mathewhe/aqua_rat huggingface dataset:
Question: If a die has 3,4 and 1,6 and 2,5 opposite each other, then how many such dies can be made.
(A) 13
(B) 3
(C) 5
(D) 12
(E) 11
Rationale: there are 3 pairs . consider it A,B,C
A-(1,6)
B-(3,4)
C-(2,5)
Now the possible combinations to place A B C is 6.
because for A - 3 possible place
B- 2 POSSIBLE PLACE
C-1 POSSIBLE PLACE
3*2*1=6
NOW A HAS TWO PAIR SO POSSIBLE COMBO FOR 1 AND 6 IS 2 ..SAME FOR B AND C
2+2+2=6
SO 6+6=12
ANSWER:D
Answer: (D) 12
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
(A) 11000
(B) 11008
(C) 11006
(D) 110054
(E) 11001
Rationale: 2 * 22/7 * 1.75 * x = 11000
x = 1000
Answer: A
Answer: (A) 11000
Question: A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 10 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 2.9 hrs
(B) 8.9 hrs
(C) 2.9 hrs
(D) 6.7 hrs
(E) 8.6 hrs
Rationale: Net part filled in 1 hour = (1/4 - 1/10)
= 3/20
The cistern will be filled in 20/3 hrs i.e., 6.7 hrs.
Answer:D
Answer: (D) 6.7 hrs
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 18
(B) 10
(C) 12
(D) 11
(E) 17
Rationale: 4/12 + x/15
= 1
x = 10
Answer: B
Answer: (B) 10
Question: 1/3rd of work is completed by kiran in 6days. In how many days he can finish the remaining work?
(A) 6days
(B) 10days
(C) 12days
(D) 15days
(E) 20days
Rationale: 1/3rd work finished in 6days
2/3rd work = 2/3*3*6 = 12days
Answer is C
Answer: (C) 12days
Question: If n is a positive integer and n^2 is divisible by 72, then the largest positive integer that must divide n is
(A) 6
(B) 12
(C) 24
(D) 36
(E) 48
Rationale: possible values of n = 12, 24, 36 and 48.
But it is 12 that can divide all the possible values of n. If we consider 48, it will not divide 12, 24 and 36.
Hence, 12 is the value that MUST divide n.
ANSWER:B
Answer: (B) 12
Question: A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr?
(A) 10 km/hr.
(B) 20 km/hr.
(C) 30 km/hr.
(D) 40 km/hr.
(E) None
Rationale: Sol.
Speed = [150 + 300 / 40.5] m/sec = [450 / 40.5 * 18/5] km/hr = 40 km/hr.
Answer D
Answer: (D) 40 km/hr.
Question: The average age of a class of 32 students is 15 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
(A) 45 Years
(B) 46 Years
(C) 49 Years
(D) 52 Years
(E) 48 Years
Rationale: Total age of students is 32X15 = 480 Years Total age inclusive of teacher = 33X (15+1) = 528 So, Teacher's age is 528-480 = 48 Yrs There is a shortcut for these type of problems Teacher's age is 15+(33X1) = 48 YearsAnswer : E
Answer: (E) 48 Years
Question: A car traveling at a certain constant speed takes 12 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 60
(B) 72
(C) 72.5
(D) 73
(E) 73.5
Rationale: Many approaches are possible, one of them:
Let the distance be 1 kilometer.
Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds;
Time to cover this distance at regular speed is 48+12=60 seconds = 60/3,600 hours = 1/60 hours;
So, we get that to cover 1 kilometer 1/60 hours is needed --> regular speed 60 kilometers per hour (rate is a reciprocal of time or rate=distance/time).
Answer: A
Answer: (A) 60
Question: A certain sum of money at simple interest amounted Rs.1448 in 9 years at 4% per annum, find the sum?
