The sum of x% of y and y% of z is z% of x. x and z are integers such that 1 =< x =< 9, 1 =< z =< 9.

M4maths Previous Puzzles

23 Jan 2015 Possibilities

The sum of x% of y and y% of z is z% of x. x and z are integers such that 1 =< x =< 9, 1 =< z =< 9. If y is a perfect square number then how many ordered pair (x, z) are possible satisfying the given condition.

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 7
9) 9
10)0

Solution

xy/100 + yz/100 = zx/100
y = xz/(x+z)
If either x or z is one then no possible case because n/(n+1) will never a perfect square.
For x=2 and z=2, y=1 (Perfect square)
Similarly for x=8 and z=8, y=4 (Perfect square)
For x=3 and z=9, sum=12
so y = 3*9/12 = 9/4 (Perfect square)
so (3,9) and (9,3) are possible pair
So total possible pairs are (2,2), (8,8), (3,9) and (2,3)
Option 4)

Correct Option: 4 Best Solution (2)

Anshul Garg   9 years AGO

The possible solutions are (2,2) , (3,9), (9,3), (8,8).

Like? Yes (9) | No   

apurva katyayni   9 years AGO

(2,2), (3,9),(8,8),(9,3)

Like? Yes (4) | No (1)