If p

Question

If p < q and p < r, is pqr < p?

(1) pq < 0
(2) pr < 0

i did it in this way:
Question : p(qr-1)<o
P<0 or qr< 1 ?

combined both statements say that p<0 
So according to the logic above, why answer C (both ) is not sufficient ?

Anybody ? 
Thanks

Bunuel · Accepted Answer

What does "C (both ) is not sufficient" mean? Anyway: If p < q and p < r, is pqr < p? Given: p0 . Since p<0 then the question becomes: Is qr-1>0 (in p(qr-1) first multiple is negative, p<0 , so in order the product to be negative second multiple must be positive, qr-1>0 ) Is qr>1 ? We know that q>0 but all we know about r is that p0 . Since p<0 then the question becomes: Is qr-1>0 ? Is qr>1 ? We know that r>0 but all we know about q is that p0 and r>0 . Again, the question becomes: is qr>1 ? Even though both q and r are positive their product still can be more than 1 (for example q=1 and r=2 ) as well as less then 1 (for example q=1 and r=\frac{1}{3} ) or even equal to 1. Not sufficient. Answer: E.

tinki · Answer

aha, Got it. i was making some stupid assumptions. (as always :-D

) + Kudo for the best explanation and swift response thanks again

gmat1220 · Answer

1) Insufficient. Does not preclude r from being zero

2) Insufficient. Does not preclude q from being zero

1) + 2)

Consider p -ve and q and r +ve.

let p = -1. q = 2 r = 3. The answer is YES
let p = -1. q = 0.5 r = 0.6. The answer is NO

Insufficient. Hence E

subhashghosh · Answer

The question asks :

pqr - p < 0

=> p(qr - 1) < 0

=> either p < 0 and qr > 1 or p > 0 and qr < 1

From (1) it can be seen that q > 0 and p < 0

But no information about r, hence insufficient

e.g. if 0 < r < 1 or if r < 0 and 0 < q < 1, then qr < 1

From (2), pr < 0 => r > 0 and p < 0

But no information about q, hence insufficient

e.g. if r > 1 and then qr > 1 and the expression is true, but may not be so otherwise

Combining (1) and (2) also, nothing is conclusive about qr, so answer is E.

bodleyev · Answer

Restate the question stem: "is p(qr - 1) < 0?"

Statement 1) pq < 0 implies that pq != 0 and that p and q have different signs. Since p < q, p < 0 < q.

Since p < 0, the question stem becomes "qr - 1 > 0?", or "qr > 1?"

We have deduced that q > 0, but nothing about r so the statement is insufficient.

Yes example: {p,q,r} = {-5, 2, 5} and pqr < p since (-5)(2)(5) < (-5)
No example: {p,q,r} = {-5, 1/2, 1} and pqr > p since (-5)(1/2)(1) > (-5)

Statement 2) Similar to statement 1, pr < 0 implies that pr != 0 and that p and r have different signs. Since p < r, p < 0 < r.

Since p < 0, the question stem becomes "qr - 1 > 0?", or "qr > 1?", which cannot be answered without more information about q.

The same yes/no examples from above can be used to illustrate this statement's insufficiency.

Combined) The combined statements tell us that p < 0 < q and that p < 0 < r. Even with this information, the inequality qr > 1 can be true or false.

Yes example: {p,q,r} = {-5, 2, 5} and pqr < p since (-5)(2)(5) < (-5)
No example: {p,q,r} = {-5, 1/2, 1} and pqr > p since (-5)(1/2)(1) > (-5)

Show Spoiler

E

IanStewart · Answer

If, from Statement 1, pq < 0, then one of p or q is negative, the other positive. Negative numbers are always smaller than positive numbers, so if p < q, then clearly p must be the negative number and q the positive number. We learn the same thing from Statement 2: p is negative, and r is positive. Now that we know that p is negative, we can rephrase the question by dividing by p on both sides, reversing the inequality when we do (because we're dividing by a negative) : Is pqr < p ? Is qr > 1 ? While we know q and r are positive, so qr > 0, we have no way to tell whether qr > 1. It might be that q = r = 2, and the answer is 'yes', or it might be that q = r = 1/2 and the answer is 'no'. So the answer is E.

imaityaroy · Answer

30 second solution:

1. from 1 and 2 we know that p is negative and q and r is positive
2. so we divide both sides by p and flip the inequality. hence the question becomes is qr >1 
3. We know qr > 0 but we cant say for sure if qr>1 
4. for eg => qr = 0.5*0.6 or qr = 10*11

hence E

If p<q and p<r, is pqr<p? (1) pq<0 (2) pr<0

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