If y > 0 and x is y percent of y, then, in terms of y, y is what

This is a copy of the following OG question: https://gmatclub.com/forum/if-m-0-and-x ... 03387.html

x is y percent of y
x = (y/100)*y = y^2/100


let y is a percent of x
y = (a/100)*x
a = 100y/x = 100y/[y^2/100] = 10000/y

ans D

it is given that x is y percent of y, so lets assume x=25 and y=50. So we get, 25(i.e. x) is 50%(i.e. y%) of 50(i.e. y).
Now clearly y is 200% of x. Put the values of x and y in options and select the one which gives 200 as answer. Only option D will fit.
Hence D

x = y%*y
=y/100 * y (here y/100 is the multiplier)
y = (100/y) * x ( where, 100/y is the multiplier)
y = (100/y)*x * 100 (convert to percent unit)
y = (10000/y) % of x

Choosing numbers is probably the easiest approach. Ordinarily, avoid using numbers that are similar to those in the answer choices.

Let y = 20

x is y percent of y
x is 20% of 20

x = .2 * 20
x = 4

y is what percent of x?

\(\frac{y}{x}\) * 100 =

\(\frac{20}{4}\) = 5 * 100 = 500%

We're looking for the answer that yields 500 when y = 20.

A) \(\frac{1}{y}=\frac{1}{20}=.05\)
Much too small. We need 500. Eliminate.

B) \(\frac{1}{100y}=\frac{1}{100(20)}=\frac{1}{2,000}=\)
Even smaller than A. (B =.0005). Eliminate

E) \(\frac{1}{10000y}=\) Even smaller than B.
Not even close to 500. Eliminate

(Typically, scan answers first and eliminate A, B, and E immediately. The fractions have y = 20 in the denominators and 1 on top. Those answers are tiny regardless and tiny when compared to 500.)

C. 100y: too large.
(20 * 100) = 2,000. Eliminate

D. \(\frac{10,000}{y}=\frac{10,000}{20}\) = 500. Correct.

Answer D

Given:
1. y > 0
2. x is y percent of y

Asked: In terms of y, y is what percent of x ?

x = y% y = y*y / 100
y = 100x/y = (10000/y)% x

IMO D

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.