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# If cd > 0, does (c-2)(d-2) = 4?

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Intern
Joined: 24 Sep 2018
Posts: 39
Location: United States (FL)
GMAT 1: 680 Q45 V38
GRE 1: Q160 V161
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If cd > 0, does (c-2)(d-2) = 4?  [#permalink]

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24 Dec 2018, 10:50
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Difficulty:

35% (medium)

Question Stats:

63% (01:22) correct 38% (01:45) wrong based on 43 sessions

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If cd > 0, does (c-2)(d-2) = 4?

(1) 2c + 2d = cd
(2) c = d

I'm having trouble understanding why item (2) isn't (also) sufficient for answering this question, if anyone can shed light I'd appreciate it!
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Joined: 02 Sep 2009
Posts: 57155
If cd > 0, does (c-2)(d-2) = 4?  [#permalink]

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24 Dec 2018, 11:09
corgigal wrote:
If cd > 0, does (c-2)(d-2) = 4?

(1) 2c + 2d = cd
(2) c = d

I'm having trouble understanding why item (2) isn't (also) sufficient for answering this question, if anyone can shed light I'd appreciate it!

If cd > 0, does (c-2)(d-2) = 4?

Does (c-2)(d-2) = 4 ?
Does cd - 2c - 2d + 4 = 4 ?
Does 2c + 2d = cd ?

(1) 2c + 2d = cd. Directly answers the question. Sufficient.

(2) c = d. The question becomes: does (c-2)(c-2) = 4 ? --> does (c - 2)^2 = 4 --> does c = 0 or c = 4. We don't know that, so this statement is not sufficient.

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Intern
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GMAT 1: 680 Q45 V38
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If cd > 0, does (c-2)(d-2) = 4?  [#permalink]

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24 Dec 2018, 11:45
Bunuel wrote:

(2) c = d. The question becomes: does (c-2)(c-2) = 4 ? --> does c^2 = 8. We don't know that, so this statement is not sufficient.

Thanks for answering Bunuel but here's my issue, and if my arithmetic is to blame please point it out, but shouldn't (c-2)(c-2) become:

C(squared) - 2C - 2C + 4 = 4
C(squared) - 4C = 0
C(squared) = 4C
C = 4?

(edit for clarification) - And if we know C = 4, and C and D are equal, then if we plug that into the question then we can answer whether it is equal to 4 or not (the answer being yes), no?
Math Expert
Joined: 02 Sep 2009
Posts: 57155
Re: If cd > 0, does (c-2)(d-2) = 4?  [#permalink]

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24 Dec 2018, 11:50
corgigal wrote:
Bunuel wrote:

(2) c = d. The question becomes: does (c-2)(c-2) = 4 ? --> does c^2 = 8. We don't know that, so this statement is not sufficient.

Thanks for answering Bunuel but here's my issue, and if my arithmetic is to blame please point it out, but shouldn't (c-2)(c-2) become:

C(squared) - 2C - 2C + 4 = 4
C(squared) - 4C = 0
C(squared) = 4C
C = 4?

Yes, the math is correct (I considered (c- 2)(c + 2) there instead of (c - 2)(c - 2). Edited.). But we don't get that c = 4. The question becomes: does c = 4? We don't know whether that's true or not, so the statement is not sufficient.
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Joined: 24 Sep 2018
Posts: 39
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GMAT 1: 680 Q45 V38
GRE 1: Q160 V161
GPA: 3.95
If cd > 0, does (c-2)(d-2) = 4?  [#permalink]

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24 Dec 2018, 11:56
Bunuel wrote:

Yes, the math is correct (I considered (c- 2)(c + 2) there instead of (c - 2)(c - 2). Edited.). But we don't get that c = 4. The question becomes: does c = 4? We don't know whether that's true or not, so the statement is not sufficient.

Oh I see now! At the end of that simplification I'm still just basically asking if c=4, not claiming it like statement (1) does. Thank you, this was driving me crazy!
If cd > 0, does (c-2)(d-2) = 4?   [#permalink] 24 Dec 2018, 11:56
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