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GMATPrep: z greater than average of x and 10

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Source: — Data Sufficiency |
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by Stuart@KaplanGMAT » Tue Jun 02, 2009 3:11 pm
JPGs are actually a bit annoying, because you can't quote the question in your reply! If you can retype the question (i.e. no big diagrams and such), it does make replying a lot easier.

Q: 0<x<10; Is z > the average of x and 10?

(1) On the number line, z is closer to 10 than x.

Well, the average of x and 10 will be exactly halfway between x and 10.

If z = average, then z would be right in the middle of x and 10. Since z is closer to 10, it's definitely greater than the average: sufficient.

If we wanted to represent the statement on the number line, it basically tells us that we have:

x ---------- avg ----- z----- 10

(2) z = 5x

Picking numbers quickly shows us that this is insufficient.

If we pick x = 2, then z = 10, which IS greater than the average of x and 10 ((2+10)/2 = 6).

If we pick x = 1, then z = 5, which is NOT greater than the average of x and 10 ((1+10)/2) = 5.5).

Since we can get both a YES and NO answer, (2) is insufficient.

(1) is sufficient, (2) is not: choose (A).
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by California4jx » Wed Jun 03, 2009 2:49 am
Stuart Kovinsky wrote:JPGs are actually a bit annoying, because you can't quote the question in your reply! If you can retype the question (i.e. no big diagrams and such), it does make replying a lot easier.

Q: 0<x<10; Is z > the average of x and 10?

(1) On the number line, z is closer to 10 than x.

Well, the average of x and 10 will be exactly halfway between x and 10.

If z = average, then z would be right in the middle of x and 10. Since z is closer to 10, it's definitely greater than the average: sufficient.

If we wanted to represent the statement on the number line, it basically tells us that we have:

x ---------- avg ----- z----- 10

(2) z = 5x

Picking numbers quickly shows us that this is insufficient.

If we pick x = 2, then z = 10, which IS greater than the average of x and 10 ((2+10)/2 = 6).

If we pick x = 1, then z = 5, which is NOT greater than the average of x and 10 ((1+10)/2) = 5.5).

Since we can get both a YES and NO answer, (2) is insufficient.

(1) is sufficient, (2) is not: choose (A).
Thanks Stuart, as always, great explanation.

I always thought JPG would be more clearer to a reader, never thought of your point, will try to take care in future posts.
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by crackgmat007 » Sun Aug 16, 2009 5:25 pm
Update - deleted the question.
Last edited by crackgmat007 on Mon Aug 17, 2009 4:52 pm, edited 1 time in total.
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by gauravgundal » Sun Aug 16, 2009 11:46 pm
Hi crackgmat007,
1. x = 7, z = 8 (closer to 10 than x). Avg of 7 & 10 = 8.5. But z < avg

may i know how z=8 is closer to 10 than to x which is 7.
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