quantity of the new solution = 15 + 5 = 20
Percentage of alcohol in the new solution
=15Ã—26/100
20
Ã—
100
=15Ã—26/10020Ã—100
=15Ã—1.3/100
=19.5%
C
Answer: (C) 19.5%
Question: A company sells pens and pencils. The Revenue from pens in 2007 was up 5% from 2006. The revenue from pencils declined 13% over the same period. Overall revenue was down 1% from 06 to 07. What was the ratio of pencil revenue to pen revenue in 2006
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: Let the revenue of pens be 'x'
Let the revenue of pencils be 'y'
the revenue of pens up from 2006 by 5%=>105%
the revenue of pencils down from 2006 by 13%=>87%
Overall revenue down by 1%=>99%
hence the ratio of pencils to pens = 6/12 = 1/2
ANSWER:A
Answer: (A) 1/2
Question: If 5 persons can do 5 times of a particular work in 5 days, then, 7 persons can do 7 times of that work in?
(A) 3 days
(B) 4 days
(C) 5 days
(D) 7 days
(E) 8 days
Rationale: That is, 1 person can do one time of the work in 5 days.
Therefore, 7 persons can do 7 times work in the same 5 days itself
C)
Answer: (C) 5 days
Question: A shopkeeper sells 200 metres of cloth for Rs. 12000 at a loss of Rs.6 per metre. Find his cost price for one metre of cloth?
(A) s.59
(B) s.58
(C) s.09
(D) s.50
(E) s.66
Rationale: SP per metre = 12000/200
= Rs. 60 Loss per metre
= Rs. 6 CP per metre = 60 + 6
= Rs.66
Answer: E
Answer: (E) s.66
Question: A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 10 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
(A) $112.00
(B) $64.80
(C) $90.00
(D) $100.80
(E) $154.80
Rationale: Correct Answer: A
The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.1 ($1120) = $112. The correct answer is A.
Answer: (A) $112.00
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
(A) 1 day
(B) 10 days
(C) 30 days
(D) 32 days
(E) 34 days
Rationale: Explanation:
C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Answer: (C) 30 days
Question: Two numbers differ by 5. If their product is 336, then the sum of the two numbers is
(A) 21
(B) 28
(C) 37
(D) 51
(E) None of these
Rationale: Sol.
Let the number be x and y.
Then, x - y = 5 and xy = 336.
⇔ (x+y)2 = (x-y)2 + 4xy = 25 + 4 x 336 = 1369
⇒ x+y = √1369 = 37.
Answer C
Answer: (C) 37
Question: The greatest common factor of two positive integers is J. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
(A) JY⁄Z
(B) XZ + YZ
(C) X⁄Z + Y
(D) X + Y⁄Z
(E) X + Z⁄Y
Rationale: Say other integer is W
Formula
GCF(WZ)*LCM(WZ) = W*Z
J*Y = W*Z
So W= JY/Z
Answer A
Answer: (A) JY⁄Z
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 60 kmh, what was the average speed of the car for the entire trip?
(A) 36 kmh
(B) 40 kmh
(C) 42 kmh
(D) 44 kmh
(E) 50 kmh
Rationale: Assume D/3 = 240 (this number is convenient because it is divisible by 80, 24 and 60)
So:
240 = 80*T1 = 3 hrs
240 = 24*T2 = 10 hrs
240 = 60*T3 = 4 hrs
T = T1 + T2 + T3 = 17 hrs
D = RT
(240*3) = R*17
R = 42.35
ANSWER: C
Answer: (C) 42 kmh
Question: There is enough provisions for 4800 boys in a hostel for 200 days. If there were 2400 men less, how long will the provision last?
(A) 300
(B) 350
(C) 400
(D) 450
(E) 500
Rationale: We have, M1D1 = M2D2
4800*200= 2400* D2
D2 = 4800*200/2400 = 400 days.
ANSWER:C
Answer: (C) 400
Question: If 8 persons meet at a reunion and each person shakes hands exactly once with each of the others, what is the total number of handshakes?
