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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.
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The Question 37, Page 155 in Data Sufficiency Sample Questions of Quant Review is as follows:
What is the value of a - b ?
(1) \(a = b + 4\) (2) \((a - b)^2 = 16\)
Solution:
Statement (1)
\(a= b+4\) Or, \(a-b=4\) As the value of a-b can be uniquely determined, statement (1) is sufficient.
Statement (2)
Solving the equation, \((a - b)^2 = 16\), we have either \(a-b= 4\) or \(a-b= -4\). As the value of \(a-b\) can not be uniquely determined, statement (2) is not sufficient.
(2) (a - b)^2 = 16 --> a-b=4 or a-b=-4. Not sufficient.
Answer: A.
how is 1 sufficient when a & b can still be any combination of numbers i.e. (0,4), (1,5) (2,6).....and on and on
Yes but we are asked to find the value of a-b, not the individual values of a and b.
Hi Bunuel,
I have learnt from GMATClub that the root of a positive number is always positive-so root of 16 should only be 4 right (for GMAT purposes). So-the answer should be D right?
how is 1 sufficient when a & b can still be any combination of numbers i.e. (0,4), (1,5) (2,6).....and on and on
Yes but we are asked to find the value of a-b, not the individual values of a and b.
Hi Bunuel,
I have learnt from GMATClub that the root of a positive number is always positive-so root of 16 should only be 4 right (for GMAT purposes). So-the answer should be D right?
The correct answer is A.
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive 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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Is this really a 550-level question? Looks like 400-level one Just kidding......;
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