A box contains 90 jelly beans, of which some are orange, some are purp

Question

A box contains 90 jelly beans, of which some are orange, some are purple, and some are black. How many black jelly beans are in the box?

(1) There are 27 orange jelly beans.
(2) There are twice as many purple jelly beans as orange jelly beans.

msk0657 · Answer

Given P+Q+B = 90 ( here p i purple, b for black and Q for orange

Stat 1: Q = 27

then P+B = 63...Insufficient...don't have information to answer B.

Stat 2: 2P = Q...

then 3Q+B = 90...Insufficient.

STat 1 + 2 : Given Q = 27 then purple will be 54 and B = 9..

IMO option C is correct answer..

BrentGMATPrepNow · Answer

Let R = # of orange jelly beans
Let P = # of purple jelly beans
Let B = # of black jelly beans

Target question :    What is the value of B?

Given :  R + P + B = 90

Statement 1 : There are 27 orange jelly beans   
So, R = 27
We now have 2 equations and 3 variables: 
 R + P + B = 90 
R = 27
This is not sufficient information to determine the  value of B 
If you're not convinced, consider these 2 conflicting cases: 
Case a: R = 27, P = 1 and  B = 62 
Case b: R = 27, P = 2 and  B = 61 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : There are twice as many purple jelly beans as orange jelly beans  
In other words, P = 2R
We now have 2 equations and 3 variables: 
 R + P + B = 90 
P = 2R
This is not sufficient information to determine the  value of B 
If you're not convinced, consider these 2 conflicting cases: 
Case a: R = 20, P = 40 and  B = 30 
Case b: R = 10, P = 20 and  B = 60 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
COMBINED, we have 3 equations and 3 variables:
 R + P + B = 90 
R = 27
P = 2R
This should be sufficient information, as long as  none of the equations are equivalent.  
Here there are no equivalent equations, so we COULD solve the system for B and answer the  target question . 
Since we COULD answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer = C

If we're not convinced, we can always solve the system. 
If R = 27, and P = 2R, then we can see that P = 54
If R = 27, P = 54 AND  R + P + B = 90 , then it must be the case that  B = 9

MarkusKarl · Answer

I want to ask Bunuel whether the wording in this problem means that the three different colours are exhaustive or does it simply mean that it contains, among other colours, the ones mentioned?

My answer will be based on the first case, when we have just three different colours of Jelly Beans.

The following is given.
Purple+Orange+Black=90

(1)
27 are orange.
P+27+B=90
P+B=63.
Not sufficient to answer the question.

(2)
P=2O
This only tells us the relationship between orange and purple. We can assume that there are atleast 2 Orange as the wording was "some of which", indicating that there are more than one. So P is atleast 4, but there are multiple values possible for Black as the value for neither Orange nor Purple can be determined.

(1)+(