(A)  10•9•8•7•6•5•4•3•2•1
(B)  10•10
(C)  10•9
(D)  45
(E)  28
Rationale: We got #10 people who shake each other's hands once ==> a pair of 2
8!/6!2! = 8*7 / 2*1 = 28.
Hence answer E.
Answer: (E)  28
Question: Zoey won the lottery and got $7,348,340. she wants to split it among herself and 5 friends evenly. how much money must she add if she wants to split it evenly?
(A) $3
(B) $2
(C) $9
(D) $1
(E) $4
Rationale: Zoey and her 5 friends is 6 people in all. $7,348,340 must be divisible by 6 if she wants to split it evenly. The money is divisible by 6 if it's divisible by 2 and 3. 7+3+4+8+3+4+0=29. 2 and 3 cant go into 29. Adding 1 dollar makes it 30. 2 and 3 can go into 30 so 6 can also. The answer is D.
Answer: (D) $1
Question: What is the place value of 8 in the numeral 2834?
(A) 800
(B) 567
(C) 560
(D) 760
(E) 650
Rationale: Option 'A'
8 * 100 = 800
Answer: (A) 800
Question: Calculate the share of profit that belongs to Elvis in a partnership business he invested Rs 21,500. His partner Daryl invested RS.28,900 and the business made a profit of Rs 12,500.
(A) 5311.34
(B) 5332.34
(C) 2132.34
(D) 5092.34
(E) 1332.34
Rationale: Explanation:
Ratio of their shares = 21,500 : 28,900 = 215 : 289.
Elvis' share = Rs. (12,500 * 215/504) = Rs. 5332.34.
Answer: B) 5332.34
Answer: (B) 5332.34
Question: We run a business that rents out canoes and kayaks. A canoe rental costs $14 per day, and a kayak rental costs $15 dollars per day. One day, our business rents out 3 canoes for every 2 kayaks and receives a total of $288 in revenue. How many more canoes than kayaks were rented out?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Let x be the number of canoes.
Then 2x/3 is the number of kayaks.
14x+(2x/3)*15=288
14x+10x=288
24x=288
x=12 (canoes)
2x/3=8 (kayaks)
There were 12-8 = 4 more canoes rented out.
The answer is B.
Answer: (B) 4
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in r hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of r?
(A) 3/4
(B) 1[1/5]
(C) 1[2/5]
(D) 1[3/4]
(E) 2
Rationale: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * r = 1 => X = 1/z
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/r = 4/3
=> 1/r = (8-3)/6 = 5/6
=> r = 6/5 = 1[1/5]
Answer B
Answer: (B) 1[1/5]
Question: O(x) represents the least odd integer greater than x, whereas o(x) represents the greatest odd integer less than x. Likewise, E(x) represents the least even integer greater than x, whereas e(x) represents the greatest even integer less than x. According to these definitions, the value of O(3.2) + E(–1.7) + o(–3.3) + e(4.7) is:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: O(3.2) + E(–1.7) + o(–3.3) + e(4.7) = 5 + 0 + (-5) + 4 = 4
The answer is B.
Answer: (B) 4
Question: A room contains 160 people, 15 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
(A) 10
(B) 20
(C) 40
(D) 60
(E) 80
Rationale: Say group of x people left the room.
# of women in the room was 0.15*160=24;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(160-x);
So, 24-0.3x= 0.1(160-x) --> x=40.
Answer: C.
Answer: (C) 40
Question: A certain gallery is hanging a series of 5 paintings. All the paintings will be exhibited in a row along a single wall. Exactly 2 of the paintings are on panel, the remainder are on canvas. In how many ways can the paintings be exhibited if the works on panel must be the second and sixth in the row?
OE
(A) 240
(B) 200
(C) 122
(D) 80
(E) 12
Rationale: We need to consider them separately because the question specifies:
1. Panel paintings have to be placed only at 2nd and 5th place.
2. Implies that Canvas has to be placed 1,3,4,th place.
So we have two separatebucketsto consider.
So panels can be ordered in 2!
