mathewhe/aqua_rat huggingface dataset:
Question: A train 165 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [165 * 3/55] sec = 9 sec
Answer: E
Answer: (E) 9
Question: A used-book dealer sells paperback books at 3 times the dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 130 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $300, how many of the books sold were paperbacks?
(A) 40
(B) 60
(C) 75
(D) 90
(E) 100
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 130 books were paperbacks, the dealer would earn a profit of $260.
Since the actual profit was $300, the dealer must have sold 40 hardbacks.
Then the number of paperbacks sold was 130-40 = 90.
The answer is D.
Answer: (D) 90
Question: A man travelled from the village to the post office at the rate of 25kmph and walked backed at the rate of 4 kmph. If the whole journey took 5 hours 48 minutes, find the distance of the post office from the village?
(A) 10km
(B) 50km
(C) 30km
(D) 25km
(E) 20km
Rationale: Average speed = 2xy/x+y = 2*25*4/25+4 = 200/29km/hr
Distance travelled in 5hr 48mnts = 200/9 * 29/5 = 40km
Distance of the post office from the village = 40/2 = 20km
Answer is E
Answer: (E) 20km
Question: Yesterday it took Robert 3 hours to drive from City X to City Y. Today it took Robert 2.5 hours to drive back from City Y to City X along the same route. If he had saved 15 minutes in both trips, the speed for the round trip would be 50 miles per hour. What is the distance between city X and city Y?
(A)  125.5
(B)  120.5
(C)  150
(D)  240.5
(E)  300
Rationale: 2d/50 = 5 ( because time = 3 + 2.5 - 0.5 hrs)
=> d = 125.5
Answer - A
Answer: (A)  125.5
Question: 87th number in the series 2, 10, 26,50,……….
(A) 29930
(B) 28930
(C) 27960
(D) 26780
(E) 25874
Rationale: 2+8*0=2
2+8*1=10
2+8*1+8*2=26
2+8*1+8*2+8*3=50...........
87th term
2+8*1+8*2+8*3+.......................................+8*86
2+8(1+2+3+4+....................+86)
2+8*(86/2)*(1+86)= 29930
ANSWER:A
Answer: (A) 29930
Question: Two numbers when divided by a divisor leave remainders of 228 and 352 respectively. The remainder obtained when the sum of the numbers is divided by the same divisor is 68. Find the divisor.
(A) 512
(B) 573
(C) 634
(D) 685
(E) 736
Rationale: Let x be the divisor.
N1 = xa + 228
N2 = xb + 352
N1 + N2 = x(a+b) + 580 = xc + 68
x(c-a-b) = 512 but we know that x > 352, thus (c-a-b) must equal 1.
The answer is A.
Answer: (A) 512
Question: A train 825 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 90 seconds. The speed of the train is:
(A) 33
(B) 27
(C) 27
(D) 50
(E) 81
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
Question: A man can row 8 kmph in still water. When the river is running at 3 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.75
(B) 5.7
(C) 5.76
(D) 5.74
(E) 6.8
Rationale: M = 8
S = 3
DS = 11
US = 5
x/11 + x/5 = 1
x = 3.4
D = 3.4 * 2 = 6.8 Answer: E
Answer: (E) 6.8
Question: If x and y are integers, what is the least positive number of 24x+20y?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: 24x+20y = 4(6x+5y) which will be a minimum positive number when 6x+5y = 1.
6(1) + 5(-1) = 1
Then 4(6x+5y) can have a minimum positive value of 4.
The answer is C.
Answer: (C) 4
Question: 100 people are attending a newspaper conference. 35 of them are writers and more than 38 are editors. Of the people at the conference, x are both writers and editors and 2x are neither. What is the largest possible number of people who are both writers and editors?
(A) 21
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: {Total}={Writers}+{Editors}-{Both}+{Neither}.
{Total}=100;
{Writers}=35;
{Editors}>38;
{Both}=x;
{Neither}=2x;
100=35+{Editors}-x+2x --> x=65-{Editors}. We want to maximize x, thus we should minimize {Editors}, minimum possible value of {Editors} is 39, thus x={Both}=65-39=26.
