Is (a/d)(b/e)(d/f) (b/d)(c/e) ? (1) bc de (2) a f

Question

Is  (\frac{a}{d})(\frac{b}{e})(\frac{c}{f}) > (\frac{b}{d})(\frac{c}{e})  ?

(1)  bc > de

(2)  a > f

siglon · Answer

When seeing  inequalities and variables , the following thoughts go through my head:
- I have to consider that variables can be zero, positive, or negative.
- I cannot cross multiply or multiply/divide by a variable without knowing if the variable is zero, positive, or negative.

I want to rewrite the question to the following:
 Is  (\frac{a}{f})(\frac{bc}{de})>(\frac{bc}{de}) ? 
If you can 100 % determine which side of the inequality sign is biggest, you can answer the question.

Statement 1: 
This statement does NOT mean that  (\frac{bc}{de})  must be more than 1. It is true that  bc  can be  5  while  de  is  2 , but it can also be true that  bc  is  2  and  de  is  -5 . Though, it cannot be between 0 and 1, since  bc  cannot be less than  de  if both are positive.
So we get that  (\frac{bc}{de})>1  or  (\frac{bc}{de})\leq{0} .
We do not know if the RHS (right-hand-side) is positive or negative, and we do not know how  \frac{a}{f}  affects the LHS (left-hand-side).
 INSUFFICIENT

Statement 2: 
From this information we can make the same inferences, only with  \frac{a}{f} .
Too little information to say which side of the inequality sign is biggest.
 INSUFFICIENT

Statement 1 and 2 together: 
Too much is still unknown...
Let us say that  (\frac{bc}{de})  is equal to  3 . Then  \frac{a}{f}  could be  2 , making the answer to the question YES.
Let us say that  (\frac{bc}{de})  is equal to  3 . Then  \frac{a}{f}  could be  -2 , making the answer to the question NO.
 INSUFFICIENT

Nidzo · Answer

Rearranging the inequality:   \frac{a}{f}*\frac{bc}{de}>\frac{bc}{de}

divide both sides by  \frac{bc}{de}

\frac{a}{f}>1

a>f

Now the question is asking merely if  a  is greater than  f .

(1)  No information is provided on  a  and  f .

INSUFFICIENT

(2)  Provides the exact information needed to answer the question stem, a  is indeed greater than  f .

SUFFICIENT

Answer B

siglon · Answer

You are implying that  \frac{bc}{de}  is positive. If  \frac{bc}{de}  is negative, you have to flip the inequality.
We do not know if  \frac{bc}{de}  is zero, positive, or negative. So your rearrangement is not correct.

Shivanibh25 · Answer

Can you please explain why is it not B?

SaquibHGMATWhiz · Answer

Solution: Pre Analysis: We are asked if (\frac{a}{d})(\frac{b}{e})(\frac{c}{f}) > (\frac{b}{d})(\frac{c}{e}) or not ⇒\frac{abc}{def}-\frac{bc}{de}>0 ⇒\frac{bc}{de}(\frac{a}{f}-1)>0 This is possible in 2 cases: Case 1: \frac{bc}{de}>0 and \frac{a}{f}>1 Case 2: \frac{bc}{de}<0 and \frac{a}{f}<1 Statement 1: bc > de We can have both the cases here Case 1: \frac{bc}{de}>0 when bc=4 and de=2 Case 2: \frac{bc}{de}<0 when bc=4 and de=-2 Thus, statement 1 alone is not sufficient and we can eliminate options A and D Statement 2: a > f We can have both the cases here Case 1: \frac{a}{f}>1 when a=4 and f=2 Case 2: \frac{a}{f}<1 when a=4 and f=-2 Thus, statement 2 alone is also not sufficient Combining: Still both the cases are possible Hence the right answer is Option E NOTE: The most important thing in this question is the ability to handle inequalities well . For example bc > de doesnt mean that we can say \frac{bc}{de}>1 . We cannot say that without knowing the positive negative nature of de

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is (a/d)(b/e)(d/f) > (b/d)(c/e) ? (1) bc > de (2) a > f

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions