Is the sum of two integers divisible by 10 ?

[AbeNeedsAnswers]

Is the sum of two integers divisible by 10 ?

(1) One of the integers is even.
(2) One of the integers is a multiple of 5.

E

Source: Official Guide 2020

[Brent@GMATPrepNow]

Is the sum of two integers divisible by 10 ?

(1) One of the integers is even.
(2) One of the integers is a multiple of 5.

Target question: Is the sum of two integers divisible by 10 ?

Statement 1: One of the integers is even.
We only have information about ONE number.
Statement 1 is NOT SUFFICIENT

Statement 2: One of the integers is a multiple of 5.
We only have information about ONE number.
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are many possible pairs of values that satisfy BOTH statements. Here are two:
Case a: The numbers are 10 (even) and 10 (divisible by 5). So, the sum = 20, which means the answer to the target question is YES, the sum of the integers IS divisible by 10.
Case b: The numbers are 2 (even) and 15 (divisible by 5). So, the sum = 17, which means the answer to the target question is NO, the sum of the integers is NOT divisible by 10.
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

[[email protected]]

Hi All,

We're asked if the sum of two integers is divisible by 10. This is a YES/NO question can be solved by TESTing VALUES.

(1) One of the integers is even.

Fact 1 tells us about just one of the numbers; we know nothing about the other number. For organizational purposes, I'll refer to the 2 numbers as X and Y.
IF....
X = 10 and Y = 0, then the answer to the question is YES.
X = 10 and Y = 5, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

(2) One of the integers is a multiple of 5.

Fact 2 tells us about just one of the numbers; we know nothing about the other number. The TESTs that we used for Fact 1 also fit the information in Fact 2 (it's worth noting that 0 IS a multiple of 5).
IF....
X = 10 and Y = 0, then the answer to the question is YES.
X = 10 and Y = 5, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know...
One of the integers is even.
One of the integers is a multiple of 5.

Since we already have two examples that fit both Facts, there's no more work to be done - the answer could be either 'YES' or 'NO.'
Combined, INSUFFICIENT

Final Answer: E

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