mathewhe/aqua_rat huggingface dataset:
Question: The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 87 cm2
(B) 28 cm2
(C) 98 cm2
(D) 26 cm2
(E) 50 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 * 40/2
= 50 cm2
Answer:E
Answer: (E) 50 cm2
Question: 8k8
+ k88
--------
1,6t6
If k and t represent non-zero digits within the integers above, what is t?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 17
Rationale: 8k8
k88
--------
16t6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and t=6.
Answer: A.
Answer: (A) 6
Question: Sam, Suresh and Sanket run a race of 1400 meters. Sam runs twice as fast as Suresh while Suresh runs thrice as fast as Sanket. If Sanket finishes the race by clocking 15 minutes, how far was Suresh from the finish line when Sam must have finished the race?
(A) 2887
(B) 278
(C) 987
(D) 700
(E) 278
Rationale: Explanation:
When Sanket finishes the race in 15 minutes, Suresh & Sam would finish the same race in 5 minutes and 2.5 minutes respectively. Thus, when Sam reaches the ”finish” mark, Suresh must be “half-way” through i.e. 700 meters behind the “finish” line when “Sam” must have finished the race.
ANSWER:D
Answer: (D) 700
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 2 kmph
(B) 4 kmph
(C) 5 kmph
(D) 7 kmph
(E) 6 kmph
Rationale: M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer:B
Answer: (B) 4 kmph
Question: In what time a sum of money double itself at 3% per annum simple interest?
(A) 33 1/8%
(B) 33 1/3%
(C) 33 3/3%
(D) 33 1/7%
(E) 32 1/3%
Rationale: P = (P*3*R)/100
R = 33 1/3%
Answer: B
Answer: (B) 33 1/3%
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
(A) 788
(B) 144
(C) 298
(D) 177
(E) 191
Rationale: Explanation:
The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer: B
Answer: (B) 144
Question: A certain number of workers can do a work in 35 days. If there were 10 workers more it could be finished in 10 days less. How many workers are there?
(A) 25
(B) 30
(C) 28
(D) 24
(E) 32
Rationale: number of workers = 10* (35-10)/10 = 25
Answer is A
Answer: (A) 25
Question: Rahul went to a shop and bought things worth Rs. 50, out of which 80 Paise went on sales tax on taxable purchases. If the tax rate was 8%, then what was the cost of the tax free items?
(A) 21.4
(B) 12.4
(C) 41.2
(D) 39.2
(E) 32.9
Rationale: Total cost of the items he purchased = Rs.50
Given that out of this Rs.50, 80 Paise is given as tax
=> Total tax incurred = 80 Paise = Rs.80/100
Let the cost of the tax free items = x
Given that tax rate = 8%
∴ (50−80/100−x)8/100 = 80/100
⇒ 8(50 −0.8 −x) = 80
⇒ (50 − 0.8 − x) = 10
⇒ x = 50 − 0.8−10 = 39.2
D)
Answer: (D) 39.2
Question: In how many ways can 4 boys and 3 girls be seated on 8 chairs so that no two girls are together?
(A) 5760
(B) 14400
(C) 480
(D) 56
(E) 40320
Rationale: Let us take opposite of the constraint.
2 girls sitting together:	:
1 case is GGBGBBBB.
Total number of ways=3!*5!*5 with just shifting the rightmost girl.
Then the 2 leftmost girls can shift one position , and using the above reasoning, the total number of ways = 3!*5!*4 and so on till the rightmost girl has 1 position.
So total number of ways = 3!*5!(5+4+3+2+1)=120*90=10800
Similarly another case is:
GBGGBBBB.
Using the above reasoning, the total number of cases is: 3!*5!*(15) =10800
Let us take 3 girls sitting together
GGGBBBBB
There are 3! *5! Ways. The 3 leftmost girls can shift 6 positions. So there are a total of 3!*5!*6=4320 ways
So total is 2*10800 + 4320=25920
The total number of possibilities = 8! Ways =40,320
Answer is 40320-25920=5760
Hence A.
Answer: (A) 5760
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 5 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
(A) 60 gallons
(B) 200 gallons
(C) 120 gallons
(D) 180 gallons
(E) 130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 5 gallons\
Volume of whole = 5 * 40 = 200 gallons.
