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If \(x\) is an integer, and \(121 < x^2 \leq 361\), which of the following is the sum of all possible values of \(x\)?
A. 135 B. 124 C. 116 D. 105 E. None of the above
Notice that since \(x\) is squared, then for every positive value of \(x\) there will be its negative pair with the same magnitude. So, the sum of all possible values of \(x\) will be 0.
[4.33] In the end, what would you gain from everlasting remembrance? Absolutely nothing. So what is left worth living for? This alone: justice in thought, goodness in action, speech that cannot deceive, and a disposition glad of whatever comes, welcoming it as necessary, as familiar, as flowing from the same source and fountain as yourself. (Marcus Aurelius)
Hi, bunnel, can we deduce from the question " x is greater or equal to -19 and less or equal +19 and x is greater than 11 or less then -11 ", meaning 19 >=x>11, In that case sum of x will be 105. Please explain why we can deduce from two different range of values to a common range of value for x ?
Hi, bunnel, can we deduce from the question " x is greater or equal to -19 and less or equal +19 and x is greater than 11 or less then -11 ", meaning 19 >=x>11, In that case sum of x will be 105. Please explain why we can deduce from two different range of values to a common range of value for x ?
Not sure I completely follow what you wrote there but anyway the ranges of x are:
-19 <= x < -11 and 11 < x < = 19:
x = +/- 19; x = +/- 18; ... x = +/- 12.
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I didn't took negative values because in GMAT sqrt(n) is only a positive value. For example sqrt(4) is only 2 and not both -2 and 2
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 \(x=\sqrt{9}=3\). _________________
Please explain my doubt: If you read the question carefully, it's written as "sum of all positive values of x" - Then we should not take negative values in my view.
Please explain my doubt: If you read the question carefully, it's written as "sum of all positive values of x" - Then we should not take negative values in my view.
Which of the following is the sum of all POSSIBLE values of x? NOT "positive values of x"?
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