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If m and r are two number on a number line, What is the [#permalink]

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12 Jan 2009, 06:23

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If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

a:r=3m (insuff) b:m+d=12=r-d or r+d=12=m-d (insuff)

If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

a:r=3m (insuff) OR r = -3*m b:m+d=12=r-d or r+d=12=m-d (insuff) 2) the average of m & r is 12 i.e. (m+r)/2=12, we can have differnt values for m & r, so insuff

together, substitute r in (2), since r has 2 different values, we still can not find out exact value of r. E

I still can't get how comes E, as I can find an exact value for r.

stmt 1: r=3m, we have a linear equation with 2 variables, thus INSUFF.

stmt 2: if 12 is the halfway between r and m, it means that the 12 is the average of r and m. It means that (r+m)/2=12 => r+m=24. Still, one linear equation with two variables, thus INSUFF.

Both stmts together: Substitute m=r/3 in the second equation yields r=18, thus SUFF and my answer is C.

Can someone please explain where my approach is flawed?

If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

a:r=3m (insuff) OR r = -3*m b:m+d=12=r-d or r+d=12=m-d (insuff) 2) the average of m & r is 12 i.e. (m+r)/2=12, we can have differnt values for m & r, so insuff

together, substitute r in (2), since r has 2 different values, we still can not find out exact value of r. E

You are right; nothing in A says that r and m>0. But both have to be on the same side of zero (either positive or negative side of zero). 12 being in the middle of the two is sufficient to pinpoint the location of both m and r. Hence, may be I am questioning the OA. Is there OE?
_________________

The best way to resolve is look for GMAT conventions. In such problems, are we to assume that the numbers are to lie on the positive side of zero.
_________________

If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

Using both statements, you still have two possibilities:

m = 6, r = 18 m = -12, r = 36.

The answer is E.
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

Statement I : This statement is insufficient as it only gives us information that r=3m.

Statement II : This statement alone is insufficient as it just says that 12 is half way between m & r. That can be any value of r.

Combined together, the only possible answer for r=18. Hence the answer is C

The best way to resolve is look for GMAT conventions. In such problems, are we to assume that the numbers are to lie on the positive side of zero.

On the GMAT, do not assume anything. If the question doesn't tell you that the numbers are positive, you'll likely be landing in a trap if you assume they are. For the question above, if you assume r and m are both positive, you'll arrive at the conclusion that the answer is C. It's not C, because m can be negative. The answer is E, as I pointed out above.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

If m and r are two number on a number line, What is the value of r? A. The distance between r and 0 is 3 times the distance between m and 0 B. 12 is the halfway between m and r

Using both statements, you still have two possibilities:

m = 6, r = 18 m = -12, r = 36.

The answer is E.

You have an interesting arguement & I believe you are right. What is the OA?