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If a is a positive integer, is b also a positive integer?

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Bunuel
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If a is a positive integer, is b also a positive integer? [#permalink] New post   25 May 2018, 02:48
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If a is a positive integer, is b also a positive integer?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive integer.
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Re: If a is a positive integer, is b also a positive integer? [#permalink] New post   25 May 2018, 02:54
Bunuel wrote:
If a is a positive integer, is b also a positive integer?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive integer.


(1) \(\frac{a+b+2+a-5}{3}=a\). From this we can find that \(b=a+3\). \(b\) is positive. Sufficient.

(2) \(b\) is negative. Sufficient.

Answer: D
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If a is a positive integer, is b also a positive integer? [#permalink] New post   Updated on: 25 May 2018, 05:16
(1){ a+(b+2)+(a−5)}/3=a. From this we can find that b=a+3. Since a is positive. therefore, b is positive as well - Sufficient
(2) (a+b)/2 = Not a positive integer. Let's take examples: a=3 & b =4. AM is 3.5 which is non-integer but b is an integer.
second example, a=3 & b =4.4. Now AM is 3.7, which is non-integer and b is also non-integer. - Not definite answer. - Not Sufficient

Answer is A

Originally posted by anuj04 on 25 May 2018, 03:01.
Last edited by anuj04 on 25 May 2018, 05:16, edited 1 time in total.
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Re: If a is a positive integer, is b also a positive integer? [#permalink] New post   25 May 2018, 03:21
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Bunuel wrote:
If a is a positive integer, is b also a positive integer?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive integer.



(Statement 1) \(\frac{a+b+2+a-5}{3}=a\). Therefore, \(b=a+3\). \(b\) is positive. Statement 1 is Sufficient.

(Statement 2). Assume a = 4, b= 3, average will be 3.5 . average is NOT a positive integer, but b is a positive integer.
Assume a = 4, b= 5.2, average will be 4.6 . average is NOT a positive integer, and b is NOT a positive integer.

Therefore,

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Hence option A is the answer.
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Re: If a is a positive integer, is b also a positive integer? [#permalink] New post   25 May 2018, 03:48
houston1980 wrote:
Bunuel wrote:
If a is a positive integer, is b also a positive integer?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive integer.



(Statement 1) \(\frac{a+b+2+a-5}{3}=a\). Therefore, \(b=a+3\). \(b\) is positive. Statement 1 is Sufficient.

(Statement 2). Assume a = 4, b= 3, average will be 3.5 . average is NOT a positive integer, but b is a positive integer.
Assume a = 4, b= 5.2, average will be 4.6 . average is NOT a positive integer, and b is NOT a positive integer.

Therefore,

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Hence option A is the answer.


Missed one subtle point: 'positive INTEGER'. Perfect explanation.
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If a is a positive integer, is b also a positive integer? [#permalink] New post   25 May 2018, 10:56
Tulkin987 wrote:
houston1980 wrote:
Bunuel wrote:
If a is a positive integer, is b also a positive integer?

(1) The average (arithmetic mean) of a, b + 2, and a - 5 is a.

(2) The average (arithmetic mean) of a and b is NOT a positive integer.



(Statement 1) \(\frac{a+b+2+a-5}{3}=a\). Therefore, \(b=a+3\). \(b\) is positive. Statement 1 is Sufficient.

(Statement 2). Assume a = 4, b= 3, average will be 3.5 . average is NOT a positive integer, but b is a positive integer.
Assume a = 4, b= 5.2, average will be 4.6 . average is NOT a positive integer, and b is NOT a positive integer.

Therefore,

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Hence option A is the answer.


Missed one subtle point: 'positive INTEGER'. Perfect explanation.



Actually, there is other case to provide insufficiency. It may help you to consinder in other questions.

Let a = 1 & b=0 ..mean = 1/2....b is integer but neither positive nor negative (character of zero)
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If a is a positive integer, is b also a positive integer? [#permalink]
25 May 2018, 10:56
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Bunuel
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