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# Is v−w<0?

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Joined: 04 Oct 2018
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Schools: Wharton '21
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Updated on: 14 Oct 2018, 19:13
5
00:00

Difficulty:

85% (hard)

Question Stats:

41% (01:51) correct 59% (01:50) wrong based on 78 sessions

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Is v−w<0?

(1) v−2w<0

(2) 5w−v<0

PrepScholar

Originally posted by wunstepcloser on 14 Oct 2018, 17:55.
Last edited by chetan2u on 14 Oct 2018, 19:13, edited 1 time in total.
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14 Oct 2018, 19:19
1
1
Is v−w<0?
Or is $$v<w?$$

(1) v−2w<0
v<2w...
if v is 4 and W is 3....v>W
If v is 4 and W is 7.....v<w
Insufficient

(2) 5w−v<0
5w<v
If both v and w are positive, w<v
If both are negative, say v=-2 and w=-1, w>v
Insufficient

Combined
2w>v>5w
So 5w<2w...3w<0....w<0 and so v<2w means v<w
Sufficient

C
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14 Oct 2018, 20:00
chetan2u wrote:
Is v−w<0?
Or is $$v<w?$$

Combined
2w<v<5w
So 5w>2w...3w>0....w>0 and so v>2w means v>w
Sufficient

C

Hi Chetan2u,

I could not get the last part. If we combine 1 and 2 should not the equation be 5w<v<2w
=> w<0 . Although the answer would still be C.
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14 Oct 2018, 20:06
dvishal387 wrote:
chetan2u wrote:
Is v−w<0?
Or is $$v<w?$$

Combined
2w<v<5w
So 5w>2w...3w>0....w>0 and so v>2w means v>w
Sufficient

C

Hi Chetan2u,

I could not get the last part. If we combine 1 and 2 should not the equation be 5w<v<2w
=> w<0 . Although the answer would still be C.

Thanks Vishal .. it was a typo corrected it.
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15 Oct 2018, 03:27
chetan2u wrote:
Is v−w<0?
Or is $$v<w?$$

(1) v−2w<0
v<2w...
if v is 4 and W is 3....v>W
If v is 4 and W is 7.....v<w
Insufficient

(2) 5w−v<0
5w<v
If both v and w are positive, w<v
If both are negative, say v=-2 and w=-1, w>v
Insufficient

Combined
2w>v>5w
So 5w<2w...3w<0....w<0 and so v<5w means v<w
Sufficient

C

I think you reversed the sign. According to statement 2: v>5w.
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15 Oct 2018, 06:39
1
Top Contributor
1
wunstepcloser wrote:
Is v − w < 0?

(1) v − 2w < 0
(2) 5w − v < 0

Target question: Is v − w < 0?
This is a good candidate for rephrasing the target question.
Take: v − w < 0
Add w to both sides to get: v < w
REPHRASED target question: Is v < w?

Statement 1: v − 2w < 0
Let's TEST some values.
There are several values of v and w that satisfy statement 1. Here are two:
Case a: v = 0 and w = 1. In this case, the answer to the REPHRASED target question is YES, it is true that v < w
Case b: v = 3 and w = 2. In this case, the answer to the REPHRASED target question is NO, it is NOT true that v < w
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 5w − v < 0
Let's TEST some values.
There are several values of v and w that satisfy statement 2. Here are two:
Case a: v = -2 and w = -1. In this case, the answer to the REPHRASED target question is YES, it is true that v < w
Case b: v = 1 and w = 0. In this case, the answer to the REPHRASED target question is NO, it is NOT true that v < w
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that v − 2w < 0
Statement 2 tells us that 5w − v < 0
If we ADD the two inequalities, we get: 3w < 0, which means w is NEGATIVE

Also, if we can take v − 2w < 0 and add 2w to both sides, we get v < 2w
And, if we can take 5w − v < 0 and add v to both sides, we get 5w < v
So, we can combine the inequalities to get: 5w < v < 2w
Since, we already know that w is NEGATIVE, we know that 2w < w
So, we can add this to our existing inequality to get: 5w < v < 2w < w
At this point, we can see that within our inequality, it is certain that v < w
In other words, the answer to the REPHRASED target question is YES, it is true that v < w
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

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06 Aug 2019, 07:19
Can someone please solve this for me, using number line ?
Is v−w<0?   [#permalink] 06 Aug 2019, 07:19
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