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

(1) pq < 0

(2) pr < 0

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

##### This topic has expert replies

answer should be E.

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.

the above should read:

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

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.

the above should read:

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.

I beat the GMAT! 760 (Q49/V44)

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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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.

The correct answer is E.

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Followed here and elsewhere by over 1900 test-takers.

I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.

My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.

I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].

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