If |a-b|=c ,what is the value of a?

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Jan 27, 2018 7:42 am

If |a-b|=c, what is the value of a?

(1) b = 2
(2) c = 7

The OA is the option E.

Why using both statements together is not sufficient? I think that a=9. Am I wrong?

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Source: Beat The GMAT — Data Sufficiency | Sat Jan 27, 2018 7:42 am

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Mon Jan 29, 2018 6:28 am

If |a-b|=c, then we can have either $$a-b=c\ \ OR\ \ a-b=-c$$ because of the properties of absolute values. For the statements to be sufficient, we need to find only one possible value for a. So unless we get a single value for a with BOTH equations, the statements are insufficient to solve.

You've already worked through why the statements individually aren't sufficient to solve, so we'll look at them together:

If b = 2 and c = 7, we can have either $$a-2=7\ \ OR\ \ a-2=-7$$
Solving for a in both equations gives $$a=9\ \ OR\ \ a=-5$$

This means that there are two possible values for a: 9 and -5. Insufficient.

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