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21 Aug 2019, 20:24
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
56% (02:39) correct
44%
(02:49)
wrong
based on 449
sessions
History
Date
Time
Result
Not Attempted Yet
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
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
22 Aug 2019, 07:28
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AbdulMalikVT
I don't understand why there are pointless complications in the question. Remainders are never negative, so there's no reason to ask for "|r|", since that is always equal to r. Nor is there any reason to write 6^2 instead of 36 in the original absolute value equation. They'd only do that in a real GMAT question if they were trying to suggest to a test taker that there would be some advantage to thinking about that number as a square, instead of as 36, but there is no reason to think about 36 as if it were "6^2" in this problem.
Since |a - b| is the distance between a and b on the number line, the original absolute value equation tells us that |z-30| and 43 are separated by 36 on the number line. So either |z-30| is 36 greater than 43, and is equal to 79, or |z-30| is 36 less than 43, and is equal to 7. So we have two equations, and again using distances (or whatever absolute value method you prefer) :
|z - 30| = 79 --> so z is either 79 less than or 79 greater than 30, and z = -49 or 109
|z - 30| = 7 --> so z is either 7 less than or 7 greater than 30, and z = 23 or 37
We can now divide each solution by 7 and see what remainders are possible. You will absolutely never need to calculate remainders when dividing negative numbers by anything on the GMAT, so the first solution, z = -49, is one you'd never get in a GMAT question about remainders. But since that number is divisible by 7, it gives a remainder of 0. The number 109 is 105 + 4, and since 105 is divisible by 7, we get a remainder of 4. Since 23 and 37 both give a remainder of 2 when we divide by 7, the answer is I, II and III.
General Discussion
22 Aug 2019, 07:55
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AbdulMalikVT
Given: z is an integer such that ||z - 30| - 43| = 6^2
Asked: Which of the following could be value of |r|, where r is the remainder obtained when z is divided by 7?
|z-30| = 43+-36 => |z-30| = 7 or 79
If |z-30| = 7 => z = 30 +-7 => z = 37 or 23
If |z-30| = 79 => z = 30 +-79 => z = 109 or -49
z= {37,23,109,-49}
Remainder r = {2,2,4,0} = {2,4,0}
IMO D
