mathewhe/aqua_rat huggingface dataset:
Question: Average of all prime numbers between 20 to 50
(A) 37
(B) 37.8
(C) 39
(D) 39.8
(E) 35.8
Rationale: Explanation:
Prime numbers between 20 and 50 are:
23, 29, 31, 37, 41, 43, 47
Average of prime numbers between 20 to 50 will be
(23+29+31+37+41+43+47 / 7)=251 / 7=35.8
Option E
Answer: (E) 35.8
Question: If the number 52,1n9, where n represents the tens digit, is a multiple of 3, then the value of n could be which of the following?
(A) 6
(B) 5
(C) 3
(D) 1
(E) 0
Rationale: Maybe you are misreading the question but it is saying that 52,1n9 is a multiple of 3 and not necessarily n is a multiple of 3.
The sum of the digits 5 + 2 + 1 + n + 9 must be a multiple of 3
17 + n must be a multiple of 3
substituting the numbers n must = 1
ANSWER:D
Answer: (D) 1
Question: A train 500 m long passed a pole in 50 sec. How long will it take to pass a platform 1000 m long?
(A) 28 sec
(B) 89 sec
(C) 85 sec
(D) 150 sec
(E) 15 sec
Rationale: Speed = 500/50 = 10 m/sec.
Required time = (500 + 1000)/10
= 150 sec.
Answer:D
Answer: (D) 150 sec
Question: 24 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) None of these
(B) 552
(C) 512
(D) 524
(E) 542
Rationale: Explanation :
He can go in any bus out of the 24 buses.
Hence He can go in 24 ways.
Since he can not come back in the same bus that he used for travelling,
He can return in 23 ways.
Total number of ways = 24x 23 = 552. Answer : Option B
Answer: (B) 552
Question: A box contains 15 mangoes out of which 8 are spoilt. If eight mangoes are chosen at random, find the probability that A number is selected at random from first twenty natural numbers. What is the chance that it is a multiple of either 4 or 15?
(A) 17/10
(B) 1/10
(C) 7/10
(D) 1/5
(E) 3/10
Rationale: The probability that the number is a multiple of 4 is 5/20. (Since 4*5 = 20).
Similarly the probability that the number is a multiple of 15 is 1/20. {Since 15*1 =
15).
Neither 4 nor 15 has common multiple from 1 to 20. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 4 or 15 is (5+1)/20 = 3/10.
ANSWER:E
Answer: (E) 3/10
Question: If a is a positive integer, and if the units digit of a^2 is 9 and the units digit of (a+1)^2 is 4, what is the units digit of (a+2)^2?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 14
Rationale: For unit digit of a^2 to be 9...unit digit of a has to be 3 or 7...
Now for unit digit of (a+1)^2 to be 4..unit digit of a has to be 1 or 7....
From the above two conditions, unit value of a has to be 7, which will satisfy both the conditions...
Now id unit digit of a is 7, unit digit of (a+2)^2 hast to be 1.
ANSWER:A
Answer: (A) 1
Question: Simplify: 3005-3000+10
(A) 2505
(B) 2509
(C) 2705
(D) 2508
(E) None of them
Rationale: 3005-3000+10
=3005-(3000/10)
=3005-300
=2705.
Answer is C
Answer: (C) 2705
Question: Mixture A is 40 percent alcohol, and mixture B is 80 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 50 percent alcohol, approximately how many gallons of mixture A are in the mixture?
(A) 1.5
(B) 1.7
(C) 2.3
(D) 2.5
(E) 2.4
Rationale: (80-50)/(50-40) = Qa/Qb
30/10 = Qa/Qb
3/1 = Qa/Qb
Qa = (3/5) * 4 = 12/5 = 2.4 approx
Answer : E
Answer: (E) 2.4
Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:
(A) 10
(B) 100
(C) 50
(D) 200
(E) 300
Rationale: 2 kmph =	(2 x	5/18	)m/sec =	5/9	m/sec.
4 kmph =	(4 x	5/18	)m/sec =	10/9	m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then,(x/y -5/9)= 9 and(x/y -10/9)= 10.
9y - 5 = x and 10(9y - 10) = 9x
=> 9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50.
Therefore Length of the train is 50 m.
Answer: C
Answer: (C) 50
Question: In how many different ways can the letters of the word 'RUMOUR' be arranged ?
(A) 90
(B) 270
(C) 350
(D) 790
(E) 180
Rationale: The word 'RUMOUR' contains 6 letters, namely 2R, 2U, 1M and 1U.
∴ Required number of ways = 6!/(2!)(2!)(1!)(1!) = 180.
Answer is E
Answer: (E) 180
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer: B
Answer: (B) 6
Question: Group A has 3 boys and 2 girls, group B has 4 boys and 4 girls and group C has 3 boys and 3 girls. One student is selected from each of the group. Find the probability that one girl and two boys are among the three selected?
(A) 2/5
(B) 1/18
(C) 9/5
(D) 2/3
(E) 77/272
Rationale: Group A has 3 boys and 2 girls; 5
Group B has 4 boys and 4 girls; 8
Group C has 3 boys and 3 girls. 6
Selected group should have one girl and two boys.
Girl from A, boy from B, boy from C: 2/5*4/8*3/6 = 1/10;
Boy from A, girl from B, boy from C: 3/5*4/8*3/6 = 3/20;
Boy from A, boy from B, girl from C: 3/5*4/8*3/6 = 6/40.
Sum = 1/10 + 3/20 + 6/40 = 2/5.
Answer: A.
Answer: (A) 2/5
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 50 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
(A) a. 43
(B) b. 45
(C) c. 75
(D) d. 68
(E) e. 60
Rationale: 50 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (50 * 12.5 * 100) / (2.5 * 200)
thus, X = 125
Thus, more men needed to finish the task = 125-50=75
hence Answer is C
Answer: (C) c. 75
Question: A 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 300m
(B) 278m
(C) 350m
(D) 228m
(E) 282m
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 36
= 50/3
3(x + 300)
= 1800 è x
= 300m.
Answer:A
Answer: (A) 300m
Question: A shopping cart contains only apples, oranges, and pears. If there are twice as many oranges as apples, and four times as many pears as oranges, then the apples are equivalent to what fraction of the pears?
(A) 1/6
(B) 1/8
(C) 2/3
(D) 1/3
(E) 1/4
Rationale: O = 2A
P = 4O = 8A
A = P/8
The answer is B.
Answer: (B) 1/8
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
(A) 15√2 cm
(B) 13√2 cm
(C) 16√2 cm
(D) 17√2 cm
(E) 18√2 cm
Rationale: 4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
ANSWER:B
Answer: (B) 13√2 cm
Question: How many positive integers except zero that are less than 10,000 can be formed using the digits 0, 1, 2, 3, 4, 6, 78?
(A) 5000
(B) 4096
(C) 6560
(D) 4095
(E) 8000
Rationale: According to what i have read - it is always better to assume natural numbers beginning from 01 onward (for the gmat) unless otherwise stated. Assuming that to be the case we can sub divide the problem into :
A) Four digit Numbers : _ _ _ _ , The ones place - hundreds place can be filled by any one of the 8 numbers given (the problem speaks nothing about NOT REPEATING the numbers so we have to assume that they can be repeated) the thousands place can be filled by any number except0.. This gives us 7 x 8 x 8 x 8 = 3584
B) Three digit Numbers : _ _ _ , The ones place - tens Place can be filled by any one of the 8 numbers given ( the problem speaks nothing about NOT REPEATING the numbers so we have to assume that they can be repeated) , the hundreds place can be filled by only 7 of the given 8 numbers (If we use0we will end up with a two digit number ). This gives us 7 x 8 x 8 = 448
C) Two digit numbers : _ _ , The ones place can be filled up by any one of the 8 numbers given , and the tens place by any 7 of the 8 ... This gives us 7 x 8 = 56
D) Assuming that zero is not a natural number , we have seven different possibilities for the one digit numbers . 7
Add A + B + C + D , This gives us 3584 + 448 + 56 + 7 = 4095 (D)
Now let us assume that ZERO is a NATURAL number (as some mathematicians do) ... A thru C is not effected by this assumption as the resultant would have meant that a four number digit with a zero at the beginning would have effectively made it a three digit no. , and a 0 to begin a three digit number would make it a two digit number etc ... The only difference including ZERO to be a natural number would have made for D , in that it would have given it 8 possibilities instead of 7 ... Which would have added 1 to our total making it 4096. Simply by looking at the answer choices we can determine that the test maker wanted natural numbers to begin from 1 and not from 0 ( as per the answer choices) ..
Answer: (D) 4095
Question: At a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint.Verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint.How many liters of yellow paint must be added to 28 liters of forest green to change it to Verdant green?
(A) 28/3
(B) 13/6
(C) 3
(D) 4
(E) 14/3
Rationale: 28 liter of Forset green have 16 liter of blue and 12 liter of yellow
Suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is
Blue/yellow =16/(12+x) = ¾
36+3x=64 => x =28/3
Answer : A
Answer: (A) 28/3
Question: A man can row his boat with the stream at 12 km/h and against the stream in 4 km/h. The man's rate is?