ANSWER:B
Answer: (B) 200 gallons
Question: One fourth of one third of two fifth of a number is 15. What will be40% of that number
(A) 140
(B) 150
(C) 180
(D) 200
(E) 220
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 15
then x = 15 * 30 = 450
40% of 450 = 180
Answer: Option C
Answer: (C) 180
Question: There are three places P, Q and R such that 3 roads connects P and Q and 4 roads connects Q and R. In how many ways can one travel from P to R?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 15
Rationale: Number of ways in which one can travel from P to R
=3×4=12
Answer: Option C
Answer: (C) 12
Question: 1000 men have provisions for 17 days. If 500 more men join them, for how many days will the provisions last now?
(A) 12.9
(B) 12.5
(C) 11.3
(D) 12.2
(E) 12.1
Rationale: 1000*17 = 1500*x
x = 11.3
Answer: C
Answer: (C) 11.3
Question: The ratio between the sale price and the cost price of an article is 7:5. What is the ratio between the profit and the cost price of that article?
(A) 2:8
(B) 2:0
(C) 2:2
(D) 2:1
(E) 2:5
Rationale: Let C.P. = Rs. 5x and S.P. = Rs. 7x.
Then, Gain = Rs. 2x
Required ratio = 2x : 5x = 2:5
Answer:E
Answer: (E) 2:5
Question: A train moves fast a telegraph post and a bridge 250 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 70
(B) 39
(C) 79
(D) 75
(E) 71
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 250)/20 = y
y = 20.83
Speed = 20.83 m/sec = 20.83 * 18/5 = 75 km/hr.
Answer:D
Answer: (D) 75
Question: A clock shows the time as 3:30 P.m. If the minute hand gains 2 minutes every hour, how many minutes will the clock gain by 6 a.m.?
(A) 23 Minutes
(B) 24 Minutes
(C) 29 Minutes
(D) 26 Minutes
(E) None of these
Rationale: if the minute hand gains 2 minutes in 1 hour the from 3:30 p.m-4:00 p.m it gains 1 min
then from 4:00p.m-6:00 a.m =14*2=28 total=29
ANSWER:C
Answer: (C) 29 Minutes
Question: The ratio of two quantities is 2 to 5. If each of the quantities is increased by 5, what is the ratio of these two new quantities?
(A) 2/5
(B) 5/8
(C) 7/13
(D) 22/25
(E) It cannot be determined from the information given.
Rationale: Correct Answer: E
Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.
For example, if x = 2 and y = 5, then (x+5)/(y+5) = (2+5)/(5+5) = 7/10. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+5)/(y+5) = (4+5)/(10+5) = 9/15. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).
Answer: (E) It cannot be determined from the information given.
Question: In a covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay double his speed, then he would take 1 hour less than Sammer. Abhay's speed is?
(A) 5 km/hr
(B) 1 km/hr
(C) 6 km/hr
(D) 3 km/hr
(E) 7 km/hr
Rationale: A
5 km/hr
Let Abhay's speed be x km//hr.
Then, 30/x - 30/2x = 3
x = 5 km/hr.
Answer: (A) 5 km/hr
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+4 ?
(A) -2
(B) 5
(C) -3
(D) -4
(E) -5
Rationale: let we put values. a=1, b=3, c=5
5-3-1=1
1+4 =5
Answer :B
Answer: (B) 5
Question: A train 240 m long is running at a speed of 60 km/hr. In what time will it pass a bridge 240 m long?
(A) 28.8 sec
(B) 20.33 sec
(C) 60 sec
(D) 48 sec
(E) 49 sec
Rationale: total length= 240+240=480
speed=60 km/h=(60*5)/18= 50/3 m/s
time=(480*3)/50=28.8 sec.
ANSWER:A
Answer: (A) 28.8 sec
Question: A sum amounts to Rs.4851 in 2 years at the rate of 5% p.a. If interest was compounded yearly then what was the principal?
(A) s.4000
(B) s.5000
(C) s.4400
(D) s.4800
(E) s.5800
Rationale: CI=4851,R=5,N=2
CI=P[1+R/100]^2
=P[1+5/100]^2
4851=P[21/20]^2
4851[20/21]^2
4400
ANSWER:C
Answer: (C) s.4400
Question: The sub-duplicate ratio of 16:36 is
(A) 4:6
(B) 1:2
(C) 1:3
(D) 1:4
(E) 2:3
Rationale: root(16):root(36)=4:6
ANSWER:A
Answer: (A) 4:6
Question: Tina and Rebecca had the same number of candies. Tina gave Rebecca 20 candies so that now Rebecca has five times as many candies as Tina has. Rebecca has now how many candies?
