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# What is the value of (p + q) (r + s)?

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Senior RC Moderator
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What is the value of (p + q) (r + s)?  [#permalink]

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15 Dec 2017, 09:14
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Difficulty:

25% (medium)

Question Stats:

76% (01:14) correct 24% (01:46) wrong based on 31 sessions

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What is the value of (p + q) (r + s)?

(1) p(r + s) = 5 and q(r + s) = 3
(2) (p + q) = (r + s)

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What is the value of (p + q) (r + s)?  [#permalink]

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15 Dec 2017, 19:09
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What is the value of (p + q) (r + s)?

(1) p(r + s) = 5 and q(r + s) = 3
(2) (p + q) = (r + s)

I'm happy to respond. This is a great question!

Statement #1: p(r + s) = 5 and q(r + s) = 3

p(r + s) + q(r + s) = 5 + 3
(p + q) (r + s) = 8

This statement leads to a direct unambiguous numerical answer to the prompt question. This statement, alone and by itself, is sufficient.

Statement #2: (p + q) = (r + s)

This tells us that
$$(p + q) \times (r + s) = (p + q) \times (p + q) = (p + q)^2$$

That's interesting, but it does not allow us to arrive at a specific numerical value. This statement, alone and by itself, is insufficient.

OA = (A). A great question!

Mike
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Mike McGarry
Magoosh Test Prep

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What is the value of (p + q) (r + s)?   [#permalink] 15 Dec 2017, 19:09
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