# 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%

Explanation:

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

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

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

Explanation:

110% of S.P. = Rs. 616

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

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

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

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.

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

Explanation:

$ASSISTANT\to AAINSSSTT$

$STATISTICS\to ACIISSSTTT$

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

Probability of choosing A =  $\frac{{2}_{{C}_{1}}}{{9}_{{C}_{1}}}×\frac{{1}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/45

Probability of choosing I = $\frac{1}{{9}_{{C}_{1}}}×\frac{{2}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/45

Probability of choosing S = $\frac{{3}_{{C}_{1}}}{{9}_{{C}_{1}}}×\frac{{3}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/10

Probability of choosing T = $\frac{{2}_{{C}_{1}}}{{9}_{{C}_{1}}}×\frac{{3}_{{C}_{1}}}{{10}_{{C}_{1}}}$ = 1/15

Hence, Required probability =

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

Explanation:

The original fraction is    = 15/17.

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

Explanation:

1/8 - 1/x = 1/10

=> x = 40 hrs

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

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 = $C_{1}^{4}×C_{4}^{6}$ = 4 x 15 = 60

In case II the number of ways = $C_{2}^{4}×C_{3}^{6}$ = 6 x 20 = 120

In case III the number of ways = $C_{3}^{4}×C_{2}^{6}$ = 4 x 15 = 60

In case IV the number of ways = $C_{4}^{4}×C_{1}^{6}$ = 1 x 6 = 6

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

5 5571
Q:

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

 A) 225 B) 425 C) 525 D) 625

Explanation:

The relationship is

Now ,

So, required number = ${\left(4+1\right)}^{\left(3+1\right)}$ = ${5}^{4}$ = 625