(A) 1064
(B) 1080
(C) 1980
(D) 646
(E) 168
Rationale: 840 = P [1 + (9*4)/100]
P = 1064
Answer:A
Answer: (A) 1064
Question: In what time a debt of Rs.7920 due may be cleared by immediate cash down
payment of Rs.3600 at 1/2% per month
(A) 10years
(B) 20years
(C) 30years
(D) 40years
(E) NONE OF THESE
Rationale: Explanation:
PW=100*Amount / 100+(R+T)
ANSWER IS B
Answer: (B) 20years
Question: A person crosses a 500 m long street in 4 minutes. What is his speed in km per hour?
(A) 7.5
(B) 2.6
(C) 3.9
(D) 8.2
(E) 2.7
Rationale: distance = 500 meter
time = 4 minutes = 4 x 60 seconds = 240 seconds
Speed = distance/time=500/240=2.08 m/s=2.08Ã—18/5 km/hr=7.5 km/hr
Answer :A
Answer: (A) 7.5
Question: In how many ways can eight different rings be worn on four fingers of one hand?
(A) 10
(B) 12
(C) 70
(D) 60
(E) 18
Rationale: Required number of ways = ways of selecting 4 objects out of 8 given objects
= 8C4 = 8x 7x 6x 5 /24= 70
Answer C
Answer: (C) 70
Question: (1^2+2^2+3^2+.....+11^2)=?
(A) 506
(B) 345
(C) 365
(D) 385
(E) None of them
Rationale: formula is (1^2+2^2+3^2+....+n^2=1/6 n(n+1)(2n+1)
n=11
=(1/6x11x12x23)
=506
Answer is A.
Answer: (A) 506
Question: The car A has an average speed of 40 miles/hour and car B has an average speed of 60. How much time(in minutes) does the car A take more than car B to cover a distance of 60 miles?
(A) 10
(B) 20
(C) 25
(D) 30
(E) 40
Rationale: Time taken by Car A=60 miles/40 mph
=1.5 hours=90min
Time taken by Car B=60miles/ 60mph
=1 hour = 60 min
Car A takes 30 min more than car B
Answer: D
Answer: (D) 30
Question: For which of the following functions is f(z+b)=f(z)+f(b) for all positive numbers z and b?
(A) a) f(x)=x^2
(B) b) f(x)=x+1
(C) c) f(x)=root x
(D) d) f(x)=2/x
(E) e) f(x)= -3x
Rationale: f(z+b)=f(z)+f(b) Its E
Answer: (E) e) f(x)= -3x
Question: In a hotel, rooms are numbered from 101 to 550. A room is chosen at random. What is the probability that room number starts with 1, 2 or 3 and ends with 4, 5 or 6?
(A) 80 rooms
(B) 90 rooms
(C) 70 rooms
(D) 60 rooms
(E) 10 rooms
Rationale: There are total 450 rooms.
Out of which 299 room number starts with either 1, 2 or 3. (as room number 100 is not there) Now out of those 299 rooms only 90 room numbers end with 4, 5 or 6.
Ans : The probability is 90/450 so 90 rooms
Answer B
Answer: (B) 90 rooms
Question: Calculate the effect changes in dimension of a rectangle will have on its area, if length is increased by 18% and its breadth is decreased by 16%?
(A) 5.88% decrease
(B) 0.88% decrease
(C) 0.88% increase
(D) 1.88% decrease
(E) 2.88% decrease
Rationale: let L and B be 100 each
100 * 100 = 10000
L increase by 18% = 118
B decrease by 16% = 84
118 * 84 = 9912
0.88% decrease
ANSWER:B
Answer: (B) 0.88% decrease
Question: How many numbers from 10 to 50 are exactly divisible by 3
(A) 11
(B) 13
(C) 15
(D) 18
(E) 19
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.
13 Numbers.
10/3 = 3 and 50/3 = 16 ==> 16 - 3 = 13. Therefore 13 digits
B)
Answer: (B) 13
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 180 votes. Find the total number of valid votes?
