What is the value of C + |C|? (1) |C| = 1 (2) C^2= C^(1/2)

I went with this explnation

S1 c can be -1 or 1 not sufficent

S2 c ^2 = sqrt( c) square both sides C ^ 4 = c or c ( c^3 - 1 ) = 0

c = 0 or c = 1 not sufficient

S1 and S2 we can say c = 1

I missed 0 too......ha silly me......

Hi All,

The others posters in this thread have properly solved the problem, so I won't rehash any of that work here. Instead, I want to point out some details on the "nature" of DS questions. DS questions are on the GMAT to test you on a variety of skills that are not strictly "math skills": organization, accuracy, attention-to-detail, thoroughness, the ability to PROVE that you're correct, etc.

Every DS question has AT LEAST one answer. Part of your job when facing any DS question is to look "beyond" the obvious. To get the points, you have to show how thorough your thinking is by finding the alternatives (if they exist).

In Fact 2, I'm sure that almost everyone would think "oh, it has to be the number 1...."; if those same Test Takers don't do the necessary extra work to realize that 0 is ALSO a possible answer, then those same people will get this easy question wrong, lose out on those points and not even know it. Get in the habit of thinking - do work, take notes, consider the possibilities and you'd be amazed how easy most DS questions actually are.

GMAT assassins aren't born, they're made,
Rich

I made a silly mistake and forgot that the square root of a negative number is i haha.

Nice post!

Whenever there is a question on absolute values (or modulus as is more popularly known as), always try to work on the inputs, rather than the output.

From statement I, |C| = 1. This means that the value of C can be +1 or -1.

If C = 1, C + |C| = 1 + 1 = 2.

If C = -1, C + |C| = -1 + 1 = 0.

Data given in statement I is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II, \(C^2\) = √C. Squaring both sides, we have \(C^4\) = C.

Transferring C on to the LHS, we have \(C^4\) – C = 0, which simplifies to \(C^3\) ( C – 1) = 0.
This means that C^3 = 0 or (C-1) = 0, which means C = 0 or C = 1.

If C = 0, C + |C| = 0 + 0 = 0.

If C = 1, C + |C| = 1 + 1 = 2.

Data given in statement II is insufficient. Answer option B can be eliminated. Possible answer options are C or E.

Combining statements I and II, the common value of C that satisfies both the pieces of data is C = 1. This means, we will also be able to obtain a unique value for the given expression.
The combination of statements gives us sufficient data. Answer option E can be eliminated.

The correct answer option is C.

Hope this helps!

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