If a and b are integers, is a + 8b even?

Question

(1) 2a + b is even

(2) a^b is even

Kudos for a correct  solution .

GMATinsight · Answer

Question  : is a + 8b even?

Since 8b will always be an Even Integer given that a and b are Integers so we only need to know about a to answer the question

Question REPHRASED  : Is a even?

Statement 1 : 2a + b is even 
Since 2a is always even so we conclude that b is even. 
But we need to know whether a is even or not hence
NOT SUFFICIENT

Statement 2 : a^b is even 
i.e. a is even
SUFFICIENT

Answer: Option B

gk3391 · Answer

From the question stem we need to find out whether a is even or odd as 8b is always even. So if a is odd, a+8b will be odd or if a is even a+8b will be even.
(1) 2a + b is even --- > This implies that b is even as 2a is always even. This is not needed to conclude a+8b. Therefore  Statement 1 is insufficient. 
(2) a^b is even -----> This implies that a is even. Because if a is odd, any number of times it is multiplied it ll always be odd (3^1, 3^2, 7^2, 7^5 - Odd power any number is odd). Whereas if a is even it would always be even any number of time it is multiplied. Therefore if a is even a+8b would always be even. We get a clear Yes. 
Hence  Statement 2 is sufficient

sharma123 · Answer

Ans is B.
Question basically asks if A is Even
Statement 1: here we can say B is even but nuthing can be said about A.
Statement 2: This clearly says A is even because if A was odd a^b can never be even. So Sufficient.

longfellow · Answer

Answer is B as any integer irrespective of its exponent (apart from 0) remains odd or even as the initial value.

BrainLab · Answer

is a + 8b even? in other words is a even, because 8b is always even ?
(1) 2a+b=even means b is even, but this gives us no info about a Not sufficient
(2)a^b=even means a is even and b is not equal to zero Sufficient
Answer (B)

thembaseeker · Answer

It's a Yes/No question.

a+8b is even? --> We need to know whether 'a' is even or odd as 8b is always even.

Statement 1 : 2a+b

Don't provide any idea about a, it can be odd or even

Insufficient

Statement 2: a^b is even

Hence a is even

Sufficient

Answer : B

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are integers, is a + 8b even? 
(1) 2a + b is even
(2) a^b is even

If we modify the original condition according to the Variable Approach Method, from a+8b, 8b is always even, so we ultimately want to know whether a is an even number.
From condition 2, in order for a^b to be even, the product of even numbers are always even, so a=even, and this condition is sufficient.
But for condition 1, 2a is always even regardless of the value of a, so we cannot determine the value of a, so this is a insufficient condition, and the answer is therefore (B).

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

IcyTropic · Answer

I think the answer is "E" and here is my logic:
you have 4 possible combos: (o for odd, e for even)
1) AeBe:
2)  AeBo : out because condition 1 
3) AoBe: 
4)  AoBo : out because condition 1 ,out because condition 2
Thus, two surviving options still can say anything about A.

If a and b are integers, is a + 8b even?

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GMAT Data Sufficiency (DS) Questions

If a and b are integers, is a + 8b even?

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