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

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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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

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

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 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

(1) Before the exchange, bowl X contained 2 black jelly beans.
case#1
Before X[B,B] Y[R, R]
After X[R,B] Y[B,R]
After the exchange, were both of the jelly beans in bowl X black? --> NO
case#2
Before X[B,B] Y[B, R]
After X[B,B] Y[B,R]
After the exchange, were both of the jelly beans in bowl X black? --> YES

Insufficient

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

We do not know anything about bowl X
Insufficient

(1)+(2)
case#1
Before X[B,B] Y[R, R]
After X[R,B] Y[B,R]
After the exchange, were both of the jelly beans in bowl X black? --> NO
case#2
Before X[B,B] Y[B, R]
After X[B,B] Y[B,R]
After the exchange, were both of the jelly beans in bowl X black? --> YES

Insufficient

OA <-- E


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Each bowl can have (R,B), (B,B), (R,R)

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.

No information on the jelly beans in Bowl Y. INSUFFICIENT.

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

No information on jelly bowls in Bowl X before the exchange. INSUFFICIENT.

(1&2) Bowl X contained (B, B) before the exchange. Bowl Y contained (B, R) after the exchange. However, we don't know what Bowl Y originally had. Bowl Y could have had (R, R) or (B, B), giving X either black or red. INSUFFICIENT.

Answer is E.
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Bowls X and Y each contained exactly 2 jelly beans, each of which was either red or black -- the statement clearly mentions that each of the set of 2 jelly beans is either red or black. How is there a possibility of red, black in a single bowl.
Please correct me if my interpretation is wrong

In case anyone else is having trouble with this one, here's a visualization for statements (1) and (2) together:­

The key to solving the question is getting all the combinations correct

(1) Before the exchange, bowl X contained 2 black jelly beans.
This could to 3 possibilities in the y bag
Clearly insufficient

(2) After the exchange, bowl Y contained 1 jelly bean of each color.
This as from the above argument leads to 3 possibilities
in the X bag
INsuff

Even when 1 and 2 is combined we get
either both black or 1 black 1 red in bag

INSUFFICIENT
HEnce IMO E­

S1. Whether the exchanged jelly bean from Y to X is black or red? not sure.
Sufficient

S2. No information to conclude which color jelly bean is transferred from Y to X. Sufficient

S1 + S2
Still not sufficient. Hence E­

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