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

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Math Expert
Joined: 02 Sep 2009
Posts: 52935
Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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24 Oct 2014, 08:20
13
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:35) correct 33% (01:42) wrong based on 453 sessions

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Tough and Tricky questions: Remainders.

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.

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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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24 Oct 2014, 13:36
2
1
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.
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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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11 Nov 2014, 20:44
2
2
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.

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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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09 Jul 2015, 05:20
Bunuel whats your take on this question?
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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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09 Jul 2015, 05:28
1
Bunuel wrote:

Tough and Tricky questions: Remainders.

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.

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.
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Posts: 52935
Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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09 Jul 2015, 05:38
1
1
honchos wrote:
Bunuel whats your take on this question?

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.

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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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14 Jul 2017, 19:02
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"
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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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12 Aug 2018, 04:18
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!
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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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12 Aug 2018, 04:35
What if there were only 10 cookies if perer eats 3

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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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13 Aug 2018, 22:17
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
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Re: Can a batch of identical cookies be split evenly between Laurel and Je  [#permalink]

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05 Oct 2018, 15:27
Bunuel wrote:

Tough and Tricky questions: Remainders.

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.

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.
Re: Can a batch of identical cookies be split evenly between Laurel and Je   [#permalink] 05 Oct 2018, 15:27
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Can a batch of identical cookies be split evenly between Laurel and Je

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