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

Question

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.

pairakesh10 · Answer

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.

rdoshi · Answer

Another approach:

let no. of cookies be x.

It is clear from the stem that if the cookies were to be divided equally between L & J, 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 L & J. SUFFICIENT.

Answer: B

honchos · Answer

Bunuel whats your take on this question?

ENGRTOMBA2018 · Answer

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.

Bunuel · Answer

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

Notice, that the question basically asks whether the number of cookies in the batch is even. If it is, then we'd be able to split the cookies evenly between two persons giving half to each of them.

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

This basically says that the number of cookies is 1 more than a multiple of 3, so it can be 1, 4, 7, 10, ... As you can see it can be even as well as odd. Not sufficient.

(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.

This tells us that x - 3 is even, x being initial number of cookies. So, x must be odd. We cannot split the cookies evenly between two. Sufficient.

Answer: B.

grimm1111 · 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"

oskarw93s · Answer

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!

Nirenjan · Answer

What if there were only 10 cookies if perer eats 3

Sent from my iPhone using  GMAT Club Forum mobile app

Praveenksinha · Answer

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

Salsanousi · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards