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# Is rw = 0?

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Re: Is rw = 0? [#permalink]
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BrainLab
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]
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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BrainLab
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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kanikab
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]
BrainLab
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
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Re: Is rw = 0? [#permalink]
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: Is rw = 0? [#permalink]
BrainLab
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]

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Re: Is rw = 0? [#permalink]
BrainLab
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]
Solution:

Question Stem Analysis:

We need to determine whether rw is 0.

Statement One Alone:

Since we don’t know anything about the value of w, we can’t determine whether rw is 0. Statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know anything about the value of r, we can’t determine whether rw is 0. Statement two alone is not sufficient.

Statements One and Two Together:

With the two statements, we still don’t have enough information to determine whether rw is 0. For example, if r = 0 and w = 7, then rw = 0. However, if r = 1 and w = 7, then rw ≠ 0. Both statements together are still not sufficient.

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Re: Is rw = 0? [#permalink]
BrainLab
Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source: [OG 2016]

If the break the question stem to its core, it is essentially asking us whether one or r or w is 0, or both are zero; either case answers the question stems. So with that in mind let's begin the statement analysis:

S1: Not sufficient. r can take any value from the given range. Additionally, we do not know anything about w. Trike off A and D.
S2. Not sufficient. w certainly isn't zero as we can see from the range. But does this statement tell us anything about r? Nope. Strike off B.

Combining S1 and S2: w cant be 0, we know that for sure. What can be said about r here? We are still stuck with the same question as our analysis of S1. r could be anything from the range. Therefore we cannot conclude whether rw=0 even after combining the statements.

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Re: Is rw = 0? [#permalink]
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Re: Is rw = 0? [#permalink]
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