Answer: B.
Answer: (B) 26
Question: How many different positive integers exist between 10^3 and 10^4, the sum of whose digits is equal to 2?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 1001
1010
1100
2000
TOTAL NO. 4
B
Answer: (B) 4
Question: If the average (arithmetic mean) of a and b is 30 and the average of b and c is 60, what is the value of c − a?
(A) 25
(B) 60
(C) 90
(D) 140
(E) It cannot be determined from the information given.
Rationale: -(a + b = 60)
b + c=120
c-a=60
B. 60
Answer: (B) 60
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50
(B) 26
(C) 27
(D) 28
(E) 21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
Answer: (A) 50
Question: A numberais squared and then multiplied by negative 3. The result of this operation W is equal to three times the sum of three timesaand two. What is one possible value ofa?
(A) -3
(B) -2
(C) 1
(D) 2
(E) 3
Rationale: W=-3*a^2=3(3a+2)
a= -2 or -1
a=-2=B
Answer: (B) -2
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?
(A) 5/20
(B) 9/25
(C) 8/20
(D) 9/20
(E) 6/20
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}
answer 9/20
Answer D
Answer: (D) 9/20
Question: The sum of five numbers is 655. The average of the first two numbers is 85 and the third number is 125. Find the average of the two numbers?
(A) 180
(B) 288
(C) 667
(D) 299
(E) 12
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 655.
(P + Q)/2 = 85 and R = 125
P + Q = 170 and R = 125
P + Q + R = 295
S + T = 655 - (P + Q + R) = 360
Average of the last two numbers = (S + T)/2 = 180.
Answer:A
Answer: (A) 180
Question: During one month at a particular restaurant, 1/6 of the burgers sold were veggie burgers and 1/2 of the rest of the burgers sold were double-meat. If x of the burgers sold were double-meat, how many were veggie burgers?
(A) x/8
(B) x/2
(C) 2x/5
(D) 3x/4
(E) 4x/5
Rationale: Let y be the number of total burgers.
veggie = y/6 , non veggie = 5y/6
1/4 of the rest of the burgers sold were double-meat
=> 5y/6 * 1/2 = double meat = x
=> y/6 = 2x/5 = veggie
Hence C
Answer: (C) 2x/5
Question: In a tree, 3/7 of the birds are parrots while the rest are toucans. If 2/3 of the parrots are female and 7/10 of the toucans are female, what fraction of the birds in the tree are male?
(A) 3/7
(B) 11/35
(C) 16/35
(D) 31/70
(E) 37/70
Rationale: Let x be the number of birds in the tree.
The fraction of birds that are male parrots is (1/3)(3/7)=1/7.
The fraction of birds that are male toucans is (3/10)(4/7)=6/35.
The total fraction of male birds is 1/7 + 6/35 = 11/35.
The answer is B.
Answer: (B) 11/35
Question: If f(x) = ax^3 + x^2 + ax – 2x, then f(b) – f(-b) will equal:
(A) 2ab^3 - 2ab
(B) 2ab
(C) 2ab^3 + 2ab - 4b
(D) - 4b
(E) 2ab^3
Rationale: f(x)=ax^3 + x^2 + ax – 2x
f(b) = ab^3 + b^2 + ab – 2b
f(-b) = - ab^3 + b^2 - ab + 2b
f(b) - f(-b) = ab^3 + b^2 + ab – 2b + ab^3 - b^2 + ab – 2b
=2ab^3 + 2ab - 4b
Answer C
Answer: (C) 2ab^3 + 2ab - 4b
Question: The length of a rectangular plot is thrice its breadth. If the area of the rectangular plot is 432 sq m, then what is the breadth of the rectangular plot?
(A) 12
(B) 17
(C) 18
(D) 19
(E) 14
Rationale: Let the breadth of the plot be b m.
Length of the plot = 3 b m
(3b)(b) = 432
3b2 = 432
b2 = 144
b = 12 m.
