DeeptiM wrote:
What is the remainder when positive integer x is divided by 4?
(1) When x is divided by 6, the remainder is 3.
(2) When x is divided by 8, the remainder is 5.
We need to determine the remainder when x is divided by 4.
Statement One Alone:
When x is divided by 6, the remainder is 3.
We see that x could be 3 because the remainder is 3 when 3 is divided by 6. If x is 3, the remainder when 3 is divided by 4 is 3.
We see that x also could be 9 because the remainder is 3 when 9 is divided by 6. If x is 9, the remainder when 9 is divided by 4 is 1. We have two different remainders when x is divided by 4. Statement one alone is not sufficient to answer the question.
Statement Two Alone:
When x is divided by 8, the remainder is 5.
We see that x could equal 5 because the remainder when 5 is divided by 8 is 5. If x is 5, the remainder when 5 is divided by 4 is 1.
We see that x also could be 13 because the remainder is 5 when 13 is divided by 8. If x is 13, the remainder when 13 is divided by 4 is 1. It seems that the remainder is always 1 when x is divided by 4. Let’s show that that is exactly the case.
Since x leaves a remainder of 5 when it’s divided by 8, we can express x as:
x = 8m + 5 for some integer m.
Now let’s divide x by 4:
x/4 = (8m + 5)/4
x/4 = 8m/4 + 5/4
x/4 = 2m + (1 + 1/4)
x/4 = (2m + 1) + 1/4
Since 2m + 1 is an integer, we see that the remainder is 1 (the numerator of the fraction 1/4).
Statement two alone is sufficient to answer the question.
Answer: B
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