If \(abc \neq 0\), is a < b < c? (1) 1/c < 1/b < 1/a (2) c > a GMAT Data Sufficiency

Question: If \(abc \neq 0\), is a < b < c ?

1. \(\frac{1}{c}<\frac{1}{b}<\frac{1}{a}\)
2. c > 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):

(1) \(\frac{1}{c} < \frac{1}{b} < \frac{1}{a}\)

Take two cases of number sets satisfying the statement 1
Since \(\frac{1}{3} < \frac{1}{2} < \frac{1}{1}\)

Case I: a = 1, b = 2, c = -3
1 < 2 < 3 so a < b < c

These values give an answer YES TO ABOVE YES/NO question.

Also, \(\frac{1}{-3} < \frac{1}{2} < \frac{1}{1}\)

So let’s take case II: a = 1, b = 2, c = -3
1 < 2 but not < -3 so a < b < c is not true in this case
Answer: NO

So statement I is not sufficient. So B, C, and E are left.

(2) c > 1

3 > 1 or -1 > -3 but there is no value or constraint for B

Case I: a = 1, b = -2, c = 3 satisfies c > a but a < b < c is not true in this case
Case II: a = 1, b = 5, c = 3 satisfies c > a but a < b < c is not true in this case
Case III: a = 1, b = 2, c = 3 satisfies c > a but a < b < c is also true in this case
Case IV: a = -3, b = -2, c = -1 satisfies c > a but a < b < c is also true in this case
Therefore statement II is also not sufficient

So either C or E

(1) and (2) together
c > a and \(\frac{1}{c} < \frac{1}{a}\)

So both C and A should have same sign i.e., either positive or negative
And b should be in between a and c as in below cases

a = 1, b = 2, c = 3
a = -1, b = -2, c = -3

Correct Option: C

“If \(abc \neq 0\), is a < b < 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.

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