(A) 430
(B) 450
(C) 436
(D) 434
(E) 422
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 180 => 4x/10 = 180
=> 4x = 1800 => x = 450.
Answer:B
Answer: (B) 450
Question: If x is a negative integer, which of the following must be a negative integer?
(A) x + 1
(B) x/2+3
(C) x^4
(D) x – y
(E) x^11
Rationale: We need to check each option here:
A. x + 1
This will depend on the value of x. Nothing can be said
B. x/2+3
This will depend on the value of x. Nothing can be said
C. x^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. x – y
This will depend on the value of x and y. Nothing can be said
E. x^11
This will always be negative. Even powers of negative numbers are positive and odd powers are negative
Correct Option: E
Answer: (E) x^11
Question: The food in a camp lasts for 40 men for 30 days. If ten more men join, how many days will the food last?
(A) 32days
(B) 30days
(C) 28days
(D) 26days
(E) 24days
Rationale: one man can consume the same food in 40*30 = 1200 days.
10 more men join, the total number of men = 50
The number of days the food will last = 1200/50 = 24 days.
Answer: E
Answer: (E) 24days
Question: 2 corner most boxes of a chess board(diagonally opposite) haven been cut out
there's a rectangular block = 2 sqaures of chess board , how many such blocks can be placed on the chess board ?”
(A) 27
(B) 28
(C) 29
(D) 30
(E) 31
Rationale: chess board has 64 squares.so we can place 32 rectangular blocks,but 2 are cut off from the corner.
hence 32-2=30 blocks
ANSWER:D
Answer: (D) 30
Question: A can finish a piece of work in 5 days. B can do it in 15 days. They work together for two days and then A goes away. In how many days will B finish the work?
(A) 3 days
(B) 5 days
(C) 4 days
(D) 6 days
(E) 7 days
Rationale: 2/5 + (2 + x)/15 = 1 => x = 7 days
ANSWER:E
Answer: (E) 7 days
Question: In Plutarch Enterprises, 70% of the employees are marketers, 20% are engineers, and the rest are managers. Marketers make an average salary of $60,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000?
(A) $80,000
(B) $130,000
(C) $240,000
(D) $290,000
(E) $220,000
Rationale: For sake of ease, let's say there are 10 employees: 7 marketers, 2 engineers, and 1 manager.
Average company salary * Number of employees = Total company salary
>>> $80,000 * 10 = $800,000
Subtract the combined salaries for the marketers (7 * $60,000) and the engineers (2 * $80,000)
>>> $800,000 - $420,000 - $160,000 = $220,000.
The correct answer is E.
Answer: (E) $220,000
Question: If |x - 20| = 40 what is the sum of all the values of x.
(A) 0
(B) 60
(C) -80
(D) 40
(E) 80
Rationale: There will be two cases
x-20 = 40 and x-20 = -40
Solve for x => x=40+20=> x=60 or x= -40 + 20 => x= -20
The sum of both values will be 60 + -20 =40
Answer is D
Answer: (D) 40
Question: If your mother asked you to bring her 7 water bottles, and one bottle costs 1.5 $, how much money should she give you?
(A) 9 $
(B) 9.5 $
(C) 10 $
(D) 10.5 $
(E) 11 $
Rationale: Simply multiply the cost of one bottle by its number you would buy.
The cost=7*1.5=10.5 $
So the correct choice is D
Answer: (D) 10.5 $
Question: At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years?
(A) 11%
(B) 8%
(C) 10%
(D) 9%
(E) 7%
Rationale: C.I=P(1+R/100)^N
12100=10000(1+R/100)^2
121/100=(1+R/100)^2
(11/10)^2=(1+R/100)
R=10%
ANSWER:C
Answer: (C) 10%
Question: 15 and 5 are the first two terms in a geometric sequence. What is the arithmetic difference between the 7th term and the 9th term?
