Can a batch of identical cookies be split evenly between

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Can a batch of identical cookies be split evenly between Laurel and Jean without leftovers and without breaking a cookie?

1) If the batch of cookies were split among Laurel, Jean, and Marc, there would be one cookie left over.
2) If Peter eats three of the cookies before they are split, there will be no leftovers when the cookies are split evenly between Laurel and Jean.

The OA is B.

I have an approach to solving this DS question,

Let no. of cookies be x.

It is clear from the stem that if the cookies were to be divided equally between Laurel & Jean, x needs to be even.

1) x = 3p + 1; if p is even, x will be odd and vice versa, hence this is INSUFFICIENT.
2) x = 2q + 3; x will always be odd, hence cookies cannot be divided equally between Laurel & Jean. SUFFICIENT.

If someone has another approach, please write it. That's would be great. Thanks!
Source: — Data Sufficiency |

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by Jay@ManhattanReview » Fri Jun 22, 2018 1:48 am

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swerve wrote:Can a batch of identical cookies be split evenly between Laurel and Jean without leftovers and without breaking a cookie?

1) If the batch of cookies were split among Laurel, Jean, and Marc, there would be one cookie left over.
2) If Peter eats three of the cookies before they are split, there will be no leftovers when the cookies are split evenly between Laurel and Jean.

The OA is B.

I have an approach to solving this DS question,

Let no. of cookies be x.

It is clear from the stem that if the cookies were to be divided equally between Laurel & Jean, x needs to be even.

1) x = 3p + 1; if p is even, x will be odd and vice versa, hence this is INSUFFICIENT.
2) x = 2q + 3; x will always be odd, hence cookies cannot be divided equally between Laurel & Jean. SUFFICIENT.

If someone has another approach, please write it. That's would be great. Thanks!
Statement 1 basically states that the number of cookies is 1 more than a multiple of 3, so the number of cookies can be 1, 4, 7, 10, ...
You can observe that the number of cookies is even or odd. If it is odd, the answer is NO; however, the number of cookies is even, the answer is YES. No unique answer. Not sufficient.

Statement 2 means that "Number of cookies - 3" is even. So, the number of cookies be odd. We cannot split the cookies evenly between Laurel and Jean. Unique answer. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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