mathewhe/aqua_rat huggingface dataset:
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
(A) 81000
(B) 33888
(C) 77678
(D) 200988
(E) 228881
Rationale: 64000* 9/8 * 9/8
= 81000
Answer: A
Answer: (A) 81000
Question: The average age of a group of n people is 14 years old. One more person aged 32 joins the group and the new average is 16 years old. What is the value of n?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 14n + 32 = 16(n+1)
2n = 16
n = 8
The answer is D.
Answer: (D) 8
Question: What should be added to 5021 so that it may become a perfect square?
(A) 20
(B) 23
(C) 26
(D) 27
(E) 29
Rationale: 71x71=5041
5041-5021 = 20
If added to 20 get perfect square
answer =A
Answer: (A) 20
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. Circle C has a center at (0, 1) and a radius of 2. Some points, such as the center (0, 1), are inside the circle, but a point such as (0, 3) is on the circle but not in the circle. How many lattice points are in circle C?
(A) 9
(B) 27
(C) 2
(D) 15
(E) 7
Rationale: The lattice points that are in the circle, that lie on the x and y axes, are (0, 1), (0, 2), (0, 0), (1, 1), and (-1, 1). The lattice points in the circle and not on the x and y axes are (-1, 0), (-1, 2), (1, 0), and (-1, 2).
There are a total of 9 lattice points in the circle.
Answer: A
Answer: (A) 9
Question: If x percent of 400 is 20 percent of 700, then x =
(A) 200
(B) 350
(C) 700
(D) 400
(E) 1,400
Rationale: x/100(400) = 2/10(700)
x = 400.
Option D.
Answer: (D) 400
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 2
(B) 1
(C) 7
(D) 6
(E) 4
Rationale: 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer:C
Answer: (C) 7
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 90 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 12 sec
(B) 24 sec
(C) 30 sec
(D) 60 sec
(E) 62 sec
Rationale: Relative speed = 90 + 30 = 120 km/hr.
120 * 5/18 = 100/3 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 3/100 = 30 sec.
ANSWER:C
Answer: (C) 30 sec
Question: In a rectangular coordinate system, what is the area of a rectangle whose vertices have the coordinates (-5, 1), (1, 1), (1, -4) and (-5, -4)?
(A) 20
(B) 30
(C) 40
(D) 55
(E) 48
Rationale: Length of side 1= 5+1=6
Length of side 2= 4+1= 5
Area of rectangle= 6*5= 30
B is the answer
Answer: (B) 30
Question: John buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.
(A) Rs. 6876.10
(B) Rs. 4500
(C) Rs. 4600
(D) Rs. 3400
(E) Rs. 7500
Rationale: Rebate = 6% of Rs. 6650 = Rs. 6 x 6650 = Rs. 399.
100
Sales tax = 10% of Rs. (6650 - 399) = Rs. 10 x 6251
= Rs. 625.10
100
Final amount = Rs. (6251 + 625.10) = Rs. 6876.10
correct answer - A
Answer: (A) Rs. 6876.10
Question: If x is to be chosen at random from the set {1, 2, 3} and y is to be chosen at random from the set {5, 6, 7}, what is the probability that xy will be even?
(A)  1/6
(B)  1/3
(C)  1/2
(D)  2/3
(E)  5/6
Rationale: Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 5/6.
Answer: E.
Answer: (E)  5/6
Question: In a fort, there are 1200 soldiers. If each soldier consumes 3 kg per day, the provisions available in the fort will last for 30 days. If some more soldiers join, the provisions available will last for 25 days given each soldier consumes 2.5 kg per day. Find the number of soldiers joining the fort in that case?
(A) 676
(B) 528
(C) 758
(D) 454
(E) 546
Rationale: Assume x soldiers join the fort. 1200 soldiers have provision for 1200 (days for which provisions last them)(rate of consumption of each soldier)
= (1200)(30)(3) kg.