(A) 50
(B) 48
(C) 54
(D) 55
(E) 60
Rationale: T = R
T - 20 ;R + 20
R + 20 = 5 ( T - 20 )
R + 20 =5T - 100
R - 5T = - 120
We knowR = T, so
R - 5T = - 120
Or, R - 5R = -120
Or, - 4R = - 120
Or, R = 30( This is the initital no of Candies Rebecca had)
Candles now she possesses is30+ 20 = 50
So , Rebecca now has 50 candies.
Answer will be (A) 50
Answer: (A) 50
Question: In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
(A) 3 years
(B) 2 years
(C) 4 years
(D) 1 year
(E) 5 years
Rationale: Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))n ] = 1331 or (11/10)n = (1331/1000) = (11/10)3
n = 3 years.
ANSWER A 3 years
Answer: (A) 3 years
Question: In given series 22, 33, 66, 99, 121, 279, 594 only one number is incorrect. Find out that wrong number
(A) 141
(B) 131
(C) 121
(D) 171
(E) 279
Rationale: Each of the number except 279 is a multiple of 11.
2 x 11=22
3 x 11=33
6 x 11=66
9 x 11=99
11 x 11=121
25 X 11= 275.... so 279 is wrong
54 x 11=594
ANSWER:E
Answer: (E) 279
Question: A committee is reviewing a total of 40x black-and-white films and 4y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?
(A) 20/11
(B) 16/11
(C) 17/11
(D) 10/11
(E) 19/11
Rationale: Say x=y=10. In this case we would have:
40x=200 black-and-white films;
4y=40 color films.
y/x%=10/10%=1% of the black-and-white films, so 4 black-and-white films and all 40 color films, thus total of 44 films were selected.
Color films thus compose 40/44=10/11 of the selected films.
Answer: D
Answer: (D) 10/11
Question: Car A is 16 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
(A) 1.5
(B) 2.0
(C) 2.5
(D) 3.0
(E) 3.5
Rationale: Relative speed of car A is 58-50=8 miles per hour, to catch up 16 miles and drive 8 miles ahead so to drive 24 miles it'll need 24/8=3 hours.
Answer: D
Answer: (D) 3.0
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
(A) 2
(B) 4
(C) 5
(D) 6
(E) 24
Rationale: C
C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5
For Rs. 6/5, toffees sold = 6. For re. 1.
Toffees sold = 6 * 5/6 = 5
Answer: (C) 5
Question: A certain list of 300 test scores has an average (arithmetic mean) of 85 and a standard deviation of d, where d is positive. Which of the following two test scores, when added to the list, must result in a list of 302 test scores with a standard deviation less than d ?
(A)  80 and 80
(B)  85 and 85
(C)  80 and 90
(D)  85 and 80
(E)  85 and 90
Rationale: The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the aboveadding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 85 and 85 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD most.
Answer: B
Answer: (B)  85 and 85
Question: If the price of a computer were reduced by 13 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
(A) $844.10
(B) $891.10
(C) $1,051.90
(D) $1,132.30
(E) $1,259.60
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-16/100)------->X(67/77)=A(say)
means X=A*(77/67).....
so initial price to be integer(As per stem) final price must be multiple of 67
if we check options all were divisible by 67 except option (A)..which is Ans.
Ans A
Answer: (A) $844.10
Question: 19 people went to a hotel for combine dinner party 13 of them spent Rs. 79 each on their dinner and rest spent 4 more than the average expenditure of all the 19. What was the total money spent by them.
(A) 1628.4
(B) 1534
(C) 1492
(D) 1496
(E) None of these
Rationale: Solution: Let average expenditure of 19 people be x.
then,
19x = 13*79+6*(x+4);
Or, 19x = 13*79+6x+24;
Or, x = 80.84;
So, total money spent = 80.84*19 = Rs. 1536.07.
Answer: Option E
Answer: (E) None of these
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, To gain 10%, at price he should sell?
(A) Rs.400
(B) Rs.450
(C) Rs.550
(D) Rs.600
(E) Rs.650
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: (C) Rs.550
Question: A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 9:00 am and some time later the drain that empties the pool was also opened. If the pool was filled by 11:00 pm and not earlier, when was the drain opened?
(A) at 10:30 am
(B) at 11:30 am
(C) at 12:30 pm
(D) at 1:30 pm
(E) at 2:30 pm
Rationale: The filling rate is 1/4 and the draining rate is 1/5.
The combined rate of filling and draining is 1/4 - 1/5 = 1/20.
Let x be the number of hours before the drain was opened.
x/4 + (14-x)/20 = 1
5x + 14 - x = 20
4x = 6
x = 1.5
The answer is 10:30 am.
The answer is A.
