If x and y are integers, is 5x + y divisible by 5?
(1) x is divisible by 5.
(2) y is divisible by 5.
[spoiler]A=B[/spoiler].
Why is the second statement sufficient? Could someone clarify this for me?
If x and y are integers, is 5x + y divisible by 5?
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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
Second statement
So, this statement is sufficient.
The answer is the option B.
I hope it helps you. <i class="em em-smiley"></i>
Let's take a look at your answer.
We need to answer if 5x + y divisible by 5.
First statement
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.(1) x is divisible by 5
Second statement
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.(2) y is divisible by 5.
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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Statement 1: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.
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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Since 5x is divisible by 5 regardless what integer x is, then the question becomes: is integer y divisible by 5?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 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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