GMATPrep: z greater than average of x and 10

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).

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.

Update - deleted the question.

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.