Also provisions available for (1200 + x) soldiers is (1200 + x)(25)(2.5) k
As the same provisions are available
=> (1200)(30)(3) = (1200 + x)(25)(2.5)
x = [(1200)(30)(3)] / (25)(2.5) - 1200 => x =528.
Answer:B
Answer: (B) 528
Question: Look at this series: 72, 76, 73, 77, 74, __, 75, ... What number should fill the blank?
(A) 70
(B) 71
(C) 75
(D) 78
(E) 74
Rationale: There will be 2 series
1st: 72 73 74 75 76 (Increasing by 1)
2nd: 76 77 78 79 (Increasing by 1)
Final: 72 76 73 77 74 78 75
ANSWER:D
Answer: (D) 78
Question: A 250 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230m
(B) 240m
(C) 250m
(D) 260m
(E) 270m
Rationale: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 250 + x
therefore, D= speed*time
thus 250 + x = 500/9 * 9
x= 500-250=250 m
ANSWER:C
Answer: (C) 250m
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 22
(B) 37
(C) 10
(D) 28
(E) 27
Rationale: speed of the bus excluding stoppages = 54 kmph
speed of the bus including stoppages = 45 kmph
Loss in speed when including stoppages = 54 - 45 = 9kmph
=> In 1 hour, bus covers 9 km less due to stoppages
Hence, time that the bus stop per hour = time taken to cover 9 km
=distancespeed=954 hour=16 hour = 606 min=10 min
Answer :C
Answer: (C) 10
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?+ 1611 + 647 equals
(A) 1261
(B) 3729
(C) 2737
(D) 1278
(E) 1276
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer: A
Answer: (A) 1261
Question: In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is
(A) 1 km/hr.
(B) 5 km/hr.
(C) 3 km/hr.
(D) 8 km/hr.
(E) 12 km/hr.
Rationale: Let Abhay's speed be x km/hr.
Then,	30/x	- 30/2 x= 3
6x = 30
x = 5 km/hr.
answer :B
Answer: (B) 5 km/hr.
Question: Given a certain number (x), find x given that 5.76 is 12% of 40% of x?
(A) 130
(B) 120
(C) 140
(D) 100
(E) 300
Rationale: Using elimination method to pick the correct option it will be discovered that option B i.e 120 is the correct option because 40% of 120 is 48 and 12% of 48 is 5.76.
ANSWER:B
Answer: (B) 120
Question: In what ratio tea of Rs.80 per kg be mixed with 12kg tea of Rs.64 per kg, so thai cost price of mixture is Rs.74 per kg?
(A) 3:5
(B) 5:3
(C) 2:5
(D) 2:3
(E) None of the above
Rationale: If 'x' kg of tea costing Rs. 80/kg is mixed with 12 kg costing Rs. 64/kg, then
Cost price of mixture= (x*80 + 12*64) /(x+12) =74 , 80x+768 =74x+888 ,x=20
Ratio of tea mixed=20/12=5/3
ANSWER:B
Answer: (B) 5:3
Question: At Rahul's party, there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?
(A) 384
(B) 258
(C) 216
(D) 120
(E) 72
Rationale: we have to work on the info and understand what that info takes us to...
1) there were five times as many females as males At Rahul's party,..
this means F=5M.. so total number=6M..
2) There were three times as many adults as children..
A=3C...
or total = 4C..
so the total is 4C or 6M..
since C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6..
or Total is multiple of LCM of 4,6..
LCM of 4,6= 12..
lets see which number is not multiple of 12..
A. 384...12*32
B. 258... no
C. 216....12*18
D. 120....12*10
E. 72......12*6..
so B is our answer..
Answer: (B) 258
Question: A train 135 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 13 km/hr
(B) 53.6 km/hr
(C) 17 km/hr
(D) 18 km/hr
(E) 12 km/hr
Rationale: Speed of the train relative to man = (125/10) m/sec
= (13.5) m/sec. [(13.5) * (18/5)] km/hr
= 48.6 km/hr. Let the speed of the train be x km/hr. Then, relative speed
= (x - 5) km/hr. x - 5 = 48.6 ==> x
= 53.6 km/hr.
