1) Stmt 1: given |b| = 2
and \(a^(1/2)=b\)
\(a^(1/2)\) can not be negative hence b has to be postive thus B = 2
sufficient
2) a+b>0
this gives no information about the sum total
only information is a and b , both are positive
Infsufficient
Hence Answer A
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given
\(\sqrt{a}=b\)
a=b^2
#1
b=|2|
lbl=√b^2
with b= 2 the value of √b^2 = 2 ; sufficient
#2
a+b>0
√b+b>0
√b(1+√b)=0
√b=0 or √b=-1
insufficeint
IMO A

square root of a natural number can be a negative as well as positive number. the equivalent value is square root always comes in pairs. sq. rt of 4 is 2,-2. because 2*2 = -2*-2 = 4.

Then how can A be sufficient.

chetan2u Bunuel VeritasKarishma
is this again a GMAT World only situation?

First of all, GMAT dose not have its own math.

Here (1) is sufficient because we want the value of b, and (1) directly gives it to us: b = |2| = 2. If we were asked to get the value of a, (1) still would have been sufficient. b = |2| = 2, so \(\sqrt{a}=2\), and a = 4 only, NOT 4 or -4 (you can square to get a = 4).

Next, 4 has two square roots 2 and -2 but \(\sqrt{}\) sign always means non-negative square root, so \(\sqrt{4}=2\) only.


\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.


The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT (and generally in math) provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;

Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
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Check this link for more such concepts:
https://www.veritasprep.com/blog/2016/0 ... oots-gmat/
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