If a, b, and c are positive and \(a^2+c^2=202\), What is the Value of b – a – c?

Question: If a, b, and c are positive and \(a^2+c^2=202 \), what is the value of b – a – c?

1.  \(b^2+c^2=225\)

2. \(a^2+b^2=265\)

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If a, b, and c are positive and \(a^2+c^2=202\) , what is the value of b – a – c?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Answer

Approach 1

Taking S1, we have: \(b^2+c^2=225\)

This statement is insufficient in itself.

Taking S2, we have: \(a^2+b^2=265\)

This statement is insufficient in itself.

Now, subtract \(a^2+c^2=202\) from S1, we will get:

\(b^2+c^2-a^2-c^2=225-202\)

\(b^2-a^2=23\)

Now, add \(b^2-a^2=23\) and S2, we will get:

\(b^2-a^2+a^2+b^2=23+265\)

\(2b^2=288\)

\(b^2=144\)

Since, b is a positive integer

Therefore, b = 12

Then, from the equation: \(b^2-a^2=23\), we will get the value of a.

\(b^2-a^2=23\)

\(12^2-a^2=23\)

a = 11

Then, from the equation: \(a^2+c^2=202\) , we will get the value of c.

\(11^2+c^2=202\)

c = 9

Hence, this is sufficient.

Correct option: C

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