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Percentage mania. confusing

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Percentage mania. confusing

by gmatruler » Thu Jul 08, 2010 11:11 am
The question below is giving me a very hard time. How am I supposed to know what is sufficient?

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?

(1) x > y
(2 xy/100 < x-y
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Source: — Data Sufficiency |
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by Patrick_GMATFix » Thu Jul 08, 2010 11:19 am
This is DS #120 from the OG12. The key to manipulating percentage change when you're dealing with variables rather than numbers is to know the algebraic representation of percent change.

If a value is increased by 10%, it's multiplied by 1.10. This is because the value is really multiplied by (1 + 10/100). Thus to raise a value by 10%, you add itself to 10% of itself.

Similarly, when a value is decreased by 10%, it's multiplied by .90. The actual operation is multiplication by (1 - 10/100). Thus to drop a value by 10% you subtract from itself 10% of itself.

With variables, things work the same way. To increase a value by x%, multiply it by (1 + x/100). To decrease a value by y%, multiply it by (1 - y/100)

This is a tough question, and the OA is B. A detailed solution is attached. Those who cannot see the attachment can read it here.

Use the reference section of the OG Companion to find similar OG questions.
-Patrick
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by gmatruler » Thu Jul 08, 2010 11:38 am
Patrick_GMATFix wrote:If a value is increased by 10%, it's multiplied by 1.10. This is because the value is really multiplied by (1 + 10/100). Thus to raise a value by 10%, you add itself to 10% of itself.

Similarly, when a value is decreased by 10%, it's multiplied by .90. The actual operation is multiplication by (1 - 10/100). Thus to drop a value by 10% you subtract from itself 10% of itself.

With variables, things work the same way. To increase a value by x%, multiply it by (1 + x/100). To decrease a value by y%, multiply it by (1 - y/100)
Patrick, the explanation and lessons you attached are very helpful! Thank you.
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