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If z is an integer such that ||z - 30| - 43| = 6^2 which of the follow

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Manager
Joined: 25 Dec 2018
Posts: 230
Location: India
Concentration: General Management, Finance
GMAT 1: 590 Q48 V23
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WE: Engineering (Consulting)
If z is an integer such that ||z - 30| - 43| = 6^2 which of the follow  [#permalink]

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29 Mar 2019, 00:13
1
4
00:00

Difficulty:

95% (hard)

Question Stats:

38% (02:30) correct 62% (02:59) wrong based on 42 sessions

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If z is an integer such that ||z - 30| - 43| = 6^2 which of the following could be value of |r|, where r is the remainder obtained when z is divided by 7?

I. 0
II. 2
III. 4

A. I and II only
B. I and III only
C. II and III only
D. I,II and III
E. None of the above
Math Expert
Joined: 02 Aug 2009
Posts: 7573
Re: If z is an integer such that ||z - 30| - 43| = 6^2 which of the follow  [#permalink]

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29 Mar 2019, 00:25
2
mangamma wrote:
If z is an integer such that ||z - 30| - 43| = 6^2 which of the following could be value of |r|, where r is the remainder obtained when z is divided by 7?

I. 0
II. 2
III. 4

A. I and II only
B. I and III only
C. II and III only
D. I,II and III
E. None of the above

We can solve for different cases of z..
$$||z - 30| - 43| = 6^2=36$$
Case I : |z-30|-43=36, that is |z-30|=79
Again two cases
A) z-30=79 or z=109
B) 30-z=79 or z=-49
Case II : 43-|z-30|=36, that is |z-30|=7
Again two cases
A) z-30=7 or z=37
B) 30-z=7 or z=23

So, four possible values of z are
109=7*15+4,
-49=7*(-7)+0,
37=7*5+2 and
23=7*3+2

Thus, the values are 0, 2 and 4

D
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Re: If z is an integer such that ||z - 30| - 43| = 6^2 which of the follow   [#permalink] 29 Mar 2019, 00:25
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