Answer: Option A
Answer: (A) 12
Question: A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
(A) 13
(B) 59
(C) 35
(D) 37
(E) 12
Rationale: Explanatory Answer
Decoding "A number when divided by a divisor leaves a remainder of 24"
Let the original number be 'a'.
Let the divisor be 'd'.
Let the quotient of dividing 'a' by 'd' be 'x'.
Therefore, we can write the division as a/d = x and the remainder is 24.
i.e., a = dx + 24
Decoding "When twice the original number is divided by the same divisor, the remainder is 11"
Twice the original number is divided by d means 2a is divided by d.
We know that a = dx + 24.
Therefore, 2a = 2(dx + 48) or 2a = 2dx + 48
When (2dx + 48) is divided by 'd' the remainder is 11.
2dx is divisible by 'd' and will therefore, not leave a remainder.
The remainder of 11 would be the remainder of dividing 48 by d.
The question is "What number will leave a remainder of 11 when it divides 48?"
When 37 divides 48, the remainder is 11.
Hence, the divisor is 37.
Choice D
Answer: (D) 37
Question: If g and s are positive integers such that (2^g)(4^s) = 16, then 2g + s =
(A)  2
(B)  3
(C)  4
(D)  5
(E)  6
Rationale: lets get the eq into simplest orm..
(2^g)(4^s) = 16..
(2^g)(2^2s) = 2^4..
or g+2s=4..
since g and s are positive integers, only g as 2 and s as 1 satisfy the Equation..
so 2g+s=2*2+1=5..
D
Answer: (D)  5
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, 35, 38, 43 x
(A) 46
(B) 26
(C) 36
(D) 35
(E) 45
Rationale: (A)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 43 + 3 = 46.
Answer: (A) 46
Question: What Is The Next Number
12 13 15 17 111 113 117 119 ?
(A) 123
(B) 220
(C) 129
(D) 428
(E) 224
Rationale: 123.
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
Answer : A
Answer: (A) 123
Question: If x and y are integers and xy = 330, x or y must be divisible by which of the following?
(A) 4
(B) 5
(C) 6
(D) 20
(E) 30
Rationale: xy = 330 = 2 * 3 * 5 * 11
One of x or y must be divisible by 5.
The answer is B.
Answer: (B) 5
Question: 60% of the employees of a company are men. 60% of the men in the company speak French and 50% of the employees of the company speak French. What is % of the women in the company who do not speak French?
(A) 4%
(B) 10%
(C) 96%
(D) 90%
(E) 65%
Rationale: No of employees=100(say)
Men=60
Women=40
Men speaking french=0.6*60=36
Employees speaking french=0.5*100=50
Therefore women speaking French=50-36=14
And women not speaking French=40-14=26
% of women not speaking French=26/40*100=65%
Answer E
Answer: (E) 65%
Question: How much is 80% of 40 is greater than 4/5 of 25?
(A) 15
(B) 7
(C) 18
(D) 12
(E) 23
Rationale: (80/100) * 40 – (4/5) * 25
32 - 20
= 12
Answer: D
Answer: (D) 12
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 57 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 63 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
(A) 19
(B) 28
(C) 30
(D) 32
(E) 44
Rationale: Using Speed Formula: Speed = Distance / Time
Distance to be covered = 51-11 = 40
Speed of approach = 57 + 63 floors/min
Time = 40/120 = 1/3
So Steve will cover 57x 1/3 floors in that time = 19
So he will be in 19 + 11 floor = 30th Floor
ANSWER:C
Answer: (C) 30
Question: A thief goes away with a SANTRO car at a speed of 25 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start?
(A) 5/7 hours
(B) 2/7 hours
(C) 2/3 hours
(D) 1/3 hours
(E) 2/5 hours
Rationale: -----------25--------------------|
60 25
D = 25
RS = 60 â€“ 25 = 35
T = 25/35 = 5/7 hours
ANSWER:A
Answer: (A) 5/7 hours
Question: A club with a total membership of 30 has formed 3 committees, M, S and R, which have 7, 12 and 5 members respectively. If no members of committee M is on either of the other 2 committees, what is the greatest possible number of members in the club who are on none of the committees?
