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# Is rw = 0?

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Updated on: 19 Sep 2015, 13:51
4
13
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Difficulty:

5% (low)

Question Stats:

92% (00:38) correct 8% (00:41) wrong based on 1466 sessions

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Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]

Originally posted by BrainLab on 19 Sep 2015, 12:08.
Last edited by ENGRTOMBA2018 on 19 Sep 2015, 13:51, edited 1 time in total.
Edited the question and renamed the topic
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Re: Is rw = 0?  [#permalink]

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19 Sep 2015, 13:56
3
BrainLab wrote:
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]

Is rw=0---> will be true if 1 of the r=0 or w=0 or r=w=0 is true.

Per statement 1, -6<r<5, you will get a "yes" with r=0 for all values of 'w' but a "no" with r=-4 and w=10. Thus not sufficient.

Per statement 2, 6<w<10, you will get a "yes" with r=0 for all values of 'w' but a "no" with r=-4 and w=8. Thus not sufficient.

Combining, -6<r<5 and 6<w<10, you get a "yes" if r=0 and w=7 but get a "no" for r=-4 and w=8. Thus still the statements are not sufficient.

E is thus the correct answer.
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13 Oct 2017, 13:48
1
Statement 1 is telling us that r could be positive or negative (i.e. r could be -4 or 3) so we do not know what r equals
This is insufficient AND we do not know what w equals.

Statement 2 is telling us that w is a positive number between 6 and 10 (but w can't be 6 or 10!) so we do not know what w equals.
This is insufficient AND we do not know what r equals

Combining both statements still gives insufficient information so the answer is E. Since we are given only inequalities for r and w, then we cannot solve the equation. You could also think of it as: combining both statements we cannot definitively say what r and/or w equals so we cannot solve rw.
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Re: Is rw = 0?  [#permalink]

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10 Jan 2018, 08:05
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1
BrainLab wrote:
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Target question: Is rw = 0?
Since each statement ALONE fails to provide information about both variables, let's jump straight to....

Statements 1 and 2 combined
There are several values of r and w that BOTH statements. Here are two:
Case a: r = 0 and w = 7, in which case rw = (0)(7) = 0
Case b: r = 1 and w = 7, in which case rw = (1)(7) = 7
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
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Re: Is rw = 0?  [#permalink]

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07 Jul 2019, 00:58
Hi - Apart from teh number substitution method, is this approach also correct -

-6 < r < 5 --------------- 1)
6 < w < 10 -------------- 2)

Multiplying 1& 2, we get -36 < rw < 50. Hence not sufficient.

Thanks,
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Re: Is rw = 0?  [#permalink]

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07 Jul 2019, 01:42
BrainLab wrote:
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]

Case I- r can be any no. between -6 and 5. It can be 0 as well, so the answer to this is NOT SUFFICIENT

Case II- w can be anything but we cannot determine the value of r, which can be 0. So the ans is NOT SUFFICIENT

Combining 1&2, we still cannot determine because r can be 0 in this case as well.

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Re: Is rw = 0?  [#permalink]

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20 Jul 2019, 10:54
kanikab wrote:
Hi - Apart from teh number substitution method, is this approach also correct -

-6 < r < 5 --------------- 1)
6 < w < 10 -------------- 2)

Multiplying 1& 2, we get -36 < rw < 50. Hence not sufficient.

Thanks,

kanikab, wouldn't suggest it as it's not intuitive.
Better to follow the order (i.e. check Statement (1), then Statement (2), so on) and insert values for the variables.

If the two statements are combined, $$-60 < rw < 50$$.
Lower limit of $$rw$$ would be $$-60$$ and not $$-36$$. (See? It isn't intuitive. You can get confused.)

Even if your resultant range of $$rw$$ is considered, can't $$rw$$ be $$0$$ since $$0$$ lies between $$-36$$ and $$50$$?
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Re: Is rw = 0?  [#permalink]

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21 Jul 2019, 02:50
BrainLab wrote:
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]

(1) −6 < r < 5
If r=0 => rw=0 otherwise rw<>0
NOT SUFFICIENT

(2) 6 < w < 10
Since w<>0 => If r=0 => rw=0 otherwise rw<>0
NOT SUFFICIENT

Combing (1) & (2)
(1) −6 < r < 5
(2) 6 < w < 10
If r=0 => rw=0 otherwise rw<>0
NOT SUFFICIENT

IMO E
Re: Is rw = 0?   [#permalink] 21 Jul 2019, 02:50
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