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# Is p + q > pq ? (1) p > 0 > q (2) |q| = p

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Director
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Is p + q > pq ? (1) p > 0 > q (2) |q| = p [#permalink]

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02 Jan 2005, 09:23
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Is p + q > pq ?

(1) p > 0 > q

(2) |q| = p

Kudos [?]: 162 [0], given: 0

Director
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 922 [0], given: 22

Location: PA

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02 Jan 2005, 09:38
A is ruled out
B is ruled out as | q | = p then q = +/- p

My answer is would be E

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Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12

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02 Jan 2005, 11:10
1 is insufficent as p=-q then p+q = 0
2 is insufficent

taking them together

P is positive and q is negative (statement 1)
q= |P| (statement 2)
given 1 and 2 we can conclude that P is equal to negative q, therefor P+q is never greater than PQ (even if P and q were 0s)

gayathri wrote:
Is p + q > pq ?

(1) p > 0 > q

(2) |q| = p

Kudos [?]: 319 [0], given: 2

VP
Joined: 25 Nov 2004
Posts: 1481

Kudos [?]: 126 [0], given: 0

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02 Jan 2005, 15:50
gayathri wrote:
Is p + q > pq ?

(1) p > 0 > q

(2) |q| = p

from (i), p is always +ve and q is always -ve. then,
p+q >=<pq

if we suppose, p=1 and q=-0.1
p+q = 0.9 and pq = -o.1
here, p+q>pq

if p=0.1 and q=-1
p+q = -0.9 and pq = -o.1
here, p+q<pq

so A is insufficient.

from (ii) p is +ve and q is +ve and -ve. it also does not solve the inequality.

if p = 1 and q=0.1
p+q = 1.1 and pq=0.1 i.e. p+q>pq.

if p=2 and q= 3
p+q = 5 and pq=6 i.e. p+q<pq.

if p is +ve and q=-ve, the same results as in (i) result.

Combining togather also doesnot give any solution to the inequality p+q>pq?

therefore E is OA.

Kudos [?]: 126 [0], given: 0

Current Student
Joined: 28 Dec 2004
Posts: 3351

Kudos [?]: 319 [0], given: 2

Location: New York City
Schools: Wharton'11 HBS'12

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02 Jan 2005, 17:36
MA can you please explain why combinging the two statements is not enough....

MA wrote:
gayathri wrote:
Is p + q > pq ?

(1) p > 0 > q

(2) |q| = p

from (i), p is always +ve and q is always -ve. then,
p+q >=<pq

if we suppose, p=1 and q=-0.1
p+q = 0.9 and pq = -o.1
here, p+q>pq

if p=0.1 and q=-1
p+q = -0.9 and pq = -o.1
here, p+q<pq

so A is insufficient.

from (ii) p is +ve and q is +ve and -ve. it also does not solve the inequality.

if p = 1 and q=0.1
p+q = 1.1 and pq=0.1 i.e. p+q>pq.

if p=2 and q= 3
p+q = 5 and pq=6 i.e. p+q<pq.

if p is +ve and q=-ve, the same results as in (i) result.

Combining togather also doesnot give any solution to the inequality p+q>pq?

therefore E is OA.

Kudos [?]: 319 [0], given: 2

Director
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 922 [0], given: 22

Location: PA

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02 Jan 2005, 18:03
guys what does the acronym OA stand for ??

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Director
Joined: 07 Nov 2004
Posts: 683

Kudos [?]: 162 [0], given: 0

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02 Jan 2005, 19:32
OA is C

Explanation given is...

The correct response is (C). Statement (1) alone establishes that pq < 0, because the product of a positive number and a negative number is always negative. If you subsetitute integers for p and q, the answer to the question is always "yes." However, if you substitute fractional values (between -1 and 1) for p and q, in some cases the answer to the question is "no." For example, if p = 1/4 and q = -1/2 , p + q = -1/4 while pq = -1/8 , and therefore p + q < pq. Thus, statement (1) alone is insufficient to answer the question.

Statement (2) alone is also insufficient to answer the question. Again, the answer to the question depends on the values of p and q. For example, If p = 3 and q = -3, then p + q > pq. But if p = 3 and q = 3, then is p + q < pq.

Statements (1) and (2) together are sufficient to answer the question. Together, statements (1) and (2) establish that q is the same non-zero number as p, except negative instead of positive. Therefore, p + q will always equal 0, while pq will always be negative. Accordingly, the answer to the question will always be "yes."

Kudos [?]: 162 [0], given: 0

VP
Joined: 25 Nov 2004
Posts: 1481

Kudos [?]: 126 [0], given: 0

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02 Jan 2005, 19:44
gayathri wrote:
OA is C

Explanation given is...

The correct response is (C). Statement (1) alone establishes that pq < 0, because the product of a positive number and a negative number is always negative. If you subsetitute integers for p and q, the answer to the question is always "yes." However, if you substitute fractional values (between -1 and 1) for p and q, in some cases the answer to the question is "no." For example, if p = 1/4 and q = -1/2 , p + q = -1/4 while pq = -1/8 , and therefore p + q < pq. Thus, statement (1) alone is insufficient to answer the question.

Statement (2) alone is also insufficient to answer the question. Again, the answer to the question depends on the values of p and q. For example, If p = 3 and q = -3, then p + q > pq. But if p = 3 and q = 3, then is p + q < pq.

Statements (1) and (2) together are sufficient to answer the question. Together, statements (1) and (2) establish that q is the same non-zero number as p, except negative instead of positive. Therefore, p + q will always equal 0, while pq will always be negative. Accordingly, the answer to the question will always be "yes."

agreed. i forget the information, modulas q = p.

Kudos [?]: 126 [0], given: 0

02 Jan 2005, 19:44
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