Answer:B
Answer: (B) 53.6 km/hr
Question: 6 boysand 8 girls can do job in 10 days ,26 boys & 48 women do work in 2 days find time taken by 15 boys and 20 girls to do same work
(A) 4 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 8 days
Rationale: 6b+8g=1/10(1 day work) ------>(I)
26b+48w=1/2 -------->(II)
Divide both sides by 2 in (I) and multiply both sides by 5
now we get
15b+20b=1/4
so ans. is 4 days.
ANSWER:A
Answer: (A) 4 days
Question: A cubical block of metal weighs 4 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
(A) 48
(B) 32
(C) 24
(D) 18
(E) 12
Rationale: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 4 pounds
If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 4 pounds = 32 pounds
So answer is B
And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3
we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
4 * 8 = 32
So answer is B
Answer: (B) 32
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 9%
(C) 15%
(D) 6%
(E) 10%
Rationale: Explanation:
1500 ---- 270
100 ---- ? => 18%
ANSWER IS A
Answer: (A) 18%
Question: Which number need to add to 956734 to get a number exactly divisible by 412?
(A) 345
(B) 342
(C) 343
(D) 342
(E) 341
Rationale: 956734 / 412 = 2322 and reminder = 70.
412-70 = 342
So, the next number divisible by 412 is 342 places in front of 956734
Which means 342 + 956734 =957076
342 should be added to 956734
B
Answer: (B) 342
Question: If x is a number such that x^2 + 4x - 5 = 0 and x^2 - 5x + 4 = 0, then x =
(A) 5
(B) 4
(C) 1
(D) -4
(E) -5
Rationale: x^2 + 4x - 5 = (x+5)(x-1) = 0
Then x=-5 or x=1.
x^2 - 5x + 4 = (x-4)(x-1) = 0
Then x=4 or x=1.
Thus x=1.
The answer is C.
Answer: (C) 1
Question: There is a square with side ‘a’ and one octagon is inscribed in it. What will be perimeter of octagon.
(A) 8a/3
(B) 7a/3
(C) 5a/3
(D) a/3
(E) 11a/3
Rationale: Well if it's a regular octagon then it actually trisects each side of the square in which 1/3 of the lenght of the side of the square is the length of one side of the octagon. If any one has a doubt he can draw the figure and see it
Going this way lenght of a side of a octagon is a/3 and thus perimeter would be 8a/3.
ANSWER:A
Answer: (A) 8a/3
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
(A) 377
(B) 480
(C) 281
(D) 267
(E) 288
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer: D
Answer: (D) 267
Question: Find the number of factors T of 180 that are in the form (4*k + 2), where k is a non-negative integer?
(A) 1
(B) 2
(C) 3
(D) 4
(E) T=6
Rationale: As for the question, the most straightforward way is to list out the factors (this is fine for this question as 180 is a relatively small number). Number of factors of 180 T(=2^2*3^2*5) = 18. So listing the factors gives us:
1, 180
2, 90
3, 60
4, 45
5, 36
6, 30
9, 20
10, 18
12, 15
As the question asks us about the factors of the form 4k+2 ---> eliminate all ODD factors. You are now left with
2,4,6,10,12,18,20,30,36,60,90,180
For the form 4k+2, the first few values are 2, 6, 10, 14, 18, 22, 26, 30 ... already giving you 5 factors (=2,6,10,18,30). You can stop here and mark 6 (6th one = 90) as the correct answer as 5 is not given.
For checking any particular factor whether they conform to the form 4k+2---> do the following
4k+2 = 36 ---> 4k = 34 --> this will NOT give you an integer value for k ---> reject. Proceed with others until you find all the values asked.
E is thus the correct answer.
Answer: (E) T=6
Question: If a is an integer from 1 to 96, what is the probability for a*(a+1)*(a+2) being divisible by 8?
