### Wordpandit Question of the day

** Question: **x, y, z, w are positive integers such that

xy + x + y = 524

yz + y + z = 146

zw + z + w = 104

xyzw = 8!

**Find x – y.**

(a) 100

(b) 4

(c) 20

(d) 2 values possible

#### Solution posted below. Click on the plus sign to view the solution.

### Answer and Explanation

Answer: (b)

xy + x + y = 524

(x + 1) (y + 1) = 525 = 3.5^{2}.7

Similarly,

(y + 1) (z + 1) = 147 = 3.7^{2}

& (z + 1) (w +1) = 3. 5. 7

Now (x + 1) (y + 1) is a multiple of 25 but (y + 1) (z + 1) is not a multiple of 25.

That implies (x + 1) is a multiple of 25.

Also (x + 1) divides 525.

So, x + 1 = 25, 75, 175, 525

x = 24, 74, 174, 524.

Also x divides 8!

So, x = 24

y = 20

x – y = + 4

x = 24; y = 20; z = 6; w =14

so, x-y = 4.

b) is the answer.

option c