(A) (40/3) * (1/3)^7
(B) (40/6) * (1/3)^7
(C) (40/9) * (1/3)^7
(D) (1/3)^7
(E) (100/3) * (1/3)^7
Rationale: Common ratio = 5/15 =1/3
7th term = 15*(1/3)^7
9th term = 15*(1/3)^9
Difference = 15 * ((1/3)^7 - (1/3)^9)
= 15 * (1/3)^7 *(1 - (1/3)^2)
= 15 * (1/3)^7 * (8/9)
= (120/9) * (1/3)^7....
= (40/3) * (1/3)^7
A
Answer: (A) (40/3) * (1/3)^7
Question: The mean of 1^3,2^3,3^3,4^3,5^3 is?
(A) 30
(B) 45
(C) 50
(D) 60
(E) 75
Rationale: 1^3+2^3+3^3+-----+n^3 = [n(n+1)/2]^2
1^3+2^3+3^3+-----+5^3 = (5*6/2)^2 = 225
Required average is = 225/5 = 45
Answer is B
Answer: (B) 45
Question: Convert the 18/42 m/s into kilometers per hour?
(A) 3.5 kmph.
(B) 2.5 kmph.
(C) 1.2 kmph.
(D) 1.54 kmph.
(E) 1.9 kmph.
Rationale: 18/42 m/s = 18/42 * 18/5 = 1 (27/50) = 1.54 kmph.
ANSWER:D
Answer: (D) 1.54 kmph.
Question: The ratio of salary of a worker in July to that in June was 21⁄2 : 21⁄4, by what % the salary of July more than salary of June. Also find by what %, salary of June was less than that of July.
(A) 11 1⁄9% and 10%
(B) 10% and 11 1⁄9%
(C) Both 10%
(D) Both 11 1⁄9%
(E) None of these
Rationale: Let the salary of July be 5⁄2 x
and the salary of June be 9⁄4 x
Required percentages
= 5/2x−9/4x /9/4x×100 and 5/2x−9/4x /5/2x×100
= 100⁄9% and 100⁄10% = 11 1⁄9% and 10%
Answer A
Answer: (A) 11 1⁄9% and 10%
Question: In expressing a length of 77.470 km as nearly as possible with the three significant digits, find the percentage error
(A) 0.39%
(B) 0.34%
(C) 0.039%
(D) 0.035%
(E) None of these
Rationale: Explanation:
Error = (77.5 - 77.470) = 0.03
Required percentage =
0.03/ 77.470Ã—100=0.039
Option C
Answer: (C) 0.039%
Question: The average of 40 numbers is 32. If two numbers namely 34 and 39 are discarded, The average of
remaining numbers is?
(A) 31.7
(B) 37.5
(C) 39.5
(D) 34.5
(E) 38.5
Rationale: Total of 50 numbers = 40 * 32 = 1280
Average of 38 numbers = 1280-(34+39) / 38
= 1207 / 38 = 31.7
Answer is A.
Answer: (A) 31.7
Question: The cube root of .000343 is
(A) 0.7
(B) 0.07
(C) 0.007
(D) 7
(E) None of these
Rationale: Explanation:
(.000343)1/3
= (343/106)1/3
= (7*7*7/ 102*102*102)1/3
= 7/102
= 7/100 = 0.07
ANSWER B
Answer: (B) 0.07
Question: The probability that a arrow fired from a point will hit the target is 1/4. Three such arrows are fired simultaneously towards the target from that very point. What is the probability that the target will be hit?
(A) 19/64
(B) 23/64
(C) 23/67
(D) 37/64
(E) 37/50
Rationale: Explanation :
Probability of a arrow not hitting the target =3/4.
Probability that none of the 3 arrow will hit the target:
=>(3/4)3.
=>27/64.
Probability that the target will hit at least once
=>1−(27/64).
=>37/64.