Answer: (A) at 10:30 am
Question: In a certain parking lot, 4% of the cars are towed for parking illegally. However 80% of the cars which are parked illegally are not towed. What percentage of cars in the parking lot are parked illegally?
(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
Rationale: Let x be the number of cars and let y be the number of cars parked illegally.
4%*x = 20%*y
y/x = 1/5 = 20%
The answer is A.
Answer: (A) 20%
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
(A) 17:9
(B) 17:76
(C) 17:9
(D) 17:2
(E) 17:3
Rationale: P:Q = 85000 : 15000 = 17:3.
Answer: E
Answer: (E) 17:3
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 10000
(C) 25000
(D) 34000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: A watch which gains uniformly is 2 minutes low at noon on monday and is 4 min.48 sec fast at 2 p.m on the following monday. when was it correct ?
(A) 2.10 p.m on wednesday.
(B) 2.20 p.m on wednesday.
(C) 2.30 p.m on wednesday.
(D) 2.40 p.m on wednesday.
(E) 2.00 p.m on wednesday.
Rationale: Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours
\therefore The watch gains \inline \left ( 2+4\frac{4}{5} \right ) min. or \inline \frac{34}{5} min. in 170 hrs.
Now, \inline \frac{34}{5} min. are gained in 170 hrs.
\inline \therefore 2 min are gained in \inline \left ( 170\times \frac{5}{34}\times 2 \right ) hrs = 50 hrs
\inline \therefore Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at 2 p.m on wednesday.
Answer E
Answer: (E) 2.00 p.m on wednesday.
Question: A portion of the 85% solution of chemicals was replaced with an equal amount of 20% solution of chemicals. As a result, 40% solution of chemicals resulted. What part of the original solution was replaced?
(A) 5/13
(B) 6/13
(C) 9/13
(D) 13/9
(E) 13/6
Rationale: Let the original amount of 85 percent solution = x and amount replaced be y
0.85(x - y)+ 0.2y = 0.4 x
0.85x -0.85y+0.2y = 0.4x
0.45x = 0.65y
9x = 13y
y = 9x/13
So, amount replaced = 9/13 of original amount
ANSWER:C
Answer: (C) 9/13
Question: Sujit incurred a loss of 45% on selling an article for Rs.3740/-. What was the cost price of the article?
(A) Rs.5725/-
(B) Rs.5080/-
(C) Rs.6250/-
(D) Rs.6750/-
(E) None of these
Rationale: Explanation:
45% loss means SP of Rs.3740/- is 55% of CP
:. CP = 3740x100/55 = Rs.6800/-
Answer: Option E
Answer: (E) None of these
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 9
(C) 12
(D) 16
(E) 18
Rationale: Explanation:
80% --- 12
120% --- ?
80/120 * 12 = 8
ANSWER IS A
Answer: (A) 8
Question: A can do a job in 18 days and B can do it in 24 days. A and B working together will finish twice the amount of work in days?
(A) 22 1/6
(B) 22 1/2
(C) 20 4/7
(D) 22 1/9
(E) 22 1/1
Rationale: 1/18 + 1/24 = 7/72
72/7 = 72/7 *2 = 20 4/7 days
Answer: C
Answer: (C) 20 4/7
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs 1920 less than the principal. What was the principal?
(A) 1500
(B) 2500
(C) 2507
(D) 3200
(E) 2400
Rationale: P - 1920 = (P*5*4)/100
P = 2400
Answer: E
Answer: (E) 2400
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 15 seconds. The speed of the train is:
(A) 22
(B) 50
(C) 99
(D) 35
(E) 12
Rationale: Speed of the train relative to man = (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr = 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 30 ==> x = 35 km/hr.Answer: D
Answer: (D) 35
Question: 3/4th of a number exceeds its 2/3rd by 8. What is the number?
(A) 22
(B) 77
(C) 28
(D) 96
(E) 26
Rationale: Explanation:
Let the number be x.
3/4x = 2/3x + 8
Multiply by 12
9x = 8x + 96
x = 96
ANSWER:D
Answer: (D) 96
Question: A and B start a business jointly. A invests Rs 16000 for 8 month and B remains in the business for 4 months. Out of total profit, B claims 2/7 of the profit . How much money was contributed by B?
(A) 12800
(B) 13000
(C) 11500
(D) 12500
(E) 12000
Rationale: B claims 2/7 of the profit
A claims remaining 5/7 of the profit
=> A : B =5/7:2/7=5:2
Let the money contributed by B =b
Then A:B =16000×8:b×4
Therefore,
16000×8:b×4=5:2
16000×8×2=b×4×5
16000×2×2=b×5
3200×2×2=b
b=12800
Answer is A.
