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

[ichai]

There is an error in the explanation.

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.

Test values above should also meet the condition p<r but the test values use r<p.

[RonPurewal]

please post the question and the answer choices.
thx.

--

by the way, there's a much quicker solution than the one posted: because we know that p is negative, we can divide by it on both sides and flip the inequality sign. this gives the new and improved question "is qr > 1?"
this can actually be done on both statements, because p is negative under either of the two constraints.

[ahistegt]

Here is the full stem - would appreciate methods different to the one included in the CAT:

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

(1) pq < 0

(2) pr < 0

[Guest]

Answer is E.
Explanation: using plugging method try to get YES and NO both for yes / no DS question.
Statement 1) Statement 2)
p q r (p < q) (p < r) (pq < 0) (pr < 0) Is (pqr < p)
Statement 1) Alone -4 2 2 TRUE TRUE TRUE - YES ( -16 < -4)
Statement 1) Alone -4 2 -2 TRUE TRUE TRUE - NO ( 16 < -4)
Statement 2) Alone -4 2 2 TRUE TRUE - TRUE YES ( -16 < -4)
Statement 2) Alone -4 -2 2 TRUE TRUE - TRUE NO ( 16 < -4)
Now1) & 2) together -4 2 2 TRUE TRUE TRUE TRUE YES ( -16 < -4)
Now 1) & 2) together -4 0.5 0.4 TRUE TRUE TRUE TRUE NO ( -0.8 < -4)

Step 1): we can see statement 1) alone is not sufficient. thus eliminate A and D
Step 2): we can see statement 2)) alone is not sufficient. thus eliminate B also
Step 3): we can see statement 1) & 2) together are not sufficient. thus eliminate C also

thus Answer is E

[Guest]

Answer is E.
Explanation: using plugging method try to get YES and NO both for yes / no DS question.

Step 1): take statement 1 alone
Put p = -4 , q = 2 and r =2 => YES ( -16 < -4)
Put p = -4 , q = 2 and r =-2 => No ( 16 < -4)
we can see statement 1) alone is not sufficient. thus eliminate A and D

Step 2): take statement 1 alone
Put p = -4 , q = 2 and r =2 => YES ( -16 < -4)
Put p = -4 , q = -2 and r =2 => No ( 16 < -4)
we can see statement 2)) alone is not sufficient. thus eliminate B also.

Step 3): take statement 1 & 2 together.
Put p = -4 , q = 2 and r =2 => YES ( -16 < -4)
Put p = -4 , q = 0.5 and r =0.4 => No ( -0.8 < -4)

we can see statement 1) & 2) together are not sufficient. thus eliminate C also



thus Answer is E[/img]

[experts]

Answer is E.
Explanation: using plugging method try to get YES and NO both for yes / no DS question.

Step 1): take statement 1 alone
Put p = -4 , q = 2 and r =2 => YES ( -16 < -4)
Put p = -4 , q = 2 and r =-2 => No ( 16 < -4)
we can see statement 1) alone is not sufficient. thus eliminate A and D

Step 2): take statement 1 alone
Put p = -4 , q = 2 and r =2 => YES ( -16 < -4)
Put p = -4 , q = -2 and r =2 => No ( 16 < -4)
we can see statement 2)) alone is not sufficient. thus eliminate B also.

Step 3): take statement 1 & 2 together.
Put p = -4 , q = 2 and r =2 => YES ( -16 < -4)
Put p = -4 , q = 0.5 and r =0.4 => No ( -0.8 < -4)

we can see statement 1) & 2) together are not sufficient. thus eliminate C also



thus Answer is E[/img]

[JonathanSchneider]

Ichai (original poster), be careful: you are taking Statement 2 into consideration when we should be looking at Statement 1 alone.

Nice work to those of you who tested all these numbers. But check Ron's original post here. Because we know that p is negative, we can divide both sides of the inequality by p and flip the sign, leaving us with the question: is qr > 1. While we know that q and r are both positive, we do not know whether their product is greater than 1.