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# If z is an integer such that ||z - 30| - 43| = 62 which of the followi

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If z is an integer such that ||z - 30| - 43| = 62 which of the followi [#permalink]
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↧↧↧ Detailed Video Solution to the Problem ↧↧↧

Given that z is an integer such that ||z - 30| - 43| = $$6^2$$ and we need to find which of the following could be value of |r|, where r is the remainder obtained when z is divided by 7

Given that r is the remainder
=> r will be non-negative
=> |r| = r

Let's simplify ||z - 30| - 43| = $$6^2$$ = 36

 We will have two cases -Case 1: |z-30| - 43 = +36=> |z-30| = 36 + 43 = 79=> z-30 = +79 or z-30 = -79=> z = 79 + 30 or z = -79 + 30=> z = 109 or -49Remainder(r) when 109 is divided by 7 = 4Remainder(r) when -49 is divided by 7 = 0 -Case 2: |z-30| - 43 = -36 => |z-30| = -36 + 43 = 7=> z-30 = +7 or z-30 = -7=> z = 7 + 30 or z = -7 + 30=> z = 37 or 23Remainder(r) when 37 is divided by 7 = 2Remainder(r) when 23 is divided by 7 = 2

So, Remainder(r) can be 0, 2, 4