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16 Sep 2014, 00:41
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If \(x\) is a positive integer, what is the remainder when \(x\) is divided by 8?
(1) The remainder when \(x\) is divided by 16 is 2.
(2) The remainder when \(x\) is divided by 24 is 10.
(1) The remainder when \(x\) is divided by 16 is 2.
(2) The remainder when \(x\) is divided by 24 is 10.
16 Sep 2014, 00:41
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Official Solution:
If \(x\) is a positive integer, what is the remainder when \(x\) is divided by 8?
(1) The remainder when \(x\) is divided by 16 is 2.
This can be written as \(x = 16q + 2\). The first term, \(16q\), is divisible by 8. The second term, 2, divided by 8 will give the remainder of 2. Sufficient.
Alternatively, we can deduce that this statement implies that \(x\) is 2 more than a multiple of 16. Since every multiple of 16 is also a multiple of 8, \(x\) must be 2 more than a multiple of 8, which means that the remainder when \(x\) is divided by 8 is 2. Sufficient.
(2) The remainder when \(x\) is divided by 24 is 10.
This can be written as \(x = 24p + 10\). The first term, \(24p\), is divisible by 8. The second term, 10, divided by 8 will give the remainder of 2. Sufficient.
Alternatively, we can deduce that this statement implies that \(x\) is 10 more than a multiple of 24. Since every multiple of 24 is also a multiple of 8, \(x\) must be 10 more than a multiple of 8. In other words, \(x\) is 2 more than a multiple of 8, which means that the remainder when \(x\) is divided by 8 is 2. Sufficient.
Answer: D
If \(x\) is a positive integer, what is the remainder when \(x\) is divided by 8?
(1) The remainder when \(x\) is divided by 16 is 2.
This can be written as \(x = 16q + 2\). The first term, \(16q\), is divisible by 8. The second term, 2, divided by 8 will give the remainder of 2. Sufficient.
Alternatively, we can deduce that this statement implies that \(x\) is 2 more than a multiple of 16. Since every multiple of 16 is also a multiple of 8, \(x\) must be 2 more than a multiple of 8, which means that the remainder when \(x\) is divided by 8 is 2. Sufficient.
(2) The remainder when \(x\) is divided by 24 is 10.
This can be written as \(x = 24p + 10\). The first term, \(24p\), is divisible by 8. The second term, 10, divided by 8 will give the remainder of 2. Sufficient.
Alternatively, we can deduce that this statement implies that \(x\) is 10 more than a multiple of 24. Since every multiple of 24 is also a multiple of 8, \(x\) must be 10 more than a multiple of 8. In other words, \(x\) is 2 more than a multiple of 8, which means that the remainder when \(x\) is divided by 8 is 2. Sufficient.
Answer: D
Updated on: 17 May 2021, 07:41
Originally posted by BrentGMATPrepNow on 30 Mar 2020, 05:43.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:41, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:41, edited 1 time in total.
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Bunuel
Target question: What is the remainder when x is divided by 8?
Statement 1: When x is divided by 16, the remainder is 2
In other words, x is 2 greater than some multiple of 16
In other words, x = 16k + 2 (for some integer k)
Rewrite this as: x = (8)(2k) + 2
This tells us that x is 2 greater than some multiple of 8
This means we get a remainder of 2 when x is divided by 8
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: When x is divided by 24, the remainder is 10
In other words, x is 10 greater than some multiple of 24
In other words, x = 24j + 10 (for some integer j)
In other words, x = 24j + 8 + 2 (for some integer j)
Rewrite this as: x = 8(3j + 1) + 2
This tells us that x is 2 greater than some multiple of 8
This means we get a remainder of 2 when x is divided by 8
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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