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

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

by netigen » Sun Jun 01, 2008 1:20 am
If p < q and p < r, is (p)(q)(r) < p?
(1) pq < 0

(2) pr < 0

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by jasonc » Sun Jun 01, 2008 4:11 am

stem1: tells us that p<0>0: insuff
stem2: tells us that p<0>0: insuff
combined still insuff

EDIT:
gosh... my posts from late late last night don't make any sense at all lol.
stem1: p<0>0
stem2: p<0>0

combined still insuff

EDIT2:
OMG its not me... its the html tags taking out my 'q's and 'r's lol
add q>0 to what I wrote for stem1
and r>0 to what I wrote for stem2
Last edited by jasonc on Sun Jun 01, 2008 1:03 pm, edited 2 times in total.
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by s_raizada » Sun Jun 01, 2008 4:51 am

1: substitute PQR
-2, 1, -1.5 : false
-2, 1, 1.5 : true
so not suff

2: substitute PQR
-2, -1.5, 1 : false
-2, 1.5, 1 : true
so not suff

combining 1 and 2 and given constraints
means
p <0
q > 0
r > 0

substitue values pqr
-1, .5, 1 : false
-1, 2, 1 : true
not suff

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### Re: If p < q and p < r, is (p)(q)(r) < p?

by GMATGuruNY » Tue Aug 25, 2020 1:31 pm
netigen wrote:
Sun Jun 01, 2008 1:20 am
If p < q and p < r, is (p)(q)(r) < p?
(1) pq < 0

(2) pr < 0
Statement 1 :
pq < 0 --> p and q have DIFFERENT SIGNS
Since p<q, p must be NEGATIVE, q must be positive.
Statement 2:
pr < 0 --> p and r have DIFFERENT SIGNS
Since p<r, p must be NEGATIVE, q must be positive.

Since both statements indicate that p is negative, we can safely divide the question stem by p, making sure to flip the inequality when we divide:
pqr < p
pqr/p > p/p ?
qr > 1

Question stem, rephrased:
Given that p is negative, is qr > 1?

Statements combined:
Case 1: p=-1, q=1, and r=1
In this case, qr=1, so the answer to the question stem is NO.
Case 2: p=-1, q=1 and r=2
In this case, qr=2, so the answer to the question stem is YES.
Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT.

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