(A) 5
(B) 7
(C) 8
(D) 10
(E) 11
Rationale: As no member of committee M is on either of the other 2 committees then 30-M=30-7=23 people are on committee S, committee R or on none of the committee. We want to maximize the last group: members in the club who are on none of the committees
General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
So we should minimize total # of people who are on committee S and committee R. Now if ALL 5 people who are the members of committee R are also the members of committee S (if R is subset of S) then total # members of committee S and committee R would be minimized and equal to 12. Which means that 23-12=11 is the greatest possible number of members in the club who are on none of the committees.
Answer: E.
Answer: (E) 11
Question: An empty fuel tank with a capacity of 200 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 28 gallons of ethanol, how many gallons of fuel A were added?
(A) 160
(B) 150
(C) 100
(D) 80
(E) 50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 200-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 200-A gallons of fuel B is 0.16(200-A);
Since the total amount of ethanol is 28 gallons then 0.12A+0.16(200-A)=28 --> A=100.
Answer: C.
Answer: (C) 100
Question: 45 x ? = 25% of 900
(A) 16.2
(B) 4
(C) 5
(D) 500
(E) None
Rationale: Answer
Let 45 x A = (25 x 900)/100
∴ A = (25 x 9)/45 = 5
Correct Option: C
Answer: (C) 5
Question: There is a sequence A(n) such that A(n+1)=2A(n)-1 and A(1)=3, where n is a positive integer. What is the value of A(66)-A(65)?
(A) 2^22+1
(B) 2^65
(C) 2^23+1
(D) 2^24
(E) 2^23+1
Rationale: A1= 3
A2= 2*3-1= 5
A3= 2*5-1= 9
A4= 2*9-1= 17
We can notice that there is a squence
A2-A1= 2^1
A3-A2= 2^2
A4-A3= 2^3
Hence A66-A65= 2^65
B is the answer
Answer: (B) 2^65
Question: At the wholesale store you can buy an 8-pack of hot dogs for $1.55, a 20-pack for $3.05, and a 250-pack for $22.95. What is the greatest number of hot dogs you can buy at this store with $205?
(A) 1,108
(B) 2,100
(C) 2,140
(D) 2,124
(E) 2,256
Rationale: I think it should be C.
I can buy 8 250-pack for Rs 22.95*8 = $183.60
Now, I can buy 7 20-pack for 3.05*7 = $21.35
Now, I am left with only $1.15. I cannot but anything with this.
Hence Total Hotdogs = 250*8 + 20*7= 2140
Answer: (C) 2,140
Question: How many integers k greater than 100 and less than 900 are there such that if the hundreds and the unit digits of k are reversed, the resulting integer is k + 99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Not sure if this is the shortest.. But this is how I did this
There are 7 sets of integers with hundreds and units digits exchanged that satisfies k + 99.
1. 102 | 201 (satisfies k+99, where k = 102)
2. 203 | 302 (satisfies k+99, where k = 203)
3. ...
4. ...
5. ...
6. ...
7. 708 | 807
Each set has 10 such numbers.
1. 102 | 201 (still k+99 holds good)
2. 112 | 211
3. 122 | 221
4. 132 | 231
5. ...
6. ...
7. ...
8. ...
9. 182 | 281
10. 192 | 291
Therefore, 7 sets with 10 such number in each set will give 7 x 10 = 70 integers.
C
Answer: (C) 70
Question: A five-person team is to be formed from a pool of 6 East All Stars and 6 West All Stars. What is the probability that the team will contain at least 2 East All Stars?
