here's the question:
What is the remainder when the positive integer x is divided by 3?
(1) when x is divided by 6, the remainder is 2.
(2) when x is divided by 15, the remainder is 2.
Both are sufficient but why?
Many thanks
Lukas
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remainder of a division
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lukaswelker
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Statement 1: When x is divided by 6, the remainder is 2.lukaswelker wrote: What is the remainder when the positive integer x is divided by 3?
(1) when x is divided by 6, the remainder is 2.
(2) when x is divided by 15, the remainder is 2.
In other words, x is 2 more than a multiple of 6:
x = 6a + 2, where a is a nonnegative integer.
Options for x: 2, 8, 14, 20...
Dividing these option by 3, we get:
2/3 = 0 R2.
8/3 = 2 R2.
14/3 = 2 R2.
Since the remainder in each case is the same, SUFFICIENT.
Statement 2: When x is divided by 15, the remainder is 2.
In other words, x is 2 more than a multiple of 15:
x = 15a + 2, where a is a nonnegative integer.
Options for x: 2, 17, 32, 47...
Dividing these options by 3, we get:
2/3 = 0 R2.
17/3 = 5 R2.
32/3 = 10 R2.
Since the remainder in each case is the same, SUFFICIENT.
The correct answer is D.
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Brent@GMATPrepNow
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Target question: What is the remainder when the positive integer x is divided by 3?lukaswelker wrote: What is the remainder when the positive integer x is divided by 3?
(1) when x is divided by 6, the remainder is 2.
(2) when x is divided by 15, the remainder is 2.
IMPORTANT CONCEPT: Notice that 3 is a factor of 6 and 12. So, if some integer k is a multiple of 6, then k is also a multiple of 3. For example, since 102 is a multiple of 6, then 102 must also be a multiple of 3. Likewise, if some integer k is a multiple of 12, then k is also a multiple of 3.
Statement 1: when x is divided by 6, the remainder is 2
In other words, x is 2 greater than some multiple of 6. (e.g., x = 2, 8, 14, 20, etc)
Applying the green concept above, we can also say that x is 2 greater than some multiple of 3.
If x is 2 greater than some multiple of 3, then the remainder must be 2 when x is divided by 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: when x is divided by 12, the remainder is 2
In other words, x is 2 greater than some multiple of 12. (e.g., x = 2, 14, 26, etc)
Applying the green concept above, we can also say that x is 2 greater than some multiple of 3.
If x is 2 greater than some multiple of 3, then the remainder must be 2 when x is divided by 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
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Brent
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