Is rw = 0?

Question

Is rw = 0?

(1) −6 < r < 5
(2) 6 < w < 10

Source:

ENGRTOMBA2018 · Accepted Answer

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.

MarcelinaT · Answer

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.

BrentGMATPrepNow · Answer

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

Answer: E

Cheers,
Brent

kanikab · Answer

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,

hriday17 · Answer

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.

So the answer is E

Palladin · Answer

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 ?

Kinshook · Answer

Asked: Is rw = 0? (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

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=WCy0LdspDIU

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=WhSn02a6BP4

ScottTargetTestPrep · Answer

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.

Answer: E

palaknayyar · Answer

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.

Hence final answer E.

Hope that is helpful.

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Is rw = 0?

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