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11 Oct 2019, 19:26
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
69% (01:06) correct
31%
(01:15)
wrong
based on 364
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If \(\sqrt{a}=b\), what is the value of integer b?
(1) b = |2|
(2) a + b > 0
(1) b = |2|
(2) a + b > 0
23 Jan 2021, 02:16
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MaryKaaviya
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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11 Oct 2019, 20:58
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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
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
