OG 216

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vinviper1: Master | Next Rank: 500 Posts; Posts: 222; Joined: Tue Mar 25, 2008 3:52 pm; Thanked: 2 times

by vinviper1 » Wed Apr 30, 2008 11:02 am

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

100m
1/100m
1/m
10/m
10000/m

[spoiler]10000/m[/spoiler]

I get the equation but get a bit confused after that. Thanks.

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Source: Beat The GMAT — Problem Solving | Wed Apr 30, 2008 11:02 am

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: OG 216

by Stuart@KaplanGMAT » Wed Apr 30, 2008 11:52 am

vinviper1 wrote:If m > 0 and x is m percent of y, then in terms of m, y is what percent of x?

100m
1/100m
1/m
10/m
10000/m

[spoiler]10000/m[/spoiler]

I get the equation but get a bit confused after that. Thanks.

This is a great question for picking numbers. Let's start with the statement "x is m percent of y".

We can say that "10 is 50% of 20".

So, we've picked:

x=10
m=50
y=20

Now, let's try the next statement:

"In terms of 50, 20 is what percent of 10?"

Well, 20 is 200% of 10.

So, we want an answer that gives us 200 when we plug 50 in for m.

100m = 5000
1/100m = fraction
1/m = fraction
10/m = fraction
10000/m = 200

Choose (e).

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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simplyjat: Master | Next Rank: 500 Posts; Posts: 423; Joined: Thu Dec 27, 2007 1:29 amFollowed by: 2 members; Location: Hyderabad, India; Thanked: 36 times; GMAT Score:770

by simplyjat » Wed Apr 30, 2008 12:31 pm

Might a simple definition help here.

"x is m percent of y means"
x = (m/100)*y ...1

and you have to find "y is what percent of x" you have to find a, where
y = (a/100)*x ...2

solve 1 to get
y = (100*x)/m
now you have to convert this equation to look like 2

y = ( (100*100/m)/100 )*x
and you get a = 100*100/m

simplyjat

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sudi760mba: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Wed Aug 13, 2008 2:21 am; Thanked: 1 times

by sudi760mba » Fri Sep 04, 2009 12:13 am

1)x is m percent of y.

m * y = x
---
100

Solves to my=100x and y= (100x/m)

2)in terms of m, y is what percent of x.

w=what or the variable you're trying to find

w * x = y
---
100

wx= 100y

3) Plug in y from the 1st equation into the 2nd,

wx=100y
wx=100(100x/m)
wx=(10000x/m)
Multiply both sides by m.

mwx=10,000x
divide by x

mw=10,000
w=10,000/m Ans E.

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boysangur: Junior | Next Rank: 30 Posts; Posts: 19; Joined: Sat Aug 14, 2010 2:57 pm

by boysangur » Sat Sep 04, 2010 6:16 pm

I'm actually more confused by the explanation OG provided for this problem.

They expressed the first info as: x=y*m/100, which I understand. Then they solved for y: y=x100/m, which I also understand.

But then they multiply the fraction by 100 to "convert to an equivalent percent," thus getting 10000/m. For the life of me, I can't understand why there is need to convert that fraction. Doesn't it already express y as the percent of x? I mean, m/100 is the same as m% so isn't y= x/(m/100) the same as y=x/m *100 and thus already a percent? Why multiply again? Someone please explain this to me.

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brianhoppe: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sat Sep 18, 2010 3:00 pm

by brianhoppe » Wed Sep 22, 2010 5:21 pm

My personally opinion is that this problem is a bit convoluted. It states that "x is m percent of y..." Technically a percent is a fraction so that m should already be expressed as 0.50, 0.30,.. etc the number doesn't matter. What does is that it is already a fraction of 1. Which means to divide and multiple by 100 is considering the percent of m percent. I know realize the book says the answer is 10,000/m but i would say its wrong and the correct answer should be 1/m.

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Sep 24, 2010 10:46 am

brianhoppe wrote:Technically a percent is a fraction so that m should already be expressed as 0.50, 0.30,.. etc the number doesn't matter.

Technically, a percent and a fraction are two completely different ways of expressing the same idea - a percent is NOT a fraction.

For example, "50% of 100"is NOT the same as ".5% of 100"; is IS the same as ".5 times 100".

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