Answer : D
Answer: (D) 37/64
Question: A and B together can do a piece of work in 3 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
(A) 0.28 days
(B) 0.45 days
(C) 0.55 days
(D) 0.25 days
(E) 0.15 days
Rationale: B = 1/2 – 1/20 =0.28 days
ANSWER:A
Answer: (A) 0.28 days
Question: By travelling at 60 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
(A) 30 kmph
(B) 28 kmph
(C) 26 kmph
(D) 24 kmph
(E) 22 kmph
Rationale: Let the time taken to reach the destination be 3x hours. Total distance = 60 * 3x = 180x km
He covered 2/3 * 180x = 120x km in 1/3 * 3x = x hours So, the remaining 60x km, he has to cover in 2x hours. Required speed = 60x/2x
=30 kmph.
Answer: A
Answer: (A) 30 kmph
Question: Find the invalid no.from the following series 10, 17, 22, 29, 34, 36
(A) 36
(B) 18
(C) 40
(D) 37
(E) 25
Rationale: The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 36 is wrong.
Answer : A
Answer: (A) 36
Question: Present ages of X and Y are in the ratio 4:5 respectively. 6 years hence this ratio will become 5:6 respectively. What is X's present age in years?
(A) 35
(B) 24
(C) 37
(D) 39
(E) 40
Rationale: Let the present ages of X and Y be 4x and 5x years respectively.
Then, (4x + 6)/(5x + 6) = 5/6
6(4x + 6) = 5(5x + 6) => 24x+36 = 25x+30 => x=6
X's present age = 4x = 4*6 = 24
ANSWER: B
Answer: (B) 24
Question: In a 2000 m race, A beats B by 100 meters or 50 seconds. Find the speed of B?
(A) 10m/s
(B) 2m/s
(C) 5m/s
(D) 7m/s
(E) 3m/s
Rationale: Since A beats B by 100 m or 50 seconds,
it implies that B covers 100 m in 50 seconds.
Hence speed of B = 100/50 = 2 m/s.
Answer: B
Answer: (B) 2m/s
Question: Two isosceles Triangles have equal vertical angles and their areas are in the ratio 16:36. Find the ratio of their corresponding heights .
(A)  4/6
(B)  5/4
(C)  3/2
(D)  5/7
(E)  2/3
Rationale: We are basically given that the triangles are similar.
In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.
Therefore, area/AREA=height^2/HEIGHT^2=16/36 --> height/HEIGHT=4/6.
Answer: A.
Answer: (A)  4/6
Question: 65% of x = 20% of 422.50. Find the value of x?
(A) 100
(B) 130
(C) 150
(D) 180
(E) 199
Rationale: 65% of x = 20% of 422.50
Then, 65/100 * x = 20/100 * 4225/10
x = 845/10 * 100/65 = 130
Answer is B
Answer: (B) 130
Question: The area of a square garden is Q square feet and the perimeter is P feet. If Q=2P+48, what is the perimeter of the garden in feet?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: Let x be the length of one side of the square garden.
x^2 = 8x + 48
x^2 - 8x - 48 = 0
(x-12)(x+4) = 0
x = 12, -4
P = 4(12) = 48
The answer is D.
Answer: (D) 48
Question: The perimeter of a triangle is 24 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 30 cm2
(B) 85 cm2
(C) 65 cm2
(D) 45 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 * 24/2 = 30 cm2
Answer:A
Answer: (A) 30 cm2
Question: What is the rate percent when the simple interest on Rs.9100 amount to Rs.455 in 3 Years?
(A) 3.7%
(B) 5.7%
(C) 6.7%
(D) 8.7%
(E) 9.7%
Rationale: 455 = (4100*3*R)/100
R = 3.7%
Answer: A
Answer: (A) 3.7%
Question: How many digits are in the number 50^8 × 8^3 × 11^2?
(A) 22
(B) 20
(C) 19
(D) 18
(E) 17
Rationale: calculate the Number of 0's through the powers of 10
50^8 × 8^3 × 11^2 = (5^2*2)^8*2^9*11^2 = 5^16*2^17*11^2 = 2*11^2*10^16 = 242*10^16
Hence we would have 16 trailing 0's and the three digits from 242
Total digits = 3 + 16 = 19
Correct Option: C
Answer: (C) 19
Question: . If the sides of two cubes are in the ratio 3: 1 the ratio of their total surface area is?
