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06 Apr 2022, 02:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
63% (01:15) correct
37%
(01:39)
wrong
based on 54
sessions
History
Date
Time
Result
Not Attempted Yet
If \((z - 6)^2 = 625\), which of the following could be the value of \(z + 6\)?
A. 31
B. 19
C. -13
D. -19
E. -31
A. 31
B. 19
C. -13
D. -19
E. -31
06 Apr 2022, 12:12
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It is given that \((z-6)^2\) = 625. Most test takers would just take the square root on both sides and say that z-6 = 25 or – 25.
Instead, if you want to build a process for solving Algebra questions on the GMAT, always keep the RHS as zero and factor out the LHS using common terms or standard algebraic identities.
Therefore, \((z-6)^2\) = 625 can be re-written as \((z-6)^2\) – 625 = 0. Now, it’s common knowledge that 625 =\( (25)^2\), hence the equation can be written as (\(z-6)^2 \)– \((25)^2\) = 0.
This equation is now in the form of\( a^2 – b^2 \)and therefore can be factored out as (a-b) (a+b).
Clearly, a = (z-6) and b = 25. Therefore, (a-b) = (z-6) - 25 = z - 31 and (a+b) = (z - 6) + 25 = z + 19.
Therefore,\( (z-6)^2\) – 625 = 0 can be written as (z – 31) (z + 19) = 0.
Hence, z = 31 or z = -19. The possible values of z + 6 are therefore 37 or -13. Since, -13 is there as one of the options, this has to be our answer.
The correct answer option is C.
Instead, if you want to build a process for solving Algebra questions on the GMAT, always keep the RHS as zero and factor out the LHS using common terms or standard algebraic identities.
Therefore, \((z-6)^2\) = 625 can be re-written as \((z-6)^2\) – 625 = 0. Now, it’s common knowledge that 625 =\( (25)^2\), hence the equation can be written as (\(z-6)^2 \)– \((25)^2\) = 0.
This equation is now in the form of\( a^2 – b^2 \)and therefore can be factored out as (a-b) (a+b).
Clearly, a = (z-6) and b = 25. Therefore, (a-b) = (z-6) - 25 = z - 31 and (a+b) = (z - 6) + 25 = z + 19.
Therefore,\( (z-6)^2\) – 625 = 0 can be written as (z – 31) (z + 19) = 0.
Hence, z = 31 or z = -19. The possible values of z + 6 are therefore 37 or -13. Since, -13 is there as one of the options, this has to be our answer.
The correct answer option is C.