(A) fraction of 29/33
(B) 81/169
(C) 57/120
(D) 47/144
(E) 119/720
Rationale: The question with at- least can be easily tackled by
At least = Total cases - unwanted cases
So atleast 2 player = total cases - cases with no east all stars person - case with only one east all person
Total number of cases = 12C5 = 798
Cases with no east all person = 6C5(All person from west all stars) = 6
Cases with exactly one east all person = 6C4*6C1 (4from west all stars and 1 from east all stars)= 90
So total no. of cases with with at least two members = 798-6-90 = 702
Probability = 702/798 = 29/33
answer:A
Answer: (A) fraction of 29/33
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 79.2 km/hr
(B) 23.9 km/hr
(C) 22.9 km/hr
(D) 22.7 km/hr
(E) 23.8 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer:D
Answer: (D) 22.7 km/hr
Question: A recycling facility is staffed by 15 floor workers and one manager. All of the floor workers are paid equal wages, but the manager is paid n times as much as a floor worker. If the manager’s wages account for 1/14 of all wages paid at the facility, what is the value of n?
(A) 8
(B) 9
(C) 10
(D) 15/13
(E) 11
Rationale: Say each floor worker is paid $x, then the manager is paid $xn.
Total salary would be 15x+xn and we are told that it equals to 14xn:
15x+xn=14xn --> reduce by x: 15+n=14n -->13n=15
n = 15/13
Answer: D
Answer: (D) 15/13
Question: A can do a piece of work in 20 days; B can do the same in 30 days. A started alone but left the work after 10 days, then B worked at it for 10 days. C finished the remaining work in 10 days. C alone can do the whole work in?
(A) 70 days
(B) 65 days
(C) 40 days
(D) 50 days
(E) 60 days
Rationale: 10/20 + 10/30 + 10/x = 1
x = 60 days
ANSWER:E
Answer: (E) 60 days
Question: In a group of ducks and cows, the total number of legs are 24 more than twice the number of heads. Find the total number of cows.
(A) A)14
(B) B)12
(C) C)16
(D) D)8
(E) E)6
Rationale: Explanation :
Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 24 more than twice the number of heads
=> 2(d + 2c) = 24 + 2(c + d)
=> d + 2c = 12 + c + d
=> 2c = 12 + c
=> c = 12
Answer : B
Answer: (B) B)12
Question: Solution Y is 30 percent liquid X and 70 percent water. If 2 kilograms of water evaporate from 10 kilograms of solution Y and 2 kilograms of solution Y are added to the remaining 6 kilograms of liquid, what percent of this new solution is liquid X?
(A) 34
(B) 35
(C) 36
(D) 37 1/25
(E) 40
Rationale: In 8 kilograms of solution Y there are 0.3*10=3 kilograms of solution X;
After 2 kilograms of water are replaced by 2 kilograms of solution Y, to the existing 2.4 kilograms of solution X, 0.3*2=0.6 kilograms of solution X are added, so in the new solution of 8 kilograms there are 3+0.6=3.6 kilograms of solution X, which is 3.6/10*100=36% of this new solution.
Answer: C.
Answer: (C) 36
Question: For an employee to qualify for early retirement at a certain company, the sum of the employee’s age and years of service must be at least 50, If Sue was K years old when she was hired by the company, what is the minimum age at which she could possibly qualify for early retirement.
(A) K+35
(B) 2K+35
(C) (70+K)/2
(D) (50+K)/2
(E) 2(70-K)
Rationale: Say Sue was hired when she was already 50 years old (k=50), then she could retire right away, at the age of 50. Now, plug k=50 in the answer choices and see which yields 50. Only C fits.
Answer: D.
Answer: (D) (50+K)/2
Question: A man purchases an electric heater whose printed price is Rs.160. If he received two successive discounts of 20% and 10%; he paid :
(A) Rs.112
(B) Rs.129.60
(C) Rs.119.60
(D) Rs.115.20
(E) None
Rationale: Explanation:
Price after Ist discount = 100% of Rs.160 = Rs. 128
Price after 2nd discount = 90% of Rs.128 = Rs.115.20
Correct Option : D
Answer: (D) Rs.115.20
Question: What are the last two digits of 24*62*33*48*39*16?
(A) 40
(B) 08
(C) 64
(D) 34
(E) 12
Rationale: 24*62*33*48*39*16?=
We have to focus on the last two digits only, so 24*62=88*33=04*48=92
39*92=88 therefore 88*16=08
Hence Answer is B
Answer: (B) 08
Question: The ratio of ages of Aman, Bren, and Charlie are in the ratio 5:8:7 respectively. If 8 years ago, the sum of their ages was 76, what will be the age of Bren 12 years from now?