(A) 3:2
(B) 9:5
(C) 9:1
(D) 9:9
(E) 9:7
Rationale: Explanation:
a1 : a2 = 3 : 1
6 a12 : 6 a22 = 9: 1
Answer: Option C
Answer: (C) 9:1
Question: If mn > 0, which of the following must be negative?
(A) mn
(B) mn^2
(C) m/-n
(D) m/n
(E) m+n
Rationale: Given mn> 0 So both will be the positive integers. If both are positive, then A,B,D,E also positive.
Answer :C
Answer: (C) m/-n
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2 hours
(B) 9 hours
(C) 6 hours
(D) 3 hours
(E) 12 hours
Rationale: Explanation:
|-----------20--------------------|
50 40
D = 20
RS = 50 – 40 = 10
T = 20/10 = 2 hours
Answer: Option A
Answer: (A) 2 hours
Question: If the radius of a circle is increased by 20% then the area is increased by:
(A) 44
(B) 219
(C) 16
(D) 18
(E) 11
Rationale: Explanation:
Let say radius = πr2πr2 = π102π102 = 100π100π
New radius = 10 × 120% = 12
New area = π122π122 = 144π144π
Increment = 144π−100π100π×100144π−100π100π×100 = 44%
Answer: A
Answer: (A) 44
Question: A certain fruit stand sold apples for $0.70 each and guava for $0.50 each. If a customer purchased both apples and bananas from the stand for a total of $6.30, what total number of apples and bananas did the customer purchase ?
(A) 12
(B) 13
(C) 11
(D) 14
(E) 5
Rationale: Some multiple of 7 + Some multiple of 5 should yield 63. To get to a some multiple of 5, we should ensure that a 3 or 8 (5+3) should be a multiple of 7.
63 is a direct multiple of 7, however in this case there won't be any guava. Hence the next option is to look for a multiple of 7 that has 8 as the unit digit. 28 satisfies this hence no. of apples is 4 and no of bananas is 7 .
C
Answer: (C) 11
Question: Cathy and Jim begin running at the same time and they start at the same place on a straight path. Cathy runs at 10 miles per hour, and Jim runs at 6 miles per hour. After 18 minutes, Cathy stops to stretch. If it takes Cathy 27 minutes to stretch and Jim continues to run during this time, how many minutes will it take Cathy to catch up to Jim?
(A) 20.5
(B) 21.5
(C) 22.5
(D) 23.5
(E) 24.5
Rationale: In 18 minutes, Cathy runs 3 miles.
In 45 minutes, Jim runs 4.5 miles.
Cathy can catch Jim at a rate of 4 miles per hour.
Since Jim is ahead by 1.5 miles, it will take Cathy 1.5 / 4 hours = 22.5 minutes to catch Jim.
The answer is C.
Answer: (C) 22.5
Question: A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 600 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day?
(A) 2880.
(B) 4320.
(C) 5780.
(D) 5760.
(E) 6380.
Rationale: Efficiency per machine = 600 watt/hr
Efficiency due to increase in wind speed = 600*120% => 720 watt/hr
Production by each machine in 2 hours is 720*2 => 1440 watt
Production by 3 machines => 1440 watt * 3 = 4320 watt
Answer will be (B)
Answer: (B) 4320.
Question: A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:
(A) 130
(B) 360
(C) 500
(D) 540
(E) 580
Rationale: L = 800 m
S = 78kmph = 65/3 mps
Time to pass tunnel = 1min = 60 sec
t.f (800+X)/(60) = (65/3)
=500
ANSWER:C
Answer: (C) 500
Question: Find the sum of all 2 digit numbers divisible by 3.
