Fun with r!

[TryHarder]

Is rs = rx - 2?
1. r is an odd number
2. x = s + 2

Note: For those of you who have seen this question in the official source, try not to copy the official explanation. Is is not very convincing, hence this query.

[raleigh]

(1) r is odd.
Choose r = 1, s = 2, x = 4. Then rs = 2, rx - 2 = 2.
Choose r = 1, s = 2, x = 2. Then rs = 2, rx - 2 = 0.

Insufficient.

(2) x = s + 2. Substitute this into rx - 2 = r (s + 2) - 2 = rs + 2r - 2.

Set this equal to rs and we see this will be valid for rs= rs + 2r - 2 which simplifies to r=1.

Choose r = 1, x = 1, s = -1. Then rs = -1, and rx - 2 = 1 -2 = -1.
Choose r = 3, x = 2, s = 0. Then rs = 0, and rx - 2 = 6 - 2 = 4.

Insufficient.

(1)+(2)
Notice that in (2) we chose r to be odd in both cases. So the argument for (2) applies to this case.

Insufficient.

The answer is E.

[TryHarder]

raleigh,
I came up with the same answer, but the official answer is B, even though is is true only when r=2.

Came an expert shed some light on this?

[raleigh]

My counter example for (2) is correct so it cannot be B.

The OA is incorrect unless you mistyped the problem. Which problem is this in the OG?

[TryHarder]

I think you misunderstood my point, I did imply that I too think the answer should be E for the very obvious reason that statement 2 is true only for r=2 and not always. Also, there is nothing wrong with the problem as stated.

[raleigh]

I understand your point. I'd like to see the actual OA; what book is this from and what is the number for this problem? It has to be wrong.

[TryHarder]

McGraw Hills GMAT 2009 Practice Test 3: Q27

[greymatter]

yes E.
B would have been the answer if it also tells us that r =1; which is is not so.

[riya.sharma.sweet1984]

Answer E

[aj5105]

In statement (2), we get r = 1. In the part underlined, you chose r = 3

Is this right? Please clarify.

IMO, you can as well use the same values what you used in Statement (1)

(1) r is odd.
Choose r = 1, s = 2, x = 4. Then rs = 2, rx - 2 = 2.
Choose r = 1, s = 2, x = 2. Then rs = 2, rx - 2 = 0.

Insufficient.

(2) x = s + 2. Substitute this into rx - 2 = r (s + 2) - 2 = rs + 2r - 2.

Set this equal to rs and we see this will be valid for rs= rs + 2r - 2 which simplifies to r=1.

Choose r = 1, x = 1, s = -1. Then rs = -1, and rx - 2 = 1 -2 = -1.
Choose r = 3, x = 2, s = 0. Then rs = 0, and rx - 2 = 6 - 2 = 4.

Insufficient.

(1)+(2)
Notice that in (2) we chose r to be odd in both cases. So the argument for (2) applies to this case.

Insufficient.

The answer is E.

[sacx]

r0 + s = r0 + x - 2
s = x -2
x = s +2

STMT I

Does not tell anything about s or x

Insuff

STMT II

this is what the question is asking

Insuff

STMT I & II

Insuff, as we do not know anything about s or x

E