If v ≠ 0, is |w|

Question

If v ≠ 0, is |w| < |v|?

(1) w/v < 1

(2) w^2/v^2 < 1

Bunuel · Accepted Answer

If v ≠ 0, is |w| < |v|?

(1) w/v < 1 --> if \(w=1\) and \(v=2\) the answer is YES but if \(w=-2\) and \(v=1\) the answer is NO. Not sufficient.

(2) w^2/v^2 < 1 --> since \(v^2>0\) then we can safely cross multiply: \(w^2<v^2\) --> \(|w|<|v|\). Sufficient.

Answer: B.

Kinshook · Answer

Asked: If v ≠ 0, is |w| < |v|?

(1) w/v < 1
If w = -5; v = 1; w/v = -5 <1 & |w| > |v|
But if w = 1; v = 5; w/v = 1/5 <1 & |w| < |v|
Since signs of w & v are unknown
NOT SUFFICIENT

(2) w^2/v^2 < 1

(|w|/|v|)^2 < 1
-1 < |w|/|v| < 1
But |w| & |v| are both positive; |w|/|v| can not be negative
|w| / |v| < 1
|w| < |v|
SUFFICIENT

IMO B

abs8 · Answer

why not cross multiply statement 1, why only 2?

Bunuel · Answer

We cannot multiply w/v < 1 by v and write w < v because we don't know the sign of v. If v is positive, then yes, we'd get w < v (keep the sign when multiplying by positive value) but if v is negative, then when we multiply by negative value we should flip the sign and we'd get w > v (recall that we should flip the sign of an inequality if we multiply/divide it by negative value)..

Never multiply (or reduce) an inequality by a variable (or the expression with a variable) if you don't know its sign.

For (2) v^2 must be positive so it's safe to multiply by it.

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.

If v ≠ 0, is |w| < |v|? (1) w/v < 1 (2) w^2/v^2 < 1

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