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27 Aug 2017, 06:17
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nishantt7
For (1): In \(|x - 2| \lt 2 - y\), the left hand side of the inequality (|x - 2|) is an absolute value. An absolute value of a number cannot be negative, so the left hand side of the inequality (|x - 2|) is not negative, which means that the right hand side of the inequality, which is greater than the left hand side, also cannot be negative. This gives \(0 \lt 2 - y\).
For (2): We know from the stem that y is a positive integer. Since y is a positive integer (1, 2, 3, ...), then 1 - y = 1 - positive = non-positive, which measn that |1-y|=-(1-y). Therefore, for (2) we'd have \(x + y - 3 = -(1-y)\), which gives \(x=2=prime\). Sufficient.
Hope it's clear.
rwx5861
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05 Jan 2020, 19:36
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Bunuel
I'm still having difficulty understanding when to consider only the positive root when GMAT gives the even square root. It seems like when the value is defined that this rule will apply (e.g. sqrt(25) is 5, not -5); when a variable is provided instead, the answer is the abs(x), and 'x' itself can be +/-.
Can you help me better understand? I only considered the pos. root in this problem and got the wrong answer as a result.
Thanks!
I'm still having difficulty understanding when to consider only the positive root when GMAT gives the even square root. It seems like when the value is defined that this rule will apply (e.g. sqrt(25) is 5, not -5); when a variable is provided instead, the answer is the abs(x), and 'x' itself can be +/-.
Can you help me better understand? I only considered the pos. root in this problem and got the wrong answer as a result.
Thanks!
05 Jan 2020, 22:13
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rwx5861
\(\sqrt{...}\) 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 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;
Similarly \(\sqrt{\frac{1}{16}} = \frac{1}{4}\), NOT +1/4 or -1/4.
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 \(x=\sqrt{9}=3\).
