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

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

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New post 15 Aug 2013, 02:22
2
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A
B
C
D
E

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63% (01:26) correct 37% (01:35) wrong based on 238 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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Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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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]

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New post 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.

Answer: A.

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

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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]

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New post 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,

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: If ab > 0, does (a - 2)(b - 2) = 4 ?  [#permalink]

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Re: If ab > 0, does (a - 2)(b - 2) = 4 ? &nbs [#permalink] 24 May 2017, 10:11
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