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# If v ≠ 0, is |w| < |v| ???

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Board of Directors
Joined: 01 Sep 2010
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If v ≠ 0, is |w| < |v| ???  [#permalink]

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05 Mar 2012, 07:13
3
2
00:00

Difficulty:

35% (medium)

Question Stats:

68% (01:32) correct 32% (01:57) wrong based on 389 sessions

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If v ≠ 0, is |w| < |v|?

(1) w/v < 1

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

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Joined: 02 Sep 2009
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If v ≠ 0, is |w| < |v| ???  [#permalink]

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05 Mar 2012, 07:21
1
1
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.

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Re: If v ≠ 0, is |w| < |v| ???  [#permalink]

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05 Mar 2012, 09:23
Bunuel wrote:
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.

I hope you are not the only user on this board, Sir.

Clear as usual. Many Thanks
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Re: If v ≠ 0, is |w| < |v| ???  [#permalink]

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05 Mar 2012, 19:11
carcass wrote:
Bunuel wrote:
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.

I hope you are not the only user on this board, Sir.

Clear as usual. Many Thanks

Bunuel is indeed a legend. I think we need to clone him.
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Re: If v ≠ 0, is |w| < |v| ???  [#permalink]

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19 Feb 2017, 05:39
IN OPTION TWO V^2>w^2 E.G 0.9>0.16 BUT THEIR UNDER ROOT IS SIMPLY OPPOSITE V<W I.E 0.3<0.4 KINDLY CLARIFY
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Re: If v ≠ 0, is |w| < |v| ???  [#permalink]

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19 Feb 2017, 08:56
sati001 wrote:
IN OPTION TWO V^2>w^2 E.G 0.9>0.16 BUT THEIR UNDER ROOT IS SIMPLY OPPOSITE V<W I.E 0.3<0.4 KINDLY CLARIFY

First of all, please turn Caps Lock off when posting.

Next, $$\sqrt{0.9}\approx 0.948683...$$, not 0.3. 0.3^2 =0.09, not 0.9.
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Re: If v ≠ 0, is |w| < |v| ???  [#permalink]

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19 Feb 2017, 10:02
|w| < |v| and w^2 < v^2 are one and the same thing. Both can be used interchangeably so clearly 2 is sufficient.

1 will be sufficient only if both v and w are both positive or both negative. If they have opposite signs then there absolute value (distance from 0 ) can not be compared.

So Answer will be B .
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Re: If v ≠ 0, is |w| < |v| ???  [#permalink]

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08 Mar 2018, 20:04
Hi All,

This question is perfect for TESTing Values (and a bit of Number Properties).

We're told that V≠0 and we're asked if |W|<|V|. This is a YES/NO question.

Fact 1: W/V < 1

Let's TEST VALUES:
If W = 1, V = 2, then the answer to the question is YES.
If W = -3, V = 2, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: W^2/V^2 < 1

This becomes W^2 < V^2.

The Number Property here is that "squaring" a term has the same "effect" as the absolute value signs in the question: any negative signs are removed. This ultimately means that the absolute value of V will ALWAYS be greater than the absolute value of W. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

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Rich
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Re: If v ≠ 0, is |w| < |v| ??? &nbs [#permalink] 08 Mar 2018, 20:04
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