(A) 1 kmph
(B) 4 kmph
(C) 98 kmph
(D) 6 kmph
(E) 4 kmph
Rationale: DS = 12
S = ?
S = (12 - 4)/2 = 4 kmph
Answer: E
Answer: (E) 4 kmph
Question: Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
(A) 1/24
(B) 1/8
(C) 1/4
(D) 1 by 3
(E) 3/8
Rationale: The number of ways to put exactly one letter in the right envelope is not equal to 4C1. There are 4C1 ways to choose which letter goes in the right envelope, but you then need to work out how many ways the remaining letters can be placed in the wrong envelope. For the first of these three letters, there are 2 wrong envelopes you could choose. Now, you still have one letter left which has its matching envelope unused; you must put this letter in the wrong envelope, so you have only 1 choice for this letter, and finally for the last letter you have only 1 choice for where to put it. So you have 2*1*1 = 2 ways to assign the remaining letters incorrectly, which is why you need to multiply your answer by 2.
I posted a slightly different solution to BTG a while ago, which I'll paste here:
One letter goes in the right envelope. It doesn't matter which envelope this is- there are three envelopes left. 2/3 chance the next letter goes in the wrong envelope, 1/2 the next one does, and 100% the last one does- its envelope must have been used already.
(2/3)(1/2) = 1/3.
Slightly old post, but very interesting explanation...
Just would like to add my 2 cents:
For 1 letter to go in right envelope - probability = 1/4
For 2nd letter to go in wrong envelope - probability = 2/3
For 3rd letter to go in wrong envelope - probability = 1/2
For 4th letter to go in wrong envelope - probability = 1
Now, in the order this arrangement can be done:
C - Letter going into correct envelope
W - Letter going into wrong envelope
No#1. C - W - W - W
No#2. W - C - W - W
No#3. W - W - C - W
No#4. W - W - W - C
There are 4 ways, it can be done
So, probability of 1 letter going in correct envelope: 4* (1/4) * (2/3) * (1/2) * 1 =1/3 D
Answer: (D) 1 by 3
Question: a person has 12004 coins of silver. How much would he need to add so that he can distribute equally among his seven children in whole numbers?
(A) 1 coin
(B) 2 coins
(C) 3 coins
(D) 4 coins
(E) coins
Rationale: He would need to add one coin more so 12005 is fully divisible by 7 and each would get 1715 coins. So the correct answer is A
Answer: (A) 1 coin
Question: The average weight of a group of boys is 20 kg. After a boy of weight 36 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
(A) 12
(B) 15
(C) 18
(D) 24
(E) 10
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 20x
After the boy weighing 36 kg joins the group, total weight of boys = 20x + 36
So 20x + 36 = 21(x + 1) = > x = 15
ANSWER:B
Answer: (B) 15
Question: A student can select one of 7 different math book, one of 3 different chemistry book & one of 4 different science book.In how many different ways students can select book of math, chemistry & science.
(A) 22
(B) 84
(C) 99
(D) 37
(E) 01
Rationale: 7C1×3C1×4C1 = 7x3x4=84 ways
Answer:B
Answer: (B) 84
Question: Three printing presses, Q, S, and T, working together at their respective constant rates, can do a certain printing job in 4 hours. S and T, working together at their respective constant rates, can do the same job in 5 hours. How many hours would it take Q, working alone at its constant rate, to do the same job?
(A) 8
(B) 10
(C) 12
(D) 15
(E) 20
Rationale: =1/4-1/5=1/20
Q can do 1/20 job in 1 hour
Q can do the whole job in 20 hours=E
Answer: (E) 20
Question: In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?
(A) 3/8
(B) 7/16
(C) 2/7
(D) 9/16
(E) 5/7
Rationale: P(getting prize)=10/(10+25)
=10/35
=2/7
Option:C
Answer: (C) 2/7
Question: A cistern 4m long and 2 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
(A) 23 m2
(B) 20 m2
(C) 52 m2
(D) 24 m2
(E) 55 m2
Rationale: Area of the wet surface	= [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (2 x 1.25 + 4 x 1.25) + 4 x 2] m2
= 23 m2.
answer :A
Answer: (A) 23 m2
Question: Of the three- digit integers greater than 700, how many have two digits E that are equal to each other and the remaining digit different from the other two?
