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16 Sep 2014, 01:48
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E
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If \(N\) is a positive, three-digit integer, what is the hundreds digit of \(N\)?
(1) The hundreds digit of \(N + 120\) is 7.
(2) The tens digit of \(N + 15\) is 9
(1) The hundreds digit of \(N + 120\) is 7.
(2) The tens digit of \(N + 15\) is 9
16 Sep 2014, 01:48
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Official Solution:
We must determine the value of the hundreds place of the three-digit positive integer \(N\).
Statement 1 tells us that \(N + 120\) has a hundreds digit with a value of 7. If \(N + 120 = 799\), the maximum value with a 7 in the hundreds place, then \(N = 679\) and has a 6 in the hundreds place. However, if \(N + 120 = 700\), the minimum number with a 7 in the hundreds place, then \(N = 580\) and has a 5 in the hundreds place. Since we cannot determine a single value for the hundreds place, Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice must be B, C, or E.
Statement 2 tells us that \(N + 15\) has a tens digit with a value of 9. This gives us no information whatsoever about the hundreds place. Statement 2 is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice is either C or E.
Taken together, Statement 1 tells us that \(N\) must be between 580 and 679, and Statement 2 tells us that \(N + 15\) has a 9 in the tens place. Note that if \(N = 580\), the tens digit of\(N + 15\) will be 9, and the hundreds digit of \(N\) is 5; however, if \(N = 679\), the tens digit of \(N + 15\) will still be 9, only now the hundreds digit of \(N\) is 6. Since these numbers, \(N = 580\) and \(N = 679\), satisfy both statements but have different hundreds digits, the two statements together are not sufficient to answer the question.
Answer: E
We must determine the value of the hundreds place of the three-digit positive integer \(N\).
Statement 1 tells us that \(N + 120\) has a hundreds digit with a value of 7. If \(N + 120 = 799\), the maximum value with a 7 in the hundreds place, then \(N = 679\) and has a 6 in the hundreds place. However, if \(N + 120 = 700\), the minimum number with a 7 in the hundreds place, then \(N = 580\) and has a 5 in the hundreds place. Since we cannot determine a single value for the hundreds place, Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice must be B, C, or E.
Statement 2 tells us that \(N + 15\) has a tens digit with a value of 9. This gives us no information whatsoever about the hundreds place. Statement 2 is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice is either C or E.
Taken together, Statement 1 tells us that \(N\) must be between 580 and 679, and Statement 2 tells us that \(N + 15\) has a 9 in the tens place. Note that if \(N = 580\), the tens digit of\(N + 15\) will be 9, and the hundreds digit of \(N\) is 5; however, if \(N = 679\), the tens digit of \(N + 15\) will still be 9, only now the hundreds digit of \(N\) is 6. Since these numbers, \(N = 580\) and \(N = 679\), satisfy both statements but have different hundreds digits, the two statements together are not sufficient to answer the question.
Answer: E
14 Sep 2016, 10:31
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Stmt 1: _ _ _ + 120 = 7 _ _
Stmt 2: _ _ _ + 15 = _ 9 _
If we say by Stmt 2 that number is _ 8 _ + 15 = _ 9_
Then combining Stmt 1 with the above stmt , we can say that _8_ + 120=7_ _ which can be 58_+120=70_ the ones digit still unsure that will affect the hundredth digit .
Therefore, finding hundredth digit is ambiguous. Hence, E option follows.
Stmt 2: _ _ _ + 15 = _ 9 _
If we say by Stmt 2 that number is _ 8 _ + 15 = _ 9_
Then combining Stmt 1 with the above stmt , we can say that _8_ + 120=7_ _ which can be 58_+120=70_ the ones digit still unsure that will affect the hundredth digit .
Therefore, finding hundredth digit is ambiguous. Hence, E option follows.
