What is the value of \(6x^2+9y^2\)?

Question: What is the value of \(6x^2+9y^2\) ?

1. x = 2
2. \(4x^2+6y^2=22\)

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.

“What is the value of  \(6x^2+9y^2\)? ” – is a topic of theGMAT 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 Solution 1

Firstly, taking statement (1), we have: x = 2

This statement is insufficient in itself. The main reason behind this is that S1 provides us with the value of x but it does not discussed about the value of y.

Now, taking statement (2), we have: \(4x^2+6y^2=22\)

This statement is sufficient in itself.

Multiply the S2 time 1.5, we will get:

\(6x^2+9y^2=33\)

Correct option: B

Approach Solution 2

Firstly, Factorize the main expression: \(6x^2+9y^2\)

Taking ‘3’ common from this expression, we will have:

3 (\(2x^2+3y^2\))

Now taking statement (1), we have: x = 2

This statement is insufficient in itself. The main reason behind this is that S1 provides us with the value of x but it does not discussed about the value of y.

Now, taking statement (2), we have: \(4x^2+6y^2=22\)

Divide this expression by 2, we will get:

\(2x^2+3y^2=11\)

Substitute 11 in the above equation, we will get:

3 (\(2x^2+3y^2\)) = 3 (11) = 33

Correct option: B

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