(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
Rationale: three-digit integers greater than 700: 701 to 999, inclusive.
possible values for hundreds-digit--> 7,8,9
possible values for tens-digit and ones-digit --> 0, 1,2,3,4,5,6,7,8,9
when hundreds-digit and tens-digit are the same: (3x1x10)-3=27 ---> we minus three to exclude 777, 888 and 999
when hundreds-digit and ones-digit are the same: (3x10x1)-3=27 ---> we minus three to exclude 777, 888 and 999
when tens-digit and hundreds-digit are the same:[(3x10x1)-3]-1=26 ---> we minus three to exclude 777, 888 and 999; we minus one to exclude 700
E=27+27+26 = 80
Answer: C
Answer: (C) 80
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 77 cm2
(B) 26 cm2
(C) 87 cm2
(D) 26 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 * 28/2 = 35 cm2
Answer: E
Answer: (E) 35 cm2
Question: The number which exceeds 16% of it by 21 is :
(A) 25
(B) 52
(C) 58
(D) 60
(E) 62
Rationale: Solution
Solution
Let the number be x.
x-16% of x =21
x-16/100x =21
x-4/25x=21
21/25x=21
x=(21x25/21)= 25
Answer A
Answer: (A) 25
Question: If 5 < x < 11 and y = x + 7, what is the greatest possible integer value of x + y?
(A) 26
(B) 27
(C) 28
(D) 29
(E) 30
Rationale: x+y = x+x+7 = 2x+7
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 10.5
Then x+y = 10.5 + 17.5 = 28.
The answer is C.
Answer: (C) 28
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 68 %
(B) 83.33%
(C) 59%
(D) 74.1%
(E) 69
Rationale: Explanation:
Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.
Answer:C
Answer: (C) 59%
Question: A person incurs a loss of 5% be selling a watch for Rs. 1140. At what price should the watch be sold to
earn 5% profit.
(A) Rs.1200
(B) Rs.1230
(C) Rs.1260
(D) Rs.1290
(E) None of these
Rationale: Explanation:
Let the new S.P. be x, then.
(100 - loss%):(1st S.P.) = (100 + gain%):(2nd S.P.)
=>(951140=105x)=>x=1260
Answer: C
Answer: (C) Rs.1260
Question: What is the next number in the sequence : 10,11,13,17,25,32,37,47, __?
(A) 59
(B) 53
(C) 51
(D) 58
(E) 52
Rationale: next no. = previous + (sum of digits)
10 + (1+0) = 11
11 + (1+1) = 13
13 + (1+3) = 17
17 + (1+7) = 25
25 + (2+5) = 32
32 + (3+2) = 37
37 +(3+7) = 47
47 + (4+7) = 58
ANSWER:D
Answer: (D) 58
Question: The length of a rectangle is increased by 25% and its breadth is decreased by 20%. What is the effect on its area?
(A) 10000
(B) 2777
(C) 2657
(D) 2876
(E) 2868
Rationale: 100 * 100 = 10000
125 * 80 = 10000
No change
Answer: A
Answer: (A) 10000
Question: John went to the Hospital at the speed of 60 km per hour while returning for his home he covered the half of the distance at the speed of 10 per hour, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest 1/2 of the distance at the speed of 30km per hour. The average speed of the John in the whole length of journey is?
(A) 16 km/hr
(B) 20 km/hr
(C) 24 km/hr
(D) 28 km/hr
(E) 29 km/hr
Rationale: Let distance between his home and hospital =
d
d km
Total distance travelled
=
d
+
d
=
2
d
=d+d=2d km
Total time taken
=
d
60
+
(
d
2
)
10
+
(
d
2
)
30
=d60+(d2)10+(d2)30
=
d
60
+
d
20
+
d
60
=
5
d
60
=
d
12
=d60+d20+d60=5d60=d12 hr
Average speed in the whole journey
=
2
d
(
d
12
)
=
2
d
×
12
d
=
24
=2d(d12)=2d×12d=24 km/hr
C
Answer: (C) 24 km/hr
Question: How many total number of ways in which x distinct objects can be put into two different boxes is
(A) n2
(B) 2x
(C) 2n
(D) 3n
(E) None of these
Rationale: Let the two boxes be B1 and B2. There are two choices for each of the x objects. So, the total number of ways is
2 × 2 ×.....× 2 (x times ) = 2x
Answer B
Answer: (B) 2x
Question: Two dice are rolled. The probability of getting a sum of at least 9 is
(A) 13/36
(B) 5/18
(C) 35/36
(D) 11/36
(E) 15/36
Rationale: Sum of 9 = {(3,6) (6,3)} = 2ways.
Sum of 10 = {(5,5) (6,4) (4,6) (5,5)} = 4 ways.
Sum of 11 = {(6,5) (5,6)} = 2 ways.
Sum of 12 = {(6,6) (6,6)} = 2 ways.