(A) 99
(B) 199
(C) 1665
(D) 2452
(E) 2547
Rationale: All 2 digit numbers divisible by 3 are :
12, 51, 18, 21, ..., 99.
This is an A.P. with a = 12 and d = 3.
Let it contain n terms. Then,
12 + (n - 1) x 3 = 99 or n = 30.
Required sum = 30 x (12+99) = 1665.
ANSWER C 1665
Answer: (C) 1665
Question: The speed of a boat in still water is 60kmph and the speed of the current is 40kmph. Find the speed downstream and upstream?
(A) 87 kmph
(B) 40 kmph
(C) 16 kmph
(D) 20 kmph
(E) 18 kmph kmph
Rationale: Speed downstream = 60 + 40
= 100 kmph
Speed upstream = 60 - 40
= 20 kmph
Answer:D
Answer: (D) 20 kmph
Question: 49 Ã— 49 = 7^?
(A) 4
(B) 7
(C) 8
(D) 16
(E) None of these
Rationale: 49 Ã— 49 = 7?
or, 7(2) Ã— 7(2) = 7?
or 7(4) = 7? or, ? = 4
Answer A
Answer: (A) 4
Question: If pipe A can fill the tank in 45 minutes and pipe B in 30 minutes, find the time to fill the tank if both the pipes are opened together.
(A) 12 minutes
(B) 20 minutes
(C) 18 minutes
(D) 15 minutes
(E) None of these
Rationale: Explanation:
In 1 minute pipe A can fill 1/45th part of the tank and pipe B can fill 1/30th part of the tank. If they are opened simultaneously then in 1 minute they can fill (1/45
+ 1/30) part of the tank = 1/18th part of the tank.
Hence, in 18 minutes the tank gets filled if pipes A & B are opened together.
ANSWER C
Answer: (C) 18 minutes
Question: The average of 5 quantities is 11. The average of 3 of them is 4. What is the average of remaining 2 numbers?
(A) 21.5
(B) 10.6
(C) 8
(D) 9.5
(E) None of these
Rationale: ANSWER: A
(5x11-3x4)/2=21.5
Answer: (A) 21.5
Question: How many cubes of 5cm edge can be cut out of a cube of 15cm edge
(A) 36
(B) 232
(C) 27
(D) 48
(E) None of these
Rationale: Explanation:
number of cubes=(15 x 15 x 15) / (5 x 5 x 5) = 27
Answer: C
Answer: (C) 27
Question: Sum of the squares of three numbers is 431 and the sum of their products taken two at a time is 265. Find the sum?
(A) 32
(B) 35
(C) 25
(D) 31
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 431 + 2* 265
a + b + c = √961 = 31
D
Answer: (D) 31
Question: In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 63 as quotient. What is the correct quotient ?
(A) 0
(B) 36
(C) 13
(D) 20
(E) 25
Rationale: 12*63=756
756%21=36
ANSWER:B
Answer: (B) 36
Question: Suresh drives his car to a place 150 km away at an average speed of 50 km/hr and returns at 30 km/hr. What is his average speed for the whole journey ?
(A) 32.5 km/hr
(B) 35 km/hr
(C) 37.5 km/hr
(D) 40 km/hr
(E) 42 km/hr
Rationale: Explanation:
If a car covers a certain distance at x kmph and an equal distance at y kmph. Then,
average speed of the whole journey = 2xy/x+y kmph.
Therefore, average speed
=2×50×30/50+30=2×50×30/80
=2×50×3/8=50×3/4
=25×3/2=75/2=37.5
Answer: Option C
Answer: (C) 37.5 km/hr
Question: The average height of 30 students in a class was calculated as 175 cm. It has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 136 cm. What was the actual average height of the students in the class?
(A) 174.5
(B) 173.5
(C) 172.5
(D) 171.5
(E) 170.5
Rationale: The total height was 15 cm too much.
The average height should be reduced by 15 cm/30 = 0.5 cm
The answer is A.
Answer: (A) 174.5