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QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum...

Is the sum of 7x and 7y divisible by 14?

(1) x = y (2) x and y are both even integers

48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes.

Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink]

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27 Oct 2015, 21:54

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EMPOWERgmatRichC wrote:

QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum...

Is the sum of 7x and 7y divisible by 14?

(1) x = y (2) x and y are both even integers

48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes.

Question stem: \(\frac{7x+7y}{14}\) \(=> \frac{7(x+y)}{14}\) \(=> \frac{x+y}{2}\) So basically we need to find whether x+y is even

S1: \(x = y\) This will work if x and y are integers. And will not work otherwise. eg: if \(x=3, y=3\) \(=> x+y = 3+3 = 6\) Even But if \(x=0.75, y=0.75\) \(=> x+y = 0.75+0.75 = 1.50\) Not even Hence Insufficient.

S2: \(x\) and \(y\) are both even integers This will always work. \(x+y\) will always yield an even integer \(even+even = even\) Hence Sufficient.

Answer B
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Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink]

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28 Oct 2015, 07:35

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EMPOWERgmatRichC wrote:

QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum...

Is the sum of 7x and 7y divisible by 14?

(1) x = y (2) x and y are both even integers

48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes.

This DS question, like many DS questions on Test Day, is meant to test the 'thoroughness' of your thinking. It's important to think about what you KNOW about the variables and what you DON'T know...

We're asked if the sum of 7X and 7Y is divisibly by 14. This is a YES/NO question. It's important to remember that we were NOT told anything about X and Y (maybe they're integers, but maybe they're not). TESTing VALUES will prove to be quite useful here.

1) X = Y

This Fact tells us that the two variables are equal to one another, but we don't know what they actually are.

IF... X = Y = 1/2 Then 7(1/2) + 7(1/2) = 7 and the answer to the question is NO.

IF... X = Y = 1 Then 7(1) + 7(1) = 14 and the answer to the question is YES. Fact 1 is INSUFFICIENT

2) X and Y are both even integers

This Fact gives us a very specific restriction - X and Y are BOTH EVEN integers. With this restriction, ANY possible values that you choose for X and Y will lead to a total that is divisible by 14.

For example... IF... X = Y = 2 Then 7(2) + 7(2) = 28 and the answer to the question is YES.

IF... X = 0 Y = 2 Then 7(0) + 7(2) = 14 and the answer to the question is YES.

IF... X = -2 Y = -4 Then 7(-2) + 7(-4) = -42 and the answer to the question is YES. Fact 2 is SUFFICIENT.

Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink]

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25 Nov 2015, 18:22

Hi Rich,

I'm also a member of your website so I follow your posts quite frequently. One question I had was why we can't use the scenario for statement 2 with x=0 and y=0. There's nothing in statement two which says that we can't set both integers equal to 0. In that case 7(0) + 7(0) equals 0 which is not divisible by 14. Therefore, my thought is that B would not be sufficient and hence the correct choice would be (E).

I would love to hear your feedback when you have a moment.

I'm also a member of your website so I follow your posts quite frequently. One question I had was why we can't use the scenario for statement 2 with x=0 and y=0. There's nothing in statement two which says that we can't set both integers equal to 0. In that case 7(0) + 7(0) equals 0 which is not divisible by 14. Therefore, my thought is that B would not be sufficient and hence the correct choice would be (E).

I would love to hear your feedback when you have a moment.

--BH

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink]

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08 Dec 2015, 06:15

EMPOWERgmatRichC wrote:

QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum...

Is the sum of 7x and 7y divisible by 14?

(1) x = y (2) x and y are both even integers

48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes.

2) x and y are even so 2 can is a common divisor of both, hence can be taken out of the brackets making the entity outside brackets as 14. Hence, sufficient.
_________________

When working through DS questions, before jumping to the two Facts, I always write down whatever information I've been given and the specific question that I'm attempting to answer. In addition, if I have not been given ANY information about the variables in the prompt, then I will physically write down that information.... "X, Y can be ANYTHING." In that way, when I'm dealing with each of the Facts and doing whatever work is required, I have a constant reminder (on the PAD) that I need to consider more than just the obvious possibilities (re: positive integers).

Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink]

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21 Feb 2016, 11:15

EMPOWERgmatRichC wrote:

Hi mvictor,

When working through DS questions, before jumping to the two Facts, I always write down whatever information I've been given and the specific question that I'm attempting to answer. In addition, if I have not been given ANY information about the variables in the prompt, then I will physically write down that information.... "X, Y can be ANYTHING." In that way, when I'm dealing with each of the Facts and doing whatever work is required, I have a constant reminder (on the PAD) that I need to consider more than just the obvious possibilities (re: positive integers).

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

thanks..i sometimes forget about this one..will definitely write on my scratch paper just the way you do.

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