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If \(m\) is a positive integer, what is the remainder when \(m\) is divided by 4?
(1) When \(m\) is divided by 16, the remainder is 4.
(2) When \(m\) is divided by 18, the remainder is 2.
(1) When \(m\) is divided by 16, the remainder is 4.
(2) When \(m\) is divided by 18, the remainder is 2.
16 Sep 2014, 00:49
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Official Solution:
If \(m\) is a positive integer, what is the remainder when \(m\) is divided by 4?
(1) When \(m\) is divided by 16, the remainder is 4.
From this, we can represent \(m\) as \(m=16q+4\). This can be further simplified to \(m=4(4q+1)\). Since \(m\) is a multiple of 4, the remainder when \(m\) is divided by 4 is zero. This is sufficient.
(2) When \(m\) is divided by 18, the remainder is 2.
We can represent \(m\) as \(m=18p+2\). Examples of such numbers include 2, 20, 38, and so on. Upon division by 4, these numbers can leave remainders of both 2 and zero. Therefore, this is not sufficient.
Answer: A
If \(m\) is a positive integer, what is the remainder when \(m\) is divided by 4?
(1) When \(m\) is divided by 16, the remainder is 4.
From this, we can represent \(m\) as \(m=16q+4\). This can be further simplified to \(m=4(4q+1)\). Since \(m\) is a multiple of 4, the remainder when \(m\) is divided by 4 is zero. This is sufficient.
(2) When \(m\) is divided by 18, the remainder is 2.
We can represent \(m\) as \(m=18p+2\). Examples of such numbers include 2, 20, 38, and so on. Upon division by 4, these numbers can leave remainders of both 2 and zero. Therefore, this is not sufficient.
Answer: A
