GATE Questions and Answers with Explanation

Q:

What will come in place of the question mark in the series below?

3, 5, 15, 45, 113, ?

A) 250	B) 243
C) 247	D) 261

Answer & Explanation Answer: B) 243

Explanation:

Ans.
5 = 3 + (13 + 1)
15 = 5 + (23 + 2)
45 = 15 + (33 + 3)
113 = 45 + (43 + 4)
? = 113 + (53 + 5), i.e. ? = 243

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Filed Under: Numbers
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0 17883

Q:

A train covers a distance between station A and station B in 45 min.If the speed of the train is reduced by 5 km/hr,then the same distance is covered in 48 min.what is the distance between the stations A and B ?

A) 80 kms	B) 60 kms
C) 45 kms	D) 32 kms

Answer & Explanation Answer: B) 60 kms

Explanation:

Let 'd' be the distance and 's' be the speed and 't' be the time
d=sxt
45 mins = 3/4 hr and 48 mins = 4/5 hr
As distance is same in both cases;
s(3/4) = (s-5)(4/5)
3s/4 = (4s-20)/5
15s = 16s-80
s = 80 km.
=> d = 80 x 3/4 = 60 kms.

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Filed Under: Problems on Trains
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19 17867

Q:

A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture ?

A) 5 lit	B) 10 lit
C) 15 lit	D) 20 lit

Answer & Explanation Answer: B) 10 lit

Explanation:

Number of liters of water in 150 liters of the mixture = 20% of 150 = 20/100 x 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 x (150 + P)
120 + 4P = 150 + P => P = 10 liters.

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Filed Under: Alligation or Mixture
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9 17833

Q:

Find the Missing Numbers in the given Number Puzzle ?

A) 169 & 81	B) 67 & 121
C) 64 & 115	D) 70 & 110

Answer & Explanation Answer: A) 169 & 81

Explanation:

Observe that in each column, square of sum of digits in the first row = Respective second row elements.

In the same way, square of sum of digits in the second row = Respective third row elements.

=> ${(6 + 4)}^{2} = 10^{2} = 100$

=> ${(4 + 9)}^{2} = 13^{2} = 169$

=> ${(8 + 1)}^{2} = 9^{2} = 81$ .

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Filed Under: Number Puzzles
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95 17825

Q:

One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

A) 27 %	B) 26 %
C) 29 %	D) 21 %

Answer & Explanation Answer: A) 27 %

Explanation:

Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135
X = 27

So, required percentage of benzene = 27 %

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Filed Under: Alligation or Mixture
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30 17784

Q:

The ratio of speeds of a car, a train and a bus is 5:9:4. The average speed of the car, the bus and the train is 72 km/hr together. What is the average speed of the car and the train together ?

A) 84 km/hr	B) 96 km/hr
C) 72 km/hr	D) 60 km/hr

Answer & Explanation Answer: A) 84 km/hr

Explanation:

Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is = $\frac{5 x + 9 x}{2}$ = 7x = 7 x 12 = 84 km/hr.

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Filed Under: Average
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20 17751

Q:

Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.85. How much was lent at 5% ?

A) Rs. 500	B) Rs. 245
C) Rs. 1250	D) Rs. 635

Answer & Explanation Answer: A) Rs. 500

Explanation:

(kx5x1)/100 + [(1500 - k)x6x1]/100 = 85

5k/100 + 90 – 6k/100 = 85

k/100 = 5

=> k = 500

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Filed Under: Simple Interest
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12 17690

Q:

Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador.

Question :

How many people live between the floors on which D and the one having a car Bedford ?

A) One	B) Two
C) Three	D) Four

Answer & Explanation Answer: B) Two

Explanation:

111-151497940723.png image

Above is the table obtained from the given information in the passage.

There are two people (B & G) live between the floors on which D and the one having a car Bedford.

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Filed Under: Deriving Conclusions From Passages
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23 17679

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