If p < q and p < r, is (p)(q)(r) < p

[dumplinghao]

If p < q and p < r, is (p)(q)(r) < p?

(1) pq < 0

(2) pr < 0


The question tells us that p < q and p < r and then asks whether the product pqr is less than p.

Statement (1) INSUFFICIENT: We learn from this statement that either p or q is negative, but since we know from the question that p < q, p must be negative. To determine whether pqr < p, let's test values for p, q, and r. Our test values must meet only 2 conditions: p must be negative and q must be positive.

I follow the explanation up to this point because next, the solution tests values, and this is where I get confused. You assign both -10 and 10 to the value r. But doesn't the parameter above state that p is less than r? So if you assign p = to -2, r cannot be -10.

[StaceyKoprince]

You are absolutely right! It should read that r = -1, not -10, which makes pqr 10, which is not less than p.

Thanks for catching that typo - great job!

[Guest]

What is the answer to this question?

I got D. For the reasons discussed above, statement one is insufficient because it only states that p is negative and q positive. Statement two is likewise insufficient because it only states that p is negative and r is positive.

Taken together, the statements indicate that q and r are both positive and p is negative. If r a dn q are both positive fractions, say 1/2 and 1/4, and p is a negative integer (like -3), then the statement pqr<p will be false. But if q and r are both positive whole numbers, then the statement pqr<p will be true.

[RonPurewal]

What is the answer to this question?

I got D. For the reasons discussed above, statement one is insufficient because it only states that p is negative and q positive. Statement two is likewise insufficient because it only states that p is negative and r is positive.

Taken together, the statements indicate that q and r are both positive and p is negative. If r a dn q are both positive fractions, say 1/2 and 1/4, and p is a negative integer (like -3), then the statement pqr<p will be false. But if q and r are both positive whole numbers, then the statement pqr<p will be true.

100% correct.

one problem only: you don't appear to have a handle on the data sufficiency answer choices. choice d means that either answer alone is sufficient. the correct answer, as you've explained quite well, is e (both together = still not sufficient).

[Ali]

You are absolutely right! It should read that r = -1, not -10, which makes pqr 10, which is not less than p.

Thanks for catching that typo - great job!

Shouldn't they fix this in the online CAT?

[RonPurewal]

Shouldn't they fix this in the online CAT?

well, sure. when we say thanks for calling the typo to our attention, we are of course implying that we'll go in and fix it asap.
we don't (yet) have time machines that will allow us to do that before the original poster posted about the typo in the first place, though, so that comment will remain on the thread.

[vivekghegde]

Stacey, Ron,

I received the exact same question in my MGMAT CAT test i took today.
The answer explanation part still carries this typo.

-Vivek

[Ben Ku]

Hi Vivek,

Thanks for pointing this out. I'll send it up again and see if it gets resolved. THanks.