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

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WoundedTiger
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If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink] New post   15 Aug 2013, 02:22
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If ab > 0, does (a - 2)(b - 2) = 4 ?

(1) 2a + 2b = ab

(2) a = b

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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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A
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blueseas
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Re: If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink] New post   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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Re: If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink] New post   15 Aug 2013, 03:45
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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.

Answer: A.

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

Thanks for your response.
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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Re: If ab > 0, does (a - 2)(b - 2) = 4 ? [#permalink] New post   15 Aug 2013, 04:02
Expert Reply
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,

Thanks for your response.
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] New post   17 Feb 2019, 21:54
WoundedTiger 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


After manipulation, question becomes ab -2a -2b +4 = 4
ab = 2a + 2b

From 1) we already get this
Sufficient

Given was ab> 0, now it can be that a & b can be +ive -ive or equal numbers integers, but we dont know about the values

from 2) a = b
This we already know from given statement, but we dont know what values they will take

Insufficient

A
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Re: If ab>0, does (a+2)(b+2) = 4? (1) ab = -2(a+b) (2) a=b [#permalink] New post   13 Nov 2022, 11:26
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Re: If ab>0, does (a+2)(b+2) = 4? (1) ab = -2(a+b) (2) a=b [#permalink]
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