(A) a. 25%
(B) b. 50%
(C) c. 62.5%
(D) d. 72.5%
(E) e. 75%
Rationale: There is another way I approach such questions if I am short of time (otherwise I prefer the logical approach given above) - Brute Force/ Pattern Recognition/Intuition - whatever you may want to call it.
We need to find the numbers in which the product is a multiple of 8. I know I get a multiple of 8 after every 8 numbers. I will also get an 8 when I multiply 4 by an even number. In first 8 numbers, I have exactly two multiples of 4.
Basically, I figure that I should look at the first 8 cases. In all other cases, the pattern will be repeated. It helps that n can be from 1 to 96 i.e. a multiple of 8:
1*2*3 N
2*3*4 Y
3*4*5 N
4*5*6 Y
5*6*7 N
6*7*8 Y
7*8*9 Y
8*9*10 Y
5 of the first 8 products are divisible by 8 so my answer would be 5/8 = 62.5% C
Answer: (C) c. 62.5%
Question: The total age of A and B is 15 years more than the total age of B and C. C is how many years younger than A?
(A) 12
(B) 15
(C) C is elder than A
(D) Data inadequate
(E) None
Rationale: Solution
[(A+B) - (B+C)]	= 15
â€¹=â€ºA - C
= 15.
Answer B
Answer: (B) 15
Question: The arithmetic mean of the scores of a group of students in a test was 80. 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) A)101.4.
(B) B)111.7
(C) C)102.27
(D) D)115.1
(E) E)121.2
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 80 * 100
= 1600 + 775 + 55x = 8000
= 55x = 5625
= x = 102.27
Answer:C
Answer: (C) C)102.27
Question: You keep tossing a fair coin for twenty times. Each time, the coin lands up with tails up.
What is the probability that if you toss it now, the coin will land with heads up this time?
(A) 30%
(B) 50%
(C) 78%
(D) 72%
(E) 91%
Rationale: B
50%
The probability will be 50% only as it always was. The next flip of coin is not dependent on what the results were in the previous flips.
Answer: (B) 50%
Question: The length of the bridge, which a train 150 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 270 m
Rationale: Let the length of the bridge:L
The equation now is L+150/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =225m
ANSWER:B
Answer: (B) 225 m
Question: A gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same. If there are 7 rows or 6 rows or 4 rows, then no tree will be left. Find the least number of trees required
(A) 22
(B) 84
(C) 28
(D) 76
(E) 21
Rationale: Explanation:
The least number of trees that are required = LCM(7,6,4) = 84.
Answer: B
Answer: (B) 84
Question: A woman buys an article for 10% less than its value and sells it for 10% more than its value. His gain or loss percent is:
(A) 12%
(B) 45%
(C) 20%
(D) 34%
(E) 78%
Rationale: C
Let the article be worth Rs. x.
C.P. 90% of Rs. x = Rs. 9x/10
S.P. = 110% of Rs. x = Rs. 11x/10
Gain = (11x/10 - 9x/10) = Rs. x/5
Gain % = x/5 * 10/9x * 100 = 22 2/9 % > 20%
Answer: (C) 20%
Question: The arithmetic mean of the set S = {8, K, 7, 13, M, 8} is 9. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
(A) 7
(B) 7.5
(C) 8
(D) 8.5
(E) 9
Rationale: The sum of the numbers is 6*9 = 54
K+M = 54 - 13 - 8 - 8 - 7 = 18
Since K ≠ M, K and M do not equal 9.
Thus one of the two numbers is 8 or less and one is 10 or more.
Then middle two numbers in the set are 8 and 8.
The median is 8.
The answer is C.
Answer: (C) 8
Question: In an election, candidate X got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate?
(A) 280000
(B) 300000
(C) 355000
(D) 356000
(E) 357000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate X = 75 %
Therefore, the number of valid votes polled in favour of candidate X = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
E)
Answer: (E) 357000
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 6 kmph, then the speed of
the boat in still water is
(A) 12 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) None of these
Rationale: Explanation:
Rate upstream = (7/42)*60 kmh = 10 kmph.
