Problem Solving

IMO: A

If X is Y percent of 4Z, where Y>0 and Z>0, then in terms of Z, Y is what percent of X?

A) 4Z
B) 25Z
C) 250/Z
D) 2500/Z
E) Z/400

Let X = 10, and Z = 10, then Y = ?
Given X = (Y/100)*4Z.
10 = (Y/100)*4*10
Y = 25
Let Y be K percent of X
Y = (K/100)*X
25 = (K/100)*200
K = 250
Let us now write K in terms of Z
K = 250 = 25*10 = 25*Z. So the answer is B

[spoiler]Is it ? You are wrong![/spoiler]

Let me try using conventional mathematics:
Given X = (Y/100)*4Z.
X = (Y/25) * Z
X = Y*(Z/25)
Y = (25/Z)*X
Y = ((2500/Z)/100)*X
Y = (K/100)*X. So K = 2500/Z
The correct answer is D

neelgandham wrote:If X is Y percent of 4Z, where Y>0 and Z>0, then in terms of Z, Y is what percent of X?

A) 4Z
B) 25Z
C) 250/Z
D) 2500/Z
E) Z/400

Let Z = 50.
Then 4Z = 4*50 = 200.
Let Y = 100.
Then X = Y% of 4Z = 100% of 200 = 200.

Y is what percent of X?
Y/X = 100/200 = 50%. This is our target.

Now we plug Z=50 into the answers to see which yields our target of 50.

Only answer choice D works:
2500/Z = 2500/50 = 50.

The correct answer is D.

Algebraically:

X is Y% of 4Z:
X = (Y/100)*4Z = (YZ)/25.

Y is what percent of X?
Y/X * 100 = Y/(YZ/25) * 100 = 1/(Z/25) * 100 = (25/Z)*100 = 2500/Z.