If (z + 3)/5 is an integer, what is the remainder when z is divided by 5? A. 2 B. 3 C. 4 D. 5 E. 6
(A) This question is related to number theory. If a number divided by 5 is an integer, it means that the number must be a multiple of 5. So we know that z + 3 must be a multiple of 5. So z must be 2 more than a multiple of 5. The correct answer is A.
This is an abstract algebra question so we can try Plug In since the question assumes the remainder to be the same for any z that satisfies the criteria. Therefore we can plug in 0, 1, 2, 3, 4 – the possible remainders and that must be enough. We see that 2 makes (z + 3)/5 to be integers. The correct answer is A. ---------- How is the answer two? I understand that (2 + 3)/5 is the only number that equals an integer, which is one. However, it asks what the remainder is when z (which is two) is divided by 5. Would not 2/5 equal .4 and not 2?
When we deal with a standard division, 2/5 = 0.4 However, division with a remainder is quite different. In this case we deal with non-negative integers only! The dividend, quotient and remainder are non-negative integers. The divisor is a positive integer.
If we divide N by D with a remainder, then the result will be two integers: Q (quotient) and R (remainder). These integers must satisfy the following equality: N = Q × D + R besides, R < D. (So R can be 0, 1, 2 ... D - 1).
In other words R is a "leftover". For example, when 9 is divided by 3, the remainder is 0. When 9 is divided by 5, the remainder is 4. When 9 is divided by 2, the remainder is 1.
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