Speed of stream = 6 kmph.
Let speed in still water is x km/hr
Then, speed upstream = (x ï¿½6) km/hr.
x-6 = 10 or x = 16 kmph
Answer: E
Answer: (E) None of these
Question: A person is traveling at 40 km/hr and reached his destiny in 6 hr then find the distance?
(A) 260 km
(B) 240 km
(C) 280 km
(D) 340 km
(E) 350 km
Rationale: T = 6 hrs
D= T*S = 40*6 = 240 km
Answer is B
Answer: (B) 240 km
Question: How many odd and even numbers are there between 42 and 400?? Find the sum of odd numbers and the sum of even numbers!
(A) 2
(B) 8
(C) 27
(D) 9
(E) 21
Rationale: Answer:D
Answer: (D) 9
Question: How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
(A) 4787
(B) 2876
(C) 2876
(D) 5040
(E) 1082
Rationale: 'LOGARITHMS' contains 10 different letters.
Required number of words = Number of arrangements of 10 letters, taking 4 at a time.
=10P_4
= 5040.
Answer: D
Answer: (D) 5040
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
(A) 33
(B) 12
(C) 66
(D) 77
(E) 88
Rationale: 63 + 83 + 103 = a3 => a
= 12
Answer: B
Answer: (B) 12
Question: Dick and Jane each saved $3,000 in 1989. In 1990 Dick saved 8 percent more than in 1989, and together he and Jane saved a total of $5,000. Approximately what percent less did Jane save in 1990 than in 1989?
(A) 8%
(B) 25%
(C) 41%
(D) 59%
(E) 70%
Rationale: Dick saved = $ 3240
Jane saved = $ 1760 (jane saved $1240 less than she did the prior year)
Jane saved approximately $1240/$3000 (close to 41%) less in 1990
Answer: C
Answer: (C) 41%
Question: A candidate got 10% of the votes polled and he lost to his rival by 16000 votes. How many votes were cast?
(A) 7500
(B) 20000
(C) 2775
(D) 5496
(E) 6851
Rationale: 10%-----------L
90%-----------W
------------------
80%----------16000
100%---------? => 20000
Answer:B
Answer: (B) 20000
Question: In a certain pond, 80 fish were caught, tagged, and returned to the pond. A few days later, 50 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A) 400
(B) 625
(C) 1,250
(D) 2,000
(E) 10,000
Rationale: This is a rather straight forward ratio problem.
1. 80 fish tagged
2. 2 out of the 50 fish caught were tagged thus 2/50
2/50=80/x
thus, x=2000
Think of the analogy: 2 fish is to 50 Fish as 50 fish is to ...?
You've tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch.
D
Answer: (D) 2,000
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
42.
(A) 7-19
(B) 8-20
(C) 10-16
(D) 11-31
(E) 20-6
Rationale: We are looking for two numbers.
#1 - x
#2 - 3x â€“ 2
The sum is 42. #1 + #2 = 42
Substituting x + 3x â€“ 2 = 42
4x â€“ 2 = 42
4x = 44
x = 11
The first number is 11, the second number is two less than three times 11 or 31.
correct answer D
Answer: (D) 11-31
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(8.3) + E(–8.7) + o(–7.3) + e(6.6) is:
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: O(8.3) + E(–8.7) + o(–7.3) + e(6.6) = 9 + (-8) + (-9) + 6 = -2
The answer is A.
Answer: (A) -2
Question: Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 8 hours. How long would it take for both hoses to fill up two-thirds of the pool?