Answer: (A) 12800
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 502 to 600 inclusive?
(A) 23,550
(B) 27,550
(C) 31,550
(D) 35,550
(E) 39,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
502 + 504 + ... + 600 = 50(500) + (2+4+...+100) = 25,000 + 2550 = 27,550
The answer is B.
Answer: (B) 27,550
Question: 0.999999+0.111111=?
(A) 1
(B) 1.0001
(C) 1.0021
(D) 1.111
(E) 1.11111
Rationale: 0.999999 + 0.111111
= 0.999999 + 0.11111 + 0.000001
= (0.999999 + 0.000001) + 0.11111
= 1 + 0.11111
= 1.11111
E
Answer: (E) 1.11111
Question: If a cyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent, what percent of the original speed is the total increase in speed?
(A) 10%
(B) 40%
(C) 43%
(D) 64%
(E) 140%
Rationale: let the sped be 100
an increase of 30%
the speed now is 130
a further increase of 10% on 130 =13
total increase =43 on 100 =43% C
Answer: (C) 43%
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *5 + 3 and *5 + 5, inclusive?
(A)  None
(B)  One
(C)  Two
(D)  Three
(E)  Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *5 would be divisible by all numbers from 1 to 5.
=> *5+3 would give me a number which is a multiple of 3 and therefore divisible (since *5 is divisible by 3)
In fact adding anyprimenumber between 1 to 5 to *5 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *5 + 3 and *5 + 11 then the answer would be 1. For *5 +3 and *5 + 13, it is 2 and so on...
A
Answer: (A)  None
Question: If P and Q are positive integers, P - 2 is divisible by 4 and Q - 1 is divisible by 6, all of the following could be the value of P - Q Except?
(A) 3
(B) 1
(C) 15
(D) 4
(E) 29
Rationale: P-2 = 4Q
=> P = 4Q + 2 = 2,6,10,14,18,22,26,30,34,38,42,46,50
Q-1 = 6P
=> Q = 6P + 1 = 1,7,13,19,25,31,37,43,49,55,61,67,73
3=10-7
1=14-13
15=34-19
29=42-13
So , we can see that all the answer choices are possible here except D
Answer: (D) 4
Question: The length of a bridge in meters, which a train 120-meters long and traveling at 45 km/hr can cross in 30 seconds is?
(A) 255
(B) 285
(C) 315
(D) 345
(E) 375
Rationale: 45 km/h = 45000 m/3600 s = 12.5 m/s
In 30 seconds, the train can go 30(12.5) = 375 meters
Let x be the length of the bridge.
x+120 = 375 meters
x = 255 meters
The answer is A.
Answer: (A) 255
Question: Q is a set of five distinct prime numbers. If the sum of the integers in Q is even and the number x is a member of Q, then what is the least value that x can be?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 7
Rationale: 2 + 3 + 5 + 7 + 11= 28 ( sum is even)
Least number = 2
A
Answer: (A) 2
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 30
(C) 35
(D) 45
(E) 50
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: (A) 20
Question: In a group of ducks and cows, the total number of legs are 36 more than twice the no. of heads. Find the total no.of buffaloes.
(A) 10
(B) 12
(C) 13
(D) 15
(E) 18
Rationale: Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 36
=> 2x = 36 => x = 18
E
Answer: (E) 18
Question: Three coworkers P , T , R meet for Dinner. P had 5 sandwiches, T had 3 and R had none. Both PT share their sandwiches with R such that each one got the same amount. If R paid $ 8 to PT, how much of $ 8 should P get? Assume both sandwiches and Dollars can be split.
(A) a) 5$
(B) b) 3 $
(C) c) 7 $
(D) d) 4 $
(E) e) 5.5 $
Rationale: we got total 8 sandwiches ....we are dividing equally in 3 people.
per person: 8/3
initially
p:8
T:3
r:0
now since r ate 8/3 so he is paying 8 dollars for 8/3 sandwiches.
now p also ate 8/3 of his 5 sandwiches = so he gave 5-8/3 to r ==>7/3 to r
ok we have 8 dollars for 8/3 sandwich
therefore for 7/3 sandwich we will get 7 dollars.
hence p should get 7 dollars.
hence C
Answer: (C) c) 7 $
Question: Which of the following could be the sum of the reciprocals of two prime numbers?
(A) 7/15
(B) 11/12
(C) 11/30
(D) 8/15
(E) 19/77
Rationale: 10/12 it is
8/15=(1/3) + (1/5)
Answer - D
Answer: (D) 8/15