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# x is what percent of y percent of z, in terms of x, y and z?

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Manager
Joined: 30 Mar 2010
Posts: 80
GMAT 1: 730 Q48 V42
x is what percent of y percent of z, in terms of x, y and z?  [#permalink]

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28 Oct 2010, 13:51
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:28) correct 23% (01:14) wrong based on 65 sessions

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x is what percent of y percent of z, in terms of x, y and z?

(A) 100xy/z
(B) 100yz/x
(C) 100yz/x
(D) 10000x/yz
(E) 10000yz/x
Math Expert
Joined: 02 Sep 2009
Posts: 56268
x is what percent of y percent of z, in terms of x, y and z?  [#permalink]

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28 Oct 2010, 14:04
afyl128 wrote:
x is what percent of y percent of z, in terms of x, y and z?

(A) 100xy/z (B) 100yz/x (C) 100yz/x, (D) 10000x/yz (E) 10000yz/x

Really struggling with these successive percent VIC style questions. Any advice?

x is what percent of ... --> $$x=\frac{?}{100}*...$$;
y percent of z --> $$z*\frac{y}{100}$$;

So, $$x=\frac{?}{100}*(z*\frac{y}{100})$$ --> $$?=\frac{10,000x}{yz}$$.

Similar questions:
http://gmatclub.com/forum/if-a-b-and-c- ... ms#p684668
http://gmatclub.com/forum/if-m-0-and-x-is-103387.html

Hope it helps.
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28 Oct 2010, 14:08
Algebraically, y% of z is just (y/100)*z, or yz/100. So we want to answer the question: x is what percent of yz/100? Say x is equal to m% of yz/100; then we have:

x = (m/100)*(yz/100)
10,000x/yz = m

and since m is what we were asked to find, the answer is 10,000x/yz.

Alternatively, if you don't see how to do the algebra very quickly, you should fall back on a number-picking strategy. Here, we can invent straightforward numbers for x, y and z, and answer the question using those numbers. We need to take a percentage of z, so we might let z = 100, and then choose smaller numbers for y and x, say y = 20, and x = 10, (though there lots of simple sets of numbers that would do just fine here). With these numbers, our question becomes: "10 is what percent of 20% of 100?", or in other words, "10 is what percent of 20?" We know the answer to that question is 50%, so we are looking for an answer that gives us 50 if we plug in our values of x, y and z. Only D works (if two answer choices work, that's an unfortunate coincidence, in which case you'd need to try again with a new set of numbers to distinguish between those two remaining choices - that's one reason that this method can sometimes be time consuming, and if you can do the algebra, you'll save time in most cases).

Incidentally, answers B and C are identical in your post above - I'm guessing one of them should read 100xz/y.
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Joined: 30 Mar 2010
Posts: 80
GMAT 1: 730 Q48 V42

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28 Oct 2010, 14:18
IanStewart wrote:

Incidentally, answers B and C are identical in your post above - I'm guessing one of them should read 100xz/y.

LOL question is actually written that way =)

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Joined: 30 Mar 2010
Posts: 80
GMAT 1: 730 Q48 V42

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28 Oct 2010, 14:23
Bunuel wrote:
afyl128 wrote:
x is what percent of y percent of z, in terms of x, y and z?

(A) 100xy/z (B) 100yz/x (C) 100yz/x, (D) 10000x/yz (E) 10000yz/x

Really struggling with these successive percent VIC style questions. Any advice?

x is what percent of ... --> $$x=\frac{?}{100}*...$$;
y percent of z --> $$z*\frac{y}{100}$$;

So, $$x=\frac{?}{100}*(z*\frac{y}{100})$$ --> $$?=\frac{10,00x}{yz}$$.

Similar questions:
if-a-b-and-c-are-greater-than-90197.html?hilit=percent%20terms#p684668
if-m-0-and-x-is-103387.html

Hope it helps.

Thanks so much, this helps a lot.. I don't know what it is about you putting the ? in there but it really did the trick.
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Concentration: Technology, Entrepreneurship
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31 Oct 2010, 04:59
afyl128 wrote:
Bunuel wrote:
afyl128 wrote:
x is what percent of y percent of z, in terms of x, y and z?

(A) 100xy/z (B) 100yz/x (C) 100yz/x, (D) 10000x/yz (E) 10000yz/x

Really struggling with these successive percent VIC style questions. Any advice?

x is what percent of ... --> $$x=\frac{?}{100}*...$$;
y percent of z --> $$z*\frac{y}{100}$$;

So, $$x=\frac{?}{100}*(z*\frac{y}{100})$$ --> $$?=\frac{10,00x}{yz}$$.

Similar questions:
if-a-b-and-c-are-greater-than-90197.html?hilit=percent%20terms#p684668
if-m-0-and-x-is-103387.html

Hope it helps.

Thanks so much, this helps a lot.. I don't know what it is about you putting the ? in there but it really did the trick.
It is better to write $$?$$ instead of some variable as there are already variables provided and can be confusing at times.
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Re: x is what percent of y percent of z, in terms of x, y and z?  [#permalink]

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22 Feb 2018, 17:44
afyl128 wrote:
x is what percent of y percent of z, in terms of x, y and z?

(A) 100xy/z
(B) 100yz/x
(C) 100yz/x
(D) 10000x/yz
(E) 10000yz/x

We can let p be the percentage. Thus, we have

x = p/100 * y/100 * z

x = pyz/10000

x*10000/yz = p

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Re: x is what percent of y percent of z, in terms of x, y and z?   [#permalink] 22 Feb 2018, 17:44
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