Is the sum of two integers divisible by 10 ? (1) One of the integers

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

Questions dealing with divisibility can often be solved Logically, without calculation.
In this case, we need to know if the sum has a zero as its unit digit, or if it has a 5 and a 2 in its factorization.
(1) and (2) each relate to one integer so are insufficient. Combining does not give us the information on the units digit of the sum or the factorization.
(E) is our answer.

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

1) We know that one of the integers is even and can test possible cases. If one of the integers is 10 and the other is also 10, then the answer to the original question is Yes. However, if one of the integers is 10 and the other is 11, then the answer to the original question is No. Thus, we can't get a definite answer to the original question. \(\implies\) Insufficient

2) We know that one of the integers is a multiple of 5 and can test possible cases. If one of the integers is 10 and the other is also 10, then the answer to the original question is Yes. However, if one of the integers is 10 and the other is 11, then the answer to the original question is No. Thus, we can't get a definite answer to the original question. \(\implies\) Insufficient

1&2) Since we can use the same cases to prove that statement 1) and 2) are insufficient, 1&2) must also be insufficient. \(\implies\) Insufficient

Answer: E

#1
even other not known
insufficient
#2
one is multiple of 5 other not know insufficeint
from 1 & 2
one is even other is multiple of 5
eg ; 5,10 ; 15 no
10,10 ; 20 ; yes
IMO E

Statement One Alone:

One of the integers is even.

If the two integers are 2 and 8, then the sum is divisible by 10. However, if the integers are 2 and 1, then the sum is not divisible by 10. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

One of the integers is a multiple of 5.

If the two integers are 5 and 15, then the sum is divisible by 10. However, if the integers are 5 and 1, then the sum is not divisible by 10. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

If the two integers are 10 and 20, then the sum is divisible by 10. However, if the integers are 2 and 10, then the sum is not divisible by 10.

Answer: E
_________________

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:

GMAT assassins aren't born, they're made,
Rich

I would only add that when testing for both statements, one can assume that both statements refer to the same integer. For example, 20 is both even and a multiple of 5. Thus, we have no information about the other integer of the sum and the answer is E.

(1) 2, 5=7 not divisible by 10, 2,8=2+8=10, is divisible 10; Insufficient

(2) Same example is applicable. Insufficient.

Considering both;

Considering the examples; Insufficient.

The answer is C.
_________________

Answer: Option E

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can we assume that one of the integers is even and the other odd ....its said that one of the integers are even so?
so wouldnt that point to a) as the solution?

Why don't we select B?

It sas "ONE of the integer is a multiple of 10". Thus it seems like only one of the two is a multiple of 10, thus 10k+ Integer not multiple than 10 will never be divisible by 10.

What's the flaw in this reasoning? I find it very ambiguous.

Hi ansarose & Scuven,

There's a BIG difference between the phrases "one of the integers is even" and "ONLY one of the integers is even."

The first type of phrasing is what we're dealing with in Fact 1 and Fact 2 here - and you should interpret it as "we know that one of the integers is even, but we don't know anything about the other integer (so maybe it's even or maybe it's odd)."

GMAT assassins aren't born, they're made,
Rich

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