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# If ab > 0, does (a - 2)(b - 2) = 4 ?

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Director
Joined: 25 Apr 2012
Posts: 683
Location: India
GPA: 3.21
If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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15 Aug 2013, 01:22
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Difficulty:

35% (medium)

Question Stats:

69% (01:43) correct 31% (02:12) wrong based on 240 sessions

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If ab > 0, does (a - 2)(b - 2) = 4 ?

(1) 2a + 2b = ab

(2) a = b

I don't agree with OA here. Experts can you please confirm whether the OA is correct.
Reasoning for 2nd statement will be appreciated

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Director
Joined: 14 Dec 2012
Posts: 748
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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15 Aug 2013, 01:36
mridulparashar1 wrote:
If ab > 0, does (a - 2)(b - 2) = 4 ?

(1) 2a + 2b = ab

(2) a = b

I don't agree with OA here. Experts can you please confirm whether the OA is correct.
Reasoning for 2nd statement will be appreciated

$$ab > 0$$
MEANS$$a,b$$ have same signs and $$a,b$$ is not equal to zero.

(1)$$2a + 2b = ab$$
$$2a+2b-ab=0$$
subtracting 4 from both sides
$$2a-ab-4+2b=-4$$
$$a(2-b)-2(2-b)=-4$$
$$(a-2)(2-b)=-4$$
or
$$(a-2)(b-2)=4$$
sufficient.

(2) $$a = b$$
let say $$a=b=2$$ then $$(a-2)(b-2) = 0$$.....NO
let$$a=b=4$$ then$$(a-2)(b-2) = 4$$.....YES
not sufficient

hence A
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Posts: 52108
Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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15 Aug 2013, 02:45
1
1
If ab > 0, does (a - 2)(b - 2) = 4 ?

Does $$(a - 2)(b - 2) = 4$$? Or: does $$ab-2a-2b+4=4$$ --> does $$2a + 2b = ab$$?

(1) 2a + 2b = ab. Directly gives an YES answer to the question. Sufficient.

(2) a = b. The questions becomes: is $$2a+2a=a^2$$? --> is $$4a=a^2$$? --> is $$a=4$$? (discard a=0, since we know that $$a\neq{0}$$ from ab>0). Since we don't know whether $$a=4$$, then the statement is not sufficient.

Hope it's clear.
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Director
Joined: 25 Apr 2012
Posts: 683
Location: India
GPA: 3.21
Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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15 Aug 2013, 02:55
blueseas wrote:
mridulparashar1 wrote:
If ab > 0, does (a - 2)(b - 2) = 4 ?

(1) 2a + 2b = ab

(2) a = b

I don't agree with OA here. Experts can you please confirm whether the OA is correct.
Reasoning for 2nd statement will be appreciated

$$ab > 0$$
MEANS$$a,b$$ have same signs and $$a,b$$ is not equal to zero.

(1)$$2a + 2b = ab$$
$$2a+2b-ab=0$$
subtracting 4 from both sides
$$2a-ab-4+2b=-4$$
$$a(2-b)-2(2-b)=-4$$
$$(a-2)(2-b)=-4$$
or
$$(a-2)(b-2)=4$$
sufficient.

(2) $$a = b$$
let say $$a=b=2$$ then $$(a-2)(b-2) = 0$$.....NO
let$$a=b=4$$ then$$(a-2)(b-2) = 4$$.....YES
not sufficient

hence A

Hi Blueseas and Bunuel,

Actually for st 2, I just plugged in the given statement a=b
to the equation which is being tested and ended up with b^2-4b=0 ie b=4= a and answer to the equation is (a - 2)(b - 2) = 4 YES

since the given equation is itself (a - 2)(b - 2) = 4 then there should have been another way to plug in the same considering
(b-2)^2 = 4 or b-2= 2 or b-2=-2

Since we do not the values of a and b the ans should be A and not D as I thought
_________________

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Math Expert
Joined: 02 Sep 2009
Posts: 52108
Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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15 Aug 2013, 03:02
mridulparashar1 wrote:
blueseas wrote:
mridulparashar1 wrote:
If ab > 0, does (a - 2)(b - 2) = 4 ?

(1) 2a + 2b = ab

(2) a = b

I don't agree with OA here. Experts can you please confirm whether the OA is correct.
Reasoning for 2nd statement will be appreciated

$$ab > 0$$
MEANS$$a,b$$ have same signs and $$a,b$$ is not equal to zero.

(1)$$2a + 2b = ab$$
$$2a+2b-ab=0$$
subtracting 4 from both sides
$$2a-ab-4+2b=-4$$
$$a(2-b)-2(2-b)=-4$$
$$(a-2)(2-b)=-4$$
or
$$(a-2)(b-2)=4$$
sufficient.

(2) $$a = b$$
let say $$a=b=2$$ then $$(a-2)(b-2) = 0$$.....NO
let$$a=b=4$$ then$$(a-2)(b-2) = 4$$.....YES
not sufficient

hence A

Hi Blueseas and Bunuel,

Actually for st 2, I just plugged in the given statement a=b
to the equation which is being tested and ended up with b^2-4b=0 ie b=4= a and answer to the equation is (a - 2)(b - 2) = 4 YES

since the given equation is itself (a - 2)(b - 2) = 4 then there should have been another way to plug in the same considering
(b-2)^2 = 4 or b-2= 2 or b-2=-2

Since we do not the values of a and b the ans should be A and not D as I thought

For (2) I plugged in too. But you are mixing what is given and what is asked: the questions asks whether (a - 2)(b - 2) = 4? When you plug, the question becomes is (b - 2)(b - 2) = 4? --> is b=0 or b=4? We know that b is not 0, but we don't know whether b=4. If b=4 the answer to the question is YES but if b is any other value than the answer to the questions is NO.

Hope it's clear.
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Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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24 May 2017, 09:11
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Re: If ab > 0, does (a - 2)(b - 2) = 4 ? &nbs [#permalink] 24 May 2017, 09:11
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