Data Sufficiency

Brent@GMATPrepNow wrote:

gmattesttaker2 wrote:Hello,

Can you please help with solving Statement2 ?

If vm is not equal to 0, is vm > 0?

1) v²m = vm²
2) |m|v = |v|m

The important rule at play here is that, if the QUOTIENT of two numbers is positive, then the PRODUCT of those same two numbers must also be positive.
For example, 6/3 is positive, and (6)(3) is also positive
Likewise, (-8)/(-4) is positive, and (-8)(-4) is also positive

Target question: Is vm positive?

Given: vm ≠ 0
In other words, v ≠ 0 and m ≠ 0

Statement 1: v²m = vm²
Take v²m = vm²
Divide both sides by v² to get: m = (vm²)/v²
Divide both sides by v to get: m/v = m²/v²
IMPORTANT: If v ≠ 0 and m ≠ 0, then v² is positive and m² is positive.
So, we get: m/v = (positive)/(positive)
In other words, m/v = some positive value
By the red rule above, we can conclude that mv is positive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: |m|v = |v|m
Take |m|v = |v|m
Divide both sides by m to get: (|m|v)/m = |v|
Divide both sides by |m| to get: v/m = |v|/|m|
IMPORTANT: If v ≠ 0 and m ≠ 0, then |v| is positive and |m| is positive.
So, we get: v/m = (positive)/(positive)
In other words, v/m = some positive value
By the red rule above, we can conclude that mv is positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent