GATE Questions

Q:

A number is increased by 20% and then decreased by 20%, the final value of the number is ?

A) increase by 2% B) decrease by 3%
C) decrease by 4% D) increase by 5%
 
Answer & Explanation Answer: C) decrease by 4%

Explanation:

Here, x = 20 and y = - 20
Therefore, the net % change in value
=x + y + xy100 %
20 + -20 + 20 × -20100%  or  - 4%

Since the sign is negative, there is a decrease in value by 4%.

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10 6537
Q:

The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is :

A) Rs. 560 B) Rs. 530
C) Rs. 500 D) Rs. 514
 
Answer & Explanation Answer: C) Rs. 500

Explanation:

110% of S.P. = Rs. 616

S.P. = (616 x 100)/110 = Rs. 560

C.P = (110 x 560)/112 = Rs. 500

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15 6278
Q:

5 C in an OF?

A) 5 Cards in an Old Fan B) 5 Circles in an Olympic Flag
C) 5 Colors in an Old Football D) 5 Colors in an Old Flag
 
Answer & Explanation Answer: B) 5 Circles in an Olympic Flag

Explanation:

5 C in an OF denotes 5 Circles in an Olympic Flag.

These are riddles of type

12 S of the Z

52 W in a Y.

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5 5861
Q:

A letter is takenout at random from 'ASSISTANT'  and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A) 35/96 B) 19/90
C) 19/96 D) None of these
 
Answer & Explanation Answer: B) 19/90

Explanation:

ASSISTANTAAINSSSTT

STATISTICSACIISSSTTT

Here N and C are not common and same letters can be A, I, S, T. Therefore

 Probability of choosing A =  2C19C1×1C110C1 = 1/45 

 Probability of choosing I = 19C1×2C110C1 = 1/45

Probability of choosing S = 3C19C1×3C110C1 = 1/10

Probability of choosing T = 2C19C1×3C110C1 = 1/15

Hence, Required probability =   145+145+110+115= 1990 

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60 5859
Q:

If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 350%, the resultant fraction is 25/51. What is the original fraction ?

A) 31/25 B) 15/17
C) 14/25 D) 11/16
 
Answer & Explanation Answer: B) 15/17

Explanation:

The original fraction is  2551 × 350+100150+100  = 15/17.

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10 5647
Q:

A cistern is normally filled in 8 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in    ?

A) 20 hrs B) 28 hrs
C) 36 hrs D) 40 hrs
 
Answer & Explanation Answer: A) 20 hrs

Explanation:

1/8 - 1/x = 1/10

 => x = 40 hrs

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14 5576
Q:

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123 B) 113
C) 246 D) 945
 
Answer & Explanation Answer: C) 246

Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking. 

 

(i) 1 lady out of 4 and 4 gentlemen out of 6 

(ii) 2 ladies out of 4 and 3 gentlemen out of 6 

(iii) 3 ladies out of 4 and 2 gentlemen out of 6 

(iv) 4 ladies out of 4 and 1 gentlemen out of 6 

 

In case I the number of ways = C14×C46 = 4 x 15 = 60 

In case II the number of ways = C24×C36 = 6 x 20 = 120 

In case III the number of ways = C34×C26 = 4 x 15 = 60

In case IV the number of ways = C44×C16 = 1 x 6 = 6 

 

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

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5 5571
Q:

is related to 81 in the same way as 64 is related to ____

A) 225 B) 425
C) 525 D) 625
 
Answer & Explanation Answer: D) 625

Explanation:

The relationship is xy  :  x+1y+1

 

Now , 64 = 43

 

So, required number = 4+13+1 = 54 = 625

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