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If x and y are integers, is 5x + y divisible by 5?

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Source: — Data Sufficiency |
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by Vincen » Mon Jun 25, 2018 12:55 am

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Hello Gmat_mission.

Let's take a look at your answer.

We need to answer if 5x + y divisible by 5.

First statement
(1) x is divisible by 5
Let's suppose that x=5 and y=1, then $$5x+y=5\left(5\right)+1=26.$$ Now, let's consider x=5 and y=0, then $$5x+y=5\left(5\right)+0=25.$$ Therefore, we get two different answers here. So, this statement is not sufficient.

Second statement
(2) y is divisible by 5.
Now, since y is divisible by 5, then y=5k, for some integer k. Therefore, $$5x+y=5x+5k=5\left(x+k\right),\ \ \ k\in\mathbb{Z}.$$ Therefore, in this case, 5x+y will always be divisible by 5, that is to say, the answer to our question is YES.

So, this statement is sufficient.

The answer is the option B.

I hope it helps you. <i class="em em-smiley"></i>
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by GMATGuruNY » Mon Jun 25, 2018 2:16 am

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Gmat_mission wrote:If x and y are integers, is 5x + y divisible by 5?

(1) x is divisible by 5.

(2) y is divisible by 5.
Statement 1:
Case 1: x=5 and y=0
In this case, 5x + y = (5*5) + 0 = 25, so the answer to the question stem is YES.
Case 2: x=5 and y=1
In this case, 5x + y = (5*5) + 1 = 26, so the answer to the question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2:
Let y = 5a.
Plugging y = 5a into 5x + y, we get:
5x + y = 5x + 5a = 5(x + a).
The resulting expression in blue is a multiple of 5, so the answer to the question stem is YES.
SUFFICIENT.

The correct answer is B.
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by Jeff@TargetTestPrep » Tue Jun 26, 2018 5:28 pm

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Gmat_mission wrote:If x and y are integers, is 5x + y divisible by 5?

(1) x is divisible by 5.

(2) y is divisible by 5.
Since 5x is divisible by 5 regardless what integer x is, then the question becomes: is integer y divisible by 5?

Statement One Alone:

x is divisible by 5.

This does not tell us anything about y. Statement one alone is not sufficient.

Statement Two Alone:

y is divisible by 5.

Since we now know that y is divisible by 5, then 5x + y IS divisible by 5. Statement two alone is sufficient.

Answer: B

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