(A) 17
(B) 25
(C) 27
(D) 52
(E) 60
Rationale: Let the present ages of Aman, Bren, and Charlie be 5x, 8x and 7x respectively.
5x-8 + 8x-8 + 7x-8 = 76
x = 5
Present age of Bren = 8*5 = 40
Bren's age 12 years hence = 40+12 = 52
Answer = E
Answer: (E) 60
Question: A father told his son "I was as old as you are at present, at the time of your birth". If the father is 38 years old now, then what was the son's age five years ago in years?
(A) 14
(B) 19
(C) 38
(D) 33
(E) 35
Rationale: et son's present age is =x
then 38-x=x
x=19
son's age 5 years back is 19-5=14 years.
ANSWER:A
Answer: (A) 14
Question: A man is walking at the rate of 10 km/hr crosses a bridge in 15 minutes. The length of the bridge is
(A) 1000 meters
(B) 1050 meters
(C) 1200 meters
(D) 1250 meters
(E) 2500 meters
Rationale: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Speed=10âˆ—5/18=25/9m/sec
Time=15âˆ—60seconds=900seconds
Distance=Timeâˆ—Speed/Distance=25/9âˆ—900=2500meter
Option E
Answer: (E) 2500 meters
Question: Three factories of Conglomerate Corporation are capable of manufacturing hubcaps. Two of the factories can each produce 1000 hubcaps in 15 days. The third factory can produce hubcaps 30% faster. Approximately how many days would it take to produce a 10,000 hubcaps with all three factories working simultaneously?
(A) 38
(B) 42
(C) 46
(D) 50
(E) 54
Rationale: since third factory is 30% faster , thus it will create 1300 hubcaps in 15 days
in 15 days total number of hubcaps made by all three will be :
1000+1000+1300=3300
in 30 days:
3300+3300=6600
in 45 days:
6600+3300=9900
now only 100 more hubcaps are required , which will take 1 day
thus in all 46 days.
Ans:C
Answer: (C) 46
Question: There are 32 balls which are red, blue or green. If 15 balls are green and the sum of red balls and green balls is less than 23, at most how many red balls are there?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: r+g+b=32
g=15
r + g < 23
=> r + 15 < 23
=> r < 8
=> at most 7 red balls
ANSWER:D
Answer: (D) 7
Question: A train 275 m long, running with a speed of 90 km / hr will pass a tree in
(A) 11 sec
(B) 15 sec
(C) 16 sec
(D) 20 sec
(E) None
Rationale: Sol.
Speed = (90 x 5/18) m/sec.
= 25 m / sec.
Time taken = (275 x 1/25) sec = 11 sec
Answer A
Answer: (A) 11 sec
Question: The smallest 3 digit positive integer obtained by adding two positive two digit numbers, one of which has the units and tens places interchanged as the other is _____
(A) 100
(B) 101
(C) 105
(D) 110 is answer
(E) 121
Rationale: Ans: D
Solution: as those numbers has digit interchanged and added to get the three digit number means the sum is: = 11(a+b)
so the final number must be multiple of 11. we are looking for smallest three digit number multiple of 11= 110 Ans D
Answer: (D) 110 is answer
Question: If one of the followings is the product of the two 3-digit integers 8K6 and 6L9 (K and L denote the tens digit of the respective integers), then that product must be
(A)  478,823
(B)  511,913
(C)  531,875
(D)  538,424
(E)  569,112
Rationale: To know the unit digit you can multiply both digit number: 6 x 9 = 54
This eliminates A,C, B, and E, because the number must end with a 4
So the answer is D
Answer: (D)  538,424
Question: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year its value at the end of 3 years was Rs.21093. Find its value at the beginning of the first year?
(A) 25600.24
(B) 25600.28
(C) 25600.26
(D) 25600.22
(E) 25600.21
Rationale: 6 1/4% = 1/16
x *15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Answer:A
Answer: (A) 25600.24