Is pqr 0 ? (1) pq 0 (2) q/r

Question

Is pqr > 0 ? (1) pq > 0 (2) q/r < 0 1 alone insufficient 2 alone insufficient combined sufficient to state that pqr < 0 answer C where do i make a mistake?

shivanisharma · Answer

1). pq > 0 --- It doesn't say anything about r,which can be 0, -ve , +ve . So insuff to figure whether pqr > 0 or not.

2) q/r < 0
Multiply both side by r
(q/r)*r < 0*r
q<0
So 2nd statement tell that q<0 but still we can not predict anything about r and hence insuff to figure whether pqr > 0 or not.

Combining both also doesn't tell anything about r.
So answer should be E

kobi90 · Answer

yeah got it now! however you've made a mistake here as we don't know if r < 0 or > 0 and therefore may need to change the sign while multiplying. hevertheless, thanks!

kobi90 · Answer

one more thought!

1). if pq>0 then p & q are both negative or both positive (still insufficient)
2). q/r<0. Lest multiply both sides by r^2 (no sign change) then we have qr<0 (still insufficient)

but combined we have 2 sets of variables and their signs:
1. p+ q+ r- then pqr<0
2. p- q- r+ then pgr>0

only now having 2 possibilities can state that E is correct!

Bunuel · Answer

Is pqr > 0 ?

(1) pq > 0 --> p and q have the same sign, but we now nothing about r, so this statement is insufficient.

(2) q/r < 0 --> q and r have the opposite signs, but we now nothing about p, so this statement is insufficient.

(1)+(2)If p and q are both positive and r is negative then pqr=positive*positive*negative=negative BUT if p and q are both negative and r is positive then pqr=negative*negative*positive=positive. Not sufficient.

Answer: E.

Hope it's clear.

dvinoth86 · Answer

1+2,

p q r pqr
- - + +
+ + - -

hence E, pqr can be + or - that is pqr can be >0 or <0.

honchos · Answer

___________________________

monirjewel · Answer

Pls put ans in the spoiler option dont show up.....

Bunuel · Answer

Done. Thank you for the suggestion.

mvictor · Answer

1 alone = p+ and q+ or p- and q-
2 alone = p+ and r- or p- and r+
alone insufficient either of them
1+2:
P+ q+ r- => negative or
p- q- r+ -> positive
so insufficient.

E.

lalania1 · Answer

pqr > 0?

stmt1. pq>0 this means same sign => (+) (+) or (-) (-) for p and q but nothing about r. NS.

stmt2. q/r<0 this means differen sign => (+) (-) or (+) (-) for p and r but nothing about p. NS.

combined. you can have (+) (+) (-) for p, q, r and (-) (-) (+) for p, q, r => this gives you negative answer or positive answer. So this is not sufficient.

Answer is E

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. This question is about an inequality. We count 1 inequality in conditions as 1 equation for inequality questions. There are 3 variables and 0 equation. Thus the answer E is most likely. When we consider both conditions 1) and 2) together, we have inequalities pq > 0 and qr < 0 which is equivalent to q/r < 0 . We can't figure our pqr > 0 from those inequalities. Therefore, E is the answer. -> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80 % chance that E is the answer, while C has 15% chance and A, B or D has 5% chance. Since E is most likely to be the answer using 1) and 2) together according to DS definition. Obviously there may be cases where the answer is A, B, C or D.

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 pqr > 0 ? (1) pq > 0 (2) q/r < 0

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