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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?

by torofish » Mon Mar 15, 2010 1:13 am
From Princeton

If ab>0 does (a+2)(b+2) = 4?
1.) ab = -2(a+b)
2.) a=b

OA is A

But I think it should be D.

1.) Rearrange the question --> ab+2a+2b+4=4 ---> ab+2a+2b = 0 yes or no
2.) ab = -2a - 2b --> substitute -2a -2b +2a +2b = 0 Yes
3.) A and D left
4.) a = b : a=b=1 --> 1+2+2 = 5 No. The only way to get a Yes is to let A and B = 0
but it states that a*b>0 so, a and b cannot be 0. Thus a and b is anything but 0. So 2 will get always NO.

Have I done anything wrong?
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by gmatmachoman » Mon Mar 15, 2010 1:30 am
torofish wrote:From Princeton

If ab>0 does (a+2)(b+2) = 4?
1.) ab = -2(a+b)
2.) a=b

OA is A

But I think it should be D.

1.) Rearrange the question --> ab+2a+2b+4=4 ---> ab+2a+2b = 0 yes or no
2.) ab = -2a - 2b --> substitute -2a -2b +2a +2b = 0 Yes
3.) A and D left
4.) a = b : a=b=1 --> 1+2+2 = 5 No. The only way to get a Yes is to let A and B = 0
but it states that a*b>0 so, a and b cannot be 0. Thus a and b is anything but 0. So 2 will get always NO.

Have I done anything wrong?
Only for the values of a =0 or b=0, (a+2)(b+2)=4. But a or b cannot be 0 as ab>0.

So st 1 or st 2 is sufficient to say that for all values of ab other than 0 ,it is not equal to 4

IMO D
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by sarthak » Mon Mar 15, 2010 2:24 am
from 1) ab = -2(a+b)
the question is (a+2)(b+2)
= ab + 2a+2b+4
=ab + 2(a+b)+4

From 1 we know that 2(a+b) = -ab
substituting we get

ab -ab + 4 =4

so 1 is sufficient to say that the value is 4

From 2) if a=b the the equation becomes (a+2)(a+2) = (a+2)^2
Now since ab>0 so a cannot be 0 so the equation cannot be equal to 4.
So 2 is always no

So IMO D
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by girish3131 » Mon Mar 15, 2010 4:00 am
no .. A is correct ans...

b'coz in B option ->

a^2 = -4a

and we are given that ab>0 ie a^2 >0 ( not a>0 remember )

if a = 4 then it's not equal

if a=-4

it's equal

so INSUFFICIENT

Hence A is ans.

ta
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by sarthak » Mon Mar 15, 2010 4:13 am
girish,

I guess U are making this statement a^2 = -4a by putting a=b in statement 1 . But we cannot substitute statement 2's value in statement 1.
correct me if I am wrong
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by girish3131 » Mon Mar 15, 2010 4:19 am
sarthak wrote:girish,

I guess U are making this statement a^2 = -4a by putting a=b in statement 1 . But we cannot substitute statement 2's value in statement 1.
correct me if I am wrong
u can't say exactly....

am jus putting a=b in given ques ( ie If ab>0 does (a+2)(b+2) = 4? )

but b'coz equation 1 is replica of given ques.... so it seems like am putting this in eq 1 .... but it is not exactlt that am trying to do....

u will be agree with me that there is no harm putting a=b in given eq.... Right Dear....
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by gmatmachoman » Mon Mar 15, 2010 6:42 am
girish3131 wrote:no .. A is correct ans...

b'coz in B option ->

a^2 = -4a

and we are given that ab>0 ie a^2 >0 ( not a>0 remember )

if a = 4 then it's not equal

if a=-4

it's equal


Hence A is ans.

ta
@Girish,

Tell me how St 2 is not sufficient to state the given term is euql to 4 or not??
St2 says a=b

For the (a+2)(b+2) = 4?;
we can have only one value i.e,a=0 &b=0 ,the it equals 4. For all other values it is not equal to 4. Since a or b CANNOT be zero, we can "surely " say that (a+2)(b+2) is NOT EQUAL to 4!
ST 2 is sufficient!!

And st 1 is already proved to be sufficient

SO D!!

Now tell me with proper wording & reasoning, how A is alone the answer & why not D?? I know u r quite busy,but for my humble request u can post some decent reasoning!
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by outreach » Mon Mar 15, 2010 10:17 am
@gmatmachoman


for a=b=-4
(a+2)(b+2) = 4

hence A is correct option.
Given
ab>0 -eq1
Question => Is (a+2)(b+2) = 4?


Stmt2.) a=b

substitute a=b in eq1
a^2>0 - eq2

substitute a=b in (a+2)(b+2) = 4
we get
(a+2)(a+2)=4
a^2+4a+4=4
a^2+4a=0
a=0 or -4

a=0 does not satisfy eq2
a=-4 satisfy eq2
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by Fiver » Tue Mar 16, 2010 6:21 am
torofish wrote:From Princeton

If ab>0 does (a+2)(b+2) = 4?
1.) ab = -2(a+b)
2.) a=b

OA is A

But I think it should be D.
Must admit that i fell to the trap at first.
But now I agree with A.

St2] a=b

Since given that ab>0, any value other than 0 would hold good for st2 to be correct.
When a=b=-4 the answer to the question is yes; for any other value the answer to the question is no.
Hence Insuff.
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