Is a Greater than b? b^2 > a^3 |b| > |a| GMAT Data Sufficiency

Question: Is a greater than b?

1. \(b^2 > a^3\)
2. \(|b| > |a|\)

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.

Answer:

Approach Solution (1):

We noticed in both the statements that signs of b are erased by simply squaring or taking the absolute value.
Hence we can vary the value of b (small or big) by simply making it positive or negative.
Now check that if a = 1, then both the statements will be true whether b = 1,000,000 or b = -1,000,000. Here we have varied the value of b by just making it positive or negative.

So we have no way to tell whether a > b or a < b

After looking at this scenario, we can say that both the statements (1) and (2) together are not sufficient in itself.

Correct Option: E

“Is a greater than b?”- 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.

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