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 = 3.52.7
Similarly,
(y + 1) (z + 1) = 147 = 3.72
& (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