GATE Questions

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The letters move 2, 2, 3, 3, 4, 4, ... steps forward.

Let the numbers be 3x, 3x + 3 and 3x + 6.
Then,
3x + (3x + 3) + (3x + 6) = 72
9x = 63
x = 7
Largest number = 3x + 6 = 27.

=> Second largest number = 27 - 3 = 24

             A              :               B
(8000x4)+(4000x8) : (9000x6)+(6000x6)
         64000           :      90000
=>        32 : 45

From the given data,

Let the two gits of a number be x & y

A) x + y = 15

B) x2 - y2 = 45

(x+y) (x - y) = 45

C) x - y = 3

From any 2 of the given 3 statements, we can find that 2 digit number as 

2x = 18 => x = 9

=> y = 6

Hence, 2 digit number is 96.

Any one pair of A and B, B and C or C and A is sufficient to find.

Speed in still water = 6 kmph

Stream speed = 1.2 kmph

Down stream  = 7.2 kmph

Up Stream = 4.8 kmph

x/7.2 + x/4.8 = 1

x = 2.88

Total Distance  = 2.88 x 2 = 5.76 kms

1/8 - 1/x = 1/10

 => x = 40 hrs

Since their HCFs are 7, numbers are divisible by 7 and are of the form 7x and 7y

Difference = 14
=> 7x - 7y = 14
=> x - y = 2

product of numbers = product of their hcf and lcm
=> 7x * 7y = 441 * 7
=> x * y = 63

Now, we have
x * y = 63 , x - y = 2
=> x = 9 , y = 7

The numbers are 7x and 7y
=> 63 and 49

Given 2 is to 55

2 + 3 = 5 

5 x 11 = 55

Similarly, 6

6 + 3 = 9

9 x 11 = 99

Hence, 2 is to 55 as 6 is to 99.