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Updated on: 26 Sep 2022, 01:45
Originally posted by LEOLUCCIOLA on 25 Sep 2022, 14:07.
Last edited by Bunuel on 26 Sep 2022, 01:45, edited 1 time in total.
Last edited by Bunuel on 26 Sep 2022, 01:45, edited 1 time in total.
Edited the question.
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Difficulty:
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Question Stats:
80% (02:13) correct
20%
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What is the largest possible value of z if \(4x + (z – 27)^2 = 36\) and \(–7 \leq x \leq 8\)?
A. 72
B. 63
C. 54
D. 36
E. 35
A. 72
B. 63
C. 54
D. 36
E. 35
What is the largest possible value of z if 4x +(z -27)^2 = 36 and -7 <=x <= 8 ? This question is from one of the Kaplan mock exams
The greatest possible value of 36 - 4x occurs when we subtract the smallest possible value of 4x from 36. Since -7 x 8, the smallest value of 4x occurs when x = -7. Thus, the greatest possible value of z occurs when x = -7 and we have that:
(z-27)^2 = 64, therefore z-27 = sq root of 64 (8)
Why can we take the sq root of (z-27)^2 and 64, if we are not told that z>0? Maybe I am missing something conceptually here
Would appreciate help clarifying.
Ans: z = 35
The greatest possible value of 36 - 4x occurs when we subtract the smallest possible value of 4x from 36. Since -7 x 8, the smallest value of 4x occurs when x = -7. Thus, the greatest possible value of z occurs when x = -7 and we have that:
(z-27)^2 = 64, therefore z-27 = sq root of 64 (8)
Why can we take the sq root of (z-27)^2 and 64, if we are not told that z>0? Maybe I am missing something conceptually here
Would appreciate help clarifying.
Ans: z = 35
25 Sep 2022, 21:20
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Hey LEOLUCCIOLA,
Considering the question you have posted above is a PS question,
you could take the square root of \((z-27)^2\) for the equation \((z-27)^2 = 64\) even if it's not mentioned that \(z < 0\).
The result would be \( + / - (z-27) = +/- 8\), which creates 4 cases based on the signs taken up by the LHS and RHS i.e. LHS RHS = + +, + -, - + and - - .
Among those 4 cases, \(z\) is the highest when LHS RHS are + + and \(z = 35\).
On a separate note, please follow the Rules for posting a New question - https://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html as listed by Bunuel.
Considering the question you have posted above is a PS question,
you could take the square root of \((z-27)^2\) for the equation \((z-27)^2 = 64\) even if it's not mentioned that \(z < 0\).
The result would be \( + / - (z-27) = +/- 8\), which creates 4 cases based on the signs taken up by the LHS and RHS i.e. LHS RHS = + +, + -, - + and - - .
Among those 4 cases, \(z\) is the highest when LHS RHS are + + and \(z = 35\).
On a separate note, please follow the Rules for posting a New question - https://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html as listed by Bunuel.
