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

Question

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

Bunuel · Answer

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} . Answer D. Similar questions: https://gmatclub.com/forum/if-a-b-and-c- ... ms#p684668 https://gmatclub.com/forum/if-m-0-and-x-is-103387.html Hope it helps.

IanStewart · Answer

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.

afyl128 · Answer

LOL question is actually written that way =)

Many thanks for the answer!

afyl128 · Answer

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.

AtifS · Answer

It is better to write  ?  instead of some variable as there are already variables provided and can be confusing at times.

JeffTargetTestPrep · Answer

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

x = p/100 * y/100 * z

x = pyz/10000

x*10000/yz = p

Answer: D

Kinshook · Answer

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

x = y% z % (x/y%z%) 
x/y%z% = 10000 x/yz

IMO D

amarsinha · Answer

y percent of z = (y/100)*z

x is what percent of y percent z = (x / (y/100)*z)*100 = 10000x/(yz)

bumpbot · Answer

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

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

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