MGMAT inequality!! right or wrong?

[bsandhyav]

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

(1) pq < 0

(2) pr < 0

Guyz share your thoughts on this MGMAT Q!!!
I strongly feel the answer is D...however MGMAT says it is C....how?

[Stuart@KaplanGMAT]

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

(1) pq < 0

(2) pr < 0

Guyz share your thoughts on this MGMAT Q!!!
I strongly feel the answer is D...however MGMAT says it is C....how?

We know that p is the smallest of the 3 variables. So, how could the product of the 3 be less than p? Most likely, either fractions or negatives will be involved to make that happen.

(1) pq < 0

To get a negative product, we need (-)*(+).
We know that p < q, so we now know that p is negative and q is positive.

However, we can still get both a yes and a no to the original question, since we don't know the sign of r.

If r is negative, then pqr = (-)(+)(-) which is positive, so we'll get a "NO" answer to the question (e.g. if p=-10, q=4, r=-3, pqr = 120).

If r is positive, then pqr = (-)(+)(+) which is negative, so we could get a "YES" answer to the question (e.g. if p=-10, q=2 and r=3, pqr = -60).

Therefore, (1) is insufficient.

(2) pr < 0

Using the exact same reasoning as above, insufficient.

We've eliminated (a), (b) and (d). We're left with (c) and (e), so we need to look at the statements together.

Combined, we know that p is - and that both q and r are +. So, pqr is negative.

HOWEVER, just because it's negative doesn't mean that pqr < p. We can still get both a yes and a no answer.

If p=-10, q=2 and r=3, pqr = -60. Is -60 < -10? YES

If p=-10, q=1 and r=1, pqr = -10. Is -10 < -10? NO

We also could have picked fractions to get a "NO" answer:

If p=-10, q=1/4 and r = 1/2, pqr = -10/8. Is -10/8 < -10? NO

So, even after combining, we can't answer the question: choose (E).

Are you sure that the OA is (C)?

[bsandhyav]

Yes...i'm sure the OA is given as C

[bsandhyav]

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

(1) pq < 0

(2) pr < 0

Guyz share your thoughts on this MGMAT Q!!!
I strongly feel the answer is D...however MGMAT says it is C....how?

We know that p is the smallest of the 3 variables. So, how could the product of the 3 be less than p? Most likely, either fractions or negatives will be involved to make that happen.

(1) pq < 0

To get a negative product, we need (-)*(+).
We know that p < q, so we now know that p is negative and q is positive.

However, we can still get both a yes and a no to the original question, since we don't know the sign of r.

If r is negative, then pqr = (-)(+)(-) which is positive, so we'll get a "NO" answer to the question (e.g. if p=-10, q=4, r=-3, pqr = 120).

If r is positive, then pqr = (-)(+)(+) which is negative, so we could get a "YES" answer to the question (e.g. if p=-10, q=2 and r=3, pqr = -60).

r cannot be positive since p<r (given in question stimulus). Therefore (1) should be sufficient.
Similar is the case with (2)
Therefore 2 is also sufficient
Am i going wrong somewhere???

[logitech]

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

(1) pq < 0

(2) pr < 0

Guyz share your thoughts on this MGMAT Q!!!
I strongly feel the answer is D...however MGMAT says it is C....how?

So Is P-PQR>0 P(1-QR)>0

P>0 and 1>QR

or

P<0 and 1<QR

Both statements give no information about both P,Q and R

ST 1+2)

(1) pq < 0

(2) pr < 0

+
---------------------

p(q+r)<0

either p<0 and q+r>0

or P>0 and q+r< 0 BUT THIS IS NOT FEASIBLE since we know that P is the smallest.

So combining these two statement will give us:

p<0 and q+r>0

So if we remember the question stem:

IS P<0 and 1<QR ?

We know that P<0 but and both Q and R are greater than 0.


q>0 and r>0 but we have not enough information to decide whether QR>1.

Hence, the correct answer neeeds to be E

[logitech]

Okay it is 2:17 AM in California and I can finally sleep now after finding out that this MGMAT question actually had a TYPO in its explanation and the OA is E

https://www.manhattangmat.com/forums/if- ... t1914.html

[austin]

Yes, the answer is E....

[Stuart@KaplanGMAT]

Okay it is 2:17 AM in California and I can finally sleep now after finding out that this MGMAT question actually had a TYPO in its explanation and the OA is E

https://www.manhattangmat.com/forums/if- ... t1914.html

Yay!

[niraj_a]

thanks stuart and logitech, i chose E and felt dejected for a second when i saw the spoiler, and then both of your messages made me happy again