Can a batch of identical cookies be split evenly between Laurel and Je

B

Total Cookies = c

Statement1: If the batch of cookies were split among Laurel, Jean and Marc, there would be one cookie left over
c=3a + 1 , c can be 4,7,10 etc. So Insufficient.

Statement2: 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.
c-3 = 2a => c=2a+3 => 2(a+1)+1. C can be 5,7,9 etc. There will always be a remainder 1. Sufficient.

Bunuel whats your take on this question?

Excellent use of remainders in this question.

Per statement 1, we have 3 people and after dividing the cookies (evenly or not!) 1 cookie will be left over. Thus the number of cookies are of the form : 3p+1 where p >0 and an integer.

2 Scenarios, if n = 3p+1 =4 , then yes the cookies can be divided among L and J but if

n =3p+1 =7, then no the cookies can not be divided between L and J (without breaking a cookie, as per the question!). Thus statement 1 is not sufficient to answer.

Per statement 2, the cookies follow the pattern : 2r+3 with 2r for r each for L and J and extra 3 for P. Thus we see that no matter what the value of r we have , 2r+3 will always be odd as 2r+3 = 2r + 2 +1 = 2(r+1) + 1. Thus the cookies can NOT be divided evenly among L and J and is thus SUFFICIENT.

B is the correct answer.

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

Question: x ≡ 0 (mod 2) ?



(A) If the batch of cookies were split among Laurel, Jean and Marc, there would be one cookie left over.

x ≡ 1 (mod 3)

INSUFFICIENT


(B) 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.

x -3 ≡ 0 (mod 2)

∴ x ≡ 1 (mod 2)

SUFFICIENT. This is enough to tell us that x ≡ 0 (mod 2) is False.


The answer is "B"

Just a question of approaching this type of problem: am I wrong to exclude s1 because the number could be 1, and hence if one cookie would be split between 3 people, there would only be one remainder.... Is this correct or is it assumed that the number of cookies are more than one? thanks!

What if there were only 10 cookies if perer eats 3


Sent from my iPhone using GMAT Club Forum mobile app

statement 1 :- 3K+1 = 4,7,10,13............ even and odd both possible so not sufficient
Statement 2 :- 2k+3 = always odd so no equal split is possible sufficient

1) Choose 4 cookies to be split among 3, we have one leftover. 4/2 is evenly split and leaves no leftover.
Choose 7 cookies to be split among 3, we have one leftover. 7/3 is not evenly split.

statement one is insufficient.

2) Choose 5 cookies. Once we take out 3 it leaves 2 thus satisfying statement 2.

However, 5 is not evenly split between 2 individuals.

The same applies for 7,9,11 etc..

B is sufficient to give a clear NO it will not be evenly split.

Bunuel

Hi Bunuel,

From statement A, wouldn't there be an infinite number of ways to split N cookies? The prompt and statement B both say that the cookies are split evenly, but statement A only says they were split.

Thanks in advance!