Therefore, Favourable cases = 10
Total cases = 6 x 6 = 36.
Therefore, Probability = 10/36 = 5/18.
ANSWER:B
Answer: (B) 5/18
Question: An unbiased die is tossed. Find the probability of getting a multiple of 3.
(A) 1/2
(B) 1/6
(C) 2/3
(D) 1/3
(E) 1/4
Rationale: here s= {1,2,3,4,5,6}
let E be the getting of a multiple of 3.
then E = {3,6}
probability = 2/6 = 1/3
correct option is D
Answer: (D) 1/3
Question: when i was of 2 years old, my sister's age was half of mine..
now i am of 100..
what is the age of my sister??
(A) 98
(B) 99
(C) 97
(D) 95
(E) 94
Rationale: 99,one less than me.
ANSWER:B
Answer: (B) 99
Question: At an international conference, “Red” world countries and “Blue” world countries are the only participants. The ratio of “Red” world participants to “Blue” world participants is 5:5. If one-third of “Red” world participants are left-handed and two-thirds of “Blue” world participants are left-handed, then what is the fraction of the participants who are left-handed?
(A) 1/4
(B) 1/8
(C) 1/6
(D) 1/2
(E) 1
Rationale: Red: Blue = 5:5
Let Red = 5x and Blue = 5x
1/3 of Red are left handed => 1/3 * 5x = 5x/3 Red left handed
2/3 of Blue are left handed => 2/3 *5x = 10x/3 blue left handed
fraction of participants who are left handed = total left handed/ total participants = (red left handed + blue left handed)/total participants = (5x/3 + 10x/3)/(5x+5x) = (15x/30x) = 1/2
Answer : D
Answer: (D) 1/2
Question: Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. Nandan earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was?
(A) Rs.28,029
(B) Rs.28,020
(C) Rs.28,298
(D) Rs.28,000
(E) Rs.28,022
Rationale: 3:1
2:1
------
6:1
1 ----- 4000
7 ----- ? => Rs.28,000
Answer: D
Answer: (D) Rs.28,000
Question: The profit obtained by selling an article for Rs. 54 is the same as the loss obtained by selling it for Rs. 40. What is the cost price of the article?
(A) Rs. 40
(B) Rs. 50
(C) Rs. 49
(D) Rs. 59
(E) Rs.47
Rationale: S.P 1- C.P = C.P – S.P 2
54- C.P = C.P - 40
2 C.P = 54 + 40;
C.P = 94/2 = 47
ANSWER:E
Answer: (E) Rs.47
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is
(A) 1200
(B) 1764
(C) 1600
(D) 1354
(E) None of these
Rationale: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
x × 16 × (9/12) × (1/100) = 189 or x = 1575.
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs.(1575
189) = Rs. 1764.
Answer: B
Answer: (B) 1764
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 299
(B) 112
(C) 500
(D) 167
(E) 123
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800 = 500 meters
Answer:C
Answer: (C) 500
Question: A train 385 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) 21
(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 = [385 * 3/55] sec
= 21 sec
Answer: A
Answer: (A) 21
Question: Tough and Tricky questions: Percents.
Over the course of a year, a certain microbrewery increased its beer output by 50 percent. At the same time, it decreased its total working hours by 0 percent. By what percent did this factory increase its output per hour?
(A) 125
(B) 130
(C) 150
(D) 155
(E) 160
Rationale: Lets assume the initial production was 100 litres of beer for 100 hr.
With the 50% increase the total amount of beer production will be 150 litres
100hr ----> 100 lts
1hr -----> 1 lts
100hr -----> 150 lts
1hr -----> 1.5 lts
Total Increase in production for 1 hr = 150%
Answer C
Answer: (C) 150
Question: Insert the missing number.
3, 9, 6, 6, 9, 3, 12, 0, 15, (....)
(A) 3
(B) 7
(C) -3
(D) 8
(E) -45
Rationale: Explanation:
There are two series, beginning respectively with 3 and 9. In one 3 is added and in another 3 is subtracted.
The next number is 0 - 3 = -3.
Answer: C) -3
Answer: (C) -3
Question: The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 50 per cent. The two reductions together are equal to a single reduction of
(A) 45%
(B) 62.5%
(C) 35%
(D) 32.5%
(E) 30%
Rationale: Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 50percent is reduced which means the new price is merely 50percent of 3/4P
==> (3/4)x(1/2)P = 3/8P is the new price after both deduction which is 37.5percent of the original value P. This implies this entire series of deduction is worth having discounted 62.5% of P. So answer is B = 62.5%
Answer: (B) 62.5%