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# Bowls X and Y each contained exactly 2 jelly beans, each of

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Status: May The Force Be With Me (D-DAY 15 May 2012)
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Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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08 Apr 2012, 09:44
3
10
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:01) correct 36% (01:48) wrong based on 632 sessions

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Project DS Butler: Day 26: Data Sufficiency (DS52)

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Bowls X and Y each contained exactly 2 jelly beans, each of which was either red or black. One of the jelly beans in bowl X was exchanged with one of the jelly beans in bowl Y. After the exchange, were both of the jelly beans in bowl X black?

(1) Before the exchange, bowl X contained 2 black jelly beans.
(2) After the exchange, bowl Y contained 1 jelly bean of each color.

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Re: Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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08 Apr 2012, 10:13
1
boomtangboy wrote:
Bowls X and Y each contained exactly 2 jelly beans, each of which was either red or black. One of the jelly beans in bowl X was exchanged with one of the jelly beans in bowl Y. After the exchange, were both of the jelly beans in bowl X black?

(1) Before the exchange, bowl X contained 2 black jelly beans.
(2) After the exchange, bowl Y contained 1 jelly bean of each color.

Consider two cases for (1)+(2):

Initially X={BB} and Y={BR} --> B was exchanged with B --> X={BB} and Y={BR}: answer is YES;
Initially X={BB} and Y={RR} --> B was exchanged with R --> X={BR} and Y={BR}: answer is NO.

Answer: E.
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Re: Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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19 Nov 2013, 21:48
1
1) NS, because it gives no information on X after the exchange.
2) NS, because the initial for both X and Y could be the following:
X=RR Y=BB
X=RB Y=BB

1+2) NS
Case 1)
Before
X=BB Y=RR

After
Y=BR Y=RB

Case 2)
Before
X=BB Y=RB

After
X=BB Y=RB
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Re: Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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24 Dec 2013, 02:21
I used very simple cases and got to the conclusion real quick.
Before
X=RR Y=RR

After
Y=RR Y=RR

Next Case
Before
X=BB Y=RR

After
X=BR Y=RB
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Re: Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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27 Jan 2015, 19:20
Question: how do you know they are not "exclusive". I misunderstood the question as meaning that there are 2 black and 2 reds, and thus had everything wrong. What clue can you pick up to know that there can be any combination of colors?
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Re: Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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11 Jul 2017, 22:32
boomtangboy wrote:
Bowls X and Y each contained exactly 2 jelly beans, each of which was either red or black. One of the jelly beans in bowl X was exchanged with one of the jelly beans in bowl Y. After the exchange, were both of the jelly beans in bowl X black?

(1) Before the exchange, bowl X contained 2 black jelly beans.
(2) After the exchange, bowl Y contained 1 jelly bean of each color.

This question tests the general ability to think of counterexamples

It cannot be (1) alone because before exchange X=BB with Y=RR and Y=BR give different results for X
It cannot be (2) alone because after exchange Y=BR can come from X= BB with Y=RR and Y=BR and can give different results for X
It cannot be (1) and (2) together also because before exchange X=BB with Y=RR and Y=BR can give different results for X with Y=BR after exchange

So the answer is E

Note: Try to use the same counter example as far as possible.
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Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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02 Dec 2018, 03:47
Bowls X and Y each contained exactly 2 jelly beans, each of which was either red or black. One of the jelly beans in bowl X was exchanged with one of the jelly beans in bowl Y. After the exchange, were both of the jelly beans in bowl X black?

(1) Before the exchange, bowl X contained 2 black jelly beans.
Before the exchange cannot tell anything regarding after exchange. Insufficient.

(2) After the exchange, bowl Y contained 1 jelly bean of each color.
After exchange, Y (RB), but X could be (RR) (BB) (RB). Not unique, insufficient.

(1) & (2)
If before exchange, bowl X is (BB), and Y can be (BR) (BB) (RR)
After exchange, bowl X can be (BR) (BB). No unique, Insufficient
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Re: Bowls X and Y each contained exactly 2 jelly beans, each of  [#permalink]

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28 Mar 2019, 22:26
1
eflores89 wrote:
Question: how do you know they are not "exclusive". I misunderstood the question as meaning that there are 2 black and 2 reds, and thus had everything wrong. What clue can you pick up to know that there can be any combination of colors?

I had that question, too. The clue seems to lie in "each of which." This wording suggests that we should apply the description "either red or black" to each individual jelly bean instead of the entire bowl of beans. Each jelly bean was either red or black. So the first jelly bean in Bowl X was red or it was black. The second jelly bean in Bowl X was red or it was black. The same logic applies to Bowl Y.

IMO if the question writer wanted to imply that each bowl had one red and one black then they would have written, "Bowls X and Y each contained exactly 2 jelly beans: one red and one black."
Re: Bowls X and Y each contained exactly 2 jelly beans, each of   [#permalink] 28 Mar 2019, 22:26
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# Bowls X and Y each contained exactly 2 jelly beans, each of

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