(A) 5/12 hours
(B) 5/8 hours
(C) 8/5 hours
(D) 16/7 hours
(E) 12/5 hours
Rationale: Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6
Hose 2 would fill the pool alone in 8 hours
i.e. 1 Hour work of Hose 2 = 1/8
i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/8) = (7/24)
i.e. (7/24) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(24/7)*(2/3) = 16/7 hour
Answer: Option D
Answer: (D) 16/7 hours
Question: A room is 20 meters long, 15 meters wide 10 meters in height. The longest possible rod which can be placed in the room is
(A) 25.93 meters
(B) 26.93 meters
(C) 24.93 meters
(D) 24.5 meters
(E) 24.75 meters
Rationale: Square root of 20^2+15^2+10^2...(Diognal) which is square root of 725 that lies 26<√725<27. Hence the answer should be B
Answer: (B) 26.93 meters
Question: Find the odd man out. 49, 65, 81, 144, 169, 225, 441
(A) 49
(B) 65
(C) 81
(D) 144
(E) 169
Rationale: Explanation :
Each of the given numbers except 65 is a perfect square
Answer : Option B
Answer: (B) 65
Question: Three bells commence tolling together and toll at intervals of 1, 3 and 5 seconds respectively. In 10 minutes, how many times do they toll together ?
(A) 39
(B) 40
(C) 41
(D) 42
(E) 43
Rationale: LCM of 1, 3 and 5 is 15.
So, after each 15 seconds, they would toll together.
Hence, in 10 minutes, they would toll 10*60 seconds / 15 seconds = 40 times
But then the question says they commence tolling together. So, they basically also toll at thebeginning(0second).
So, total tolls together = 40+1 = 41
Answer C
Answer: (C) 41
Question: The true-discount on Rs.2480 due after a certain period at 5% is Rs.80. Find the
due period.
(A) 6months
(B) 5months
(C) 8months
(D) 3months
(E) None of these
Rationale: Explanation:
P.W= Amount – (T.D)
Time = 100xTD/PWx R
Answer: C
Answer: (C) 8months
Question: In the coordinate plane a slope of the line K is 4 times the x-intercept of the line K. What is the y-intercept of the line K?
(A) -4
(B) 4
(C) -1/4
(D) 1/4
(E) 2
Rationale: As 4y=mx+c, from 4y=0m+m we get y=1/4. Hence, the correct answer choice is D.
Answer: (D) 1/4
Question: If a certain number X is divided by 82, the reminder is 5. what is the reminder when X+7 is divided by 41?
(A) 12
(B) 5
(C) 6
(D) 16
(E) 18
Rationale: X can be written as 82K + 5 or X = 5,87,169,etc. when K =0,1,2 etc
X + 7 = 82K + 5+7= 82K +12 or X +7 = 12,94, 176 etc. k=0,1,2
When divided by 41, we will get the remainder 12.
A
Answer: (A) 12
Question: David invested certain amount in three different schemes A, B and C with the rate of interest 10% p.a., 12% p.a. and 15% p.a. respectively. If the the total interest accrued in one year was 3200 and the amount invested in Scheme C was 150% of the amount invested in Scheme A and 240% of the amount invested in Scheme B, what was the amount invested in Scheme B?
(A) 5000
(B) 6500
(C) 8000
(D) cannot be determined
(E) None of these
Rationale: Let x, y and z be the amounts invested in schemes A, B and C respectively. Then,
(x×10×1/100)+(y×12×1/100)+(z×15×1/100)=3200
⇒ 10x + 12y + 15z = 320000 ..... (i)
Now, z = 240% of y = 12⁄5y..... (ii)
And, z = 150% of x = 3⁄2x
⇒ x = 2⁄3z = (2⁄3 × 12⁄5)y = 8⁄5y......(iii)
From (i),(ii) and (iii), we have :
16y + 12y + 36y = 320000 ⇒ 64y = 320000 ⇒ y = 5000.
∴ Sum invested in Scheme B = 5000.
Answer A
Answer: (A) 5000
Question: A train 240 m long, running with a speed of 108 km/hr will pass a tree in?
(A) 8 sec
(B) 16 sec
(C) 18 sec
(D) 14 sec
(E) 12 sec
Rationale: Speed = 108 * 5/18
= 30 m/sec
Time taken = 240 * 1/30
= 8 sec
Answer: A
Answer: (A) 8 sec