Canvas can be ordered in 3!
since relative position of panels to canvas is fixed (Panels 2nd and 5th) the answer is 2! x 3! = 12
E
Answer: (E) 12
Question: a number divided by 64 leaves remainder 37 what is the remainder when same number divided by 5
(A) 7
(B) 8
(C) 6
(D) 3
(E) 1
Rationale: add 64+37=101
now 101 divided by 5 so we get 1 as reaminder
ANSWER:E
Answer: (E) 1
Question: In how many different ways can the letters of the word ‘PREPTY’ be arranged?
(A) 160
(B) 190
(C) 210
(D) 368
(E) 360
Rationale: Number of ways = 61/21 6X5X4X3X2X1 - 360
E
Answer: (E) 360
Question: The ages of Nishi and vinnee are in the ratio of 6: 5 respectively. After 9 yr the ratio of their ages will be 9: 8. What is the difference in their ages?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 1
Rationale: Answer:C
Answer: (C) 7
Question: Susan has four apples. How many ways can she eat one or more apples?
(A) 15
(B) 44
(C) 38
(D) 12
(E) 23
Rationale: Susan can eat one or more of four apples
= > 2 ^ 4 -1 = 15
A
Answer: (A) 15
Question: A completes a work in 8 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be?
(A) 6 days
(B) 11 days
(C) 21 days
(D) 22 days
(E) 24 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 8 Ã— 24/ 32 = 6 days.
Option 'A'
Answer: (A) 6 days
Question: In a certain country ½ of 7 = 3. Assuming the same proportion, what would be the value of 1/3 of 21 ?
(A) 7
(B) 6
(C) 3
(D) 4
(E) 5
Rationale: B
6
Answer: (B) 6
Question: A man walks at a rate of 10 mph. After every ten miles, he rests for 8 minutes. How much time does he take to walk 50 miles?
(A)  300
(B)  318
(C)  322
(D)  324
(E)  332
Rationale: To cover 50 miles the man needs (time) = (distance)/(rate) = 50/10 = 5 hours = 300 minutes. He will also rest 4 times (after 10, 20, 30 and 40 miles), so total resting time = 4*8 = 32 minutes.
Total time = 300 + 32 = 332 minutes.
Answer: E.
Answer: (E)  332
Question: What is the difference between 62% of 150 nd 20% of 250.
(A) 16
(B) 17
(C) 43
(D) 19
(E) 20
Rationale: (62/100) * 150 â€“ (20/100) * 250
93 - 50 = 43
Answer: C
Answer: (C) 43
Question: For what values of k will the pair of equations 6x + 8y = 24 and kx + 12y = 30 does not have a unique solution?
(A) 12
(B) 9
(C) 3
(D) 7.5
(E) 2.5
Rationale: we have 2 equations
1. 6x + 8y = 24 --> 3x + 4y = 12 -- > 9x + 12y = 36
2. kx + 12y = 30
substract 1-2, we get (9-K)x = 6
i.e. x = 6/(9-k)
then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is B
Answer: (B) 9
Question: T and F represent two distinct digits. If the number 457T89F is divisible by 36, what is the value of (T+F)?
(A) a) 9
(B) b) 3
(C) c) 12
(D) d) 6
(E) e) 10
Rationale: A no. divisible by 36 means it is div by 49 .
to be div by 4 last 2 digits to be multiple of 4 So, F could be either 2 or 6 only
similarly for a number to be div by 9 its sum must be multiple of 9 first. filtering we find T could be either 1,4,7 only.
To be divisible by 9 only 1 works .(if we choose f=6 then T have to be 6 but as per condition TF are distinct) So
T=1
F=2
Ans:- 3.B
Answer: (B) b) 3
Question: X and Y are integers, X is even and negative, Y is odd and positive. Which of the following could be false?
1. (X + Y) is an even number.
2. Y^(X + Y) is an integer.
3. X^Y is a positive number.
(A) 2 only.
(B) 3 only.
(C) 1 and 3 only.
(D) 2 and 3 only.
(E) None of these
Rationale: Statement I is not TRUE
Statement II is not TRUE
Statement III is not TRUE
Answer : E
Answer: (E) None of these