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

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corgilover
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If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   24 Dec 2018, 10:50
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If cd > 0, does (c-2)(d-2) = 4?

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

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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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Bunuel
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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   24 Dec 2018, 11:09
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corgigal wrote:
If cd > 0, does (c-2)(d-2) = 4?

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

Show Spoiler
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.

Answer: A.
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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   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.

Answer: A.


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?
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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   24 Dec 2018, 11:50
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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.

Answer: A.


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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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   31 Jan 2022, 22:20
If cd > 0, does (c-2)(d-2) = 4?

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


Break down stem into cd - 2c - 2d + 4 = 4

(1)
sub eqn into the stem, 4 = 4. Sufficient

(2)

c=d does not tell us anything. Insufficient

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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   30 Jun 2022, 18:10
Regarding statement (2):

What if c = 5 ??? So d = 5 ! So (c-2)(d-2) is NOT equal to 4. But if c = 2 → d = 2, so the equation IS equal to 4. So we have different conclusions from (2), so it is not possible to answer with just (2) statement.
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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   19 Jul 2022, 10:05
why is statement 2 insufficient? from c^2=4c we can find that C could be 0 or 4 but the question has already provided to us that cd>0 if C is 0 then the product of C and D would be equal to 0 therefore not satisfy the given cd>0. So it means that C is 4 which answers our question. Bunuel can you please explain
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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink] New post   20 Jul 2022, 01:57
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finaliguess wrote:
why is statement 2 insufficient? from c^2=4c we can find that C could be 0 or 4 but the question has already provided to us that cd>0 if C is 0 then the product of C and D would be equal to 0 therefore not satisfy the given cd>0. So it means that C is 4 which answers our question. Bunuel can you please explain



Your doubt is already addressed above couple of times. When considering the second statement, the question becomes: does c = 4 or c = 0? We know that c cannot be 0 (because cd > 0) but we don't know whether c = 4. If for (2) c = 4, the answer to the question is YES ((c-2)(d-2) = 4) but if c is any other number, then the answer to the question is NO ((c-2)(d-2) ≠ 4)
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Re: If cd > 0, does (c-2)(d-2) = 4? [#permalink]
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