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

Question

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.

Tulkin987 · Answer

(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

anuj04 · Answer

(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

houston1980 · Answer

(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.

Tulkin987 · Answer

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

Mo2men · Answer

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)

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia