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

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Director
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink]

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15 Aug 2013, 02:22
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Difficulty:

35% (medium)

Question Stats:

64% (01:26) correct 36% (01:35) wrong based on 235 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: 810
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, 02:36
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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Math Expert
Joined: 02 Sep 2009
Posts: 46191
Re: If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink]

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15 Aug 2013, 03:45
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: 702
Location: India
GPA: 3.21
Re: If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink]

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15 Aug 2013, 03:55
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
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Math Expert
Joined: 02 Sep 2009
Posts: 46191
Re: If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink]

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15 Aug 2013, 04:02
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, 10:11
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Re: If ab > 0, does (a - 2)(b - 2) = 4 ?   [#permalink] 24 May 2017, 10:11
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