Question: Is 2ab > ab?

(1) a^4/b^3 < (−17)
(2) (ab)^3 < (ab)^4

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.

Correct Answer: E
Solution and Explanation:
Approach Solution 1:
Given in the question, two statements are given and it is asked to find out if the two statements are sufficient to get the answer.

It Is asked if 2ab > ab or not.

The given two statements are –

(1) a^4/b^3 < (−17)
(2) (ab)^3 < (ab)^4

First, we’ll check the first statement,

(1) a^4/b^3 < (−17)

The term a^4 is positive, but “a” could be any number as it has even power.
But “b” should be a negative number, as “b” has odd power.
Hence, “a” is positive, the answer to this question will be Yes. That is, “2ab” is greater than “ab”.
And if “b” is 0 or any positive number, then the answer is no. That is “2ab” is not greater than “ab”

Therefore the statement is not sufficient to get the answer.
Now checking the second statement,

(2) (ab)^3 < (ab)^4
(ab)^3 < (ab)^4..........(ab)^4−(ab)^3 > 0......(ab)^3(ab−1) > 0
(ab)^3 < (ab)^4−(ab)^3 > 0......(ab)^3(ab−1) > 0

We can conclude from (ab)4−(ab)3 > 0, that ab could be both positive and negative

Otherwise, (ab)^3(ab−1) > 0(ab)^3(ab−1) > 0 gives the two cases.

(i) ab > 0, ab-1 > 0 or ab > 1
(ii) ab < 0, ab-1 < 0 or ab < 1.....

so ab > 1 or ab < 0

Hence, this is insufficient data

When two cases are combined,

For the first case, the value of “b” is negative but the value of “ab” > 1, then “a” < 0 and the answer is YES, That is “2ab” is greater than “ab”.

For the second case, the value “b” is negative but if the value of “ab”< 0, then “a” is positive and the answer is NO, That is “2ab” is not greater than “ab”

Therefore, the data given is Insufficient.
Thus the answer is E, which says, Statements (1) and (2) TOGETHER are NOT sufficient

Approach Solution 2:
(1) a^4/a^3 < −17

Now a^4 is positive but a could be anything as it has EVEN power..

b is surely negative.
If a is negative ans is YES, if b is 0 or positive, ans is NO..
Insufficient

(2) (ab)^3 < (ab)^4..…
(ab)^3 < (ab)^4..........(ab)^4−(ab)^3 > 0......(ab)^3(ab−1) > 0
we can easily see from (ab)^4−(ab)^3 > 0, ab could be positive or negative..
otherwise (ab)^3(ab−1) > 0 gives two cases..

(i) ab > 0, ab-1 > 0 or ab > 1
(ii) ab < 0, ab-1 < 0 or ab < 1.....

so ab > 1 or ab < 0
insufficient

Combining
b is negative but ab > 1, then a < 0 and ans is YES
b is negative but ab < 0, then a is positive and ans is NO
Insufficient

Approach Solution 3:
Is 2ab > ab ?
or is 2ab−ab=ab > 0? The question asks if a,b have the same sign (and are non zero numbers).

1. a^4/b^3 < −17

The sign of a^4 is +, and because the fraction is less than a negative number => b must be negative. No info about a, not sufficient.

2. (ab)^3 < (ab)^4

or (ab)^4−(ab)^3 > 0, (ab)^3(ab−1) > 0. The first (ab)^3 is positive if ab > 0, the second term is positive if

ab > 1, so overall that equation is positive is ab > 1 or ab < 0. Not sufficient
(1+2) From statement 1 we know that the sign of b is -, but we cannot say anything about the sign of a (that can be positive or negative as long as the conditions of statement 2, ab > 1 or ab < 0, are respected).
Not sufficient

“Is 2ab > ab?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT official Guide 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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