GATE Questions

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Let the first number be x and the second number be y.

Given

5% of x = (25% of y) + y

=> 5x/100 = 5y/4

=> x = 25y ......(1)

and also given that, x - y = 96

=> x = 96 + y .....(2)

From (1)&(2)

25y = 96 + y

=> 24y = 96

=> y = 4

From (1)

x = 96 + 4 = 100

Hence, the numbers are 100 & 4.

Here by observing the figure, 

we can complete the above incomplete cube with 2 cubes in 2 rows and 2 columns

=> 2 x 4 = 8.

Hence, with 8 small cubes we can complete the cube.

Given, y/(x - z) = (y + x)/z = x/y
yz = xy + x2 - yz - xz ....(1)
Also xy = yx-z ⇒x2 -xz = y2 ....(2)
Using (1) and (2), we get yz = xy - yz + y2
2yz = xy + y2
2z = x + y
Only option (B) satisfies the equation.

1. Answer (b)

Santosh , Ujjwal and Varun must each receive at least three pieces, but Tarun must receive at least four pieces. The maximum number of pieces that any person may receive is six ( 6 + 3+ 3+3 = 15 ), and only Tarun may receive six pieces. Ujjwal and Varun each may receive as many as five pieces, while Santosh may receive only four pieces at maximum.
At least one pear.

2. Answer (c)

Varun may receive no more than five pieces and Tarun may receive no fewer than four pieces. As a result, if Varun receives more pieces than Tarun, then Varun must receive five pieces, and Tarun must receive four pieces. Thus, statement (a) must be true. Since Varun will receive five pieces, none of the other three friends will receive any apple, accordingly, each of the other three friends must receive at least one orange and at least one pear. Thus, statement (b) and (d) must be true.

4 x 27 x 3125 = 22 × 33 × 55 ;

8 x 9 x 25 x 7 = 23 × 32 × 52 × 7

16 x 81 x 5 x 11 x 49 = 24 × 34 × 5 × 11 × 72

H.C.F = 22 × 32 × 5 = 180.

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120

For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120

So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120

Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes

Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.

Given word is TIRADES
Now the consonants T, R, D, S are replaced by S, Q, C, R
And Vowels are I, A, E are replaced by J, B and F
They are arranged alphabetically
New word is BCFJQRS

The fourth letter from the right end is J.

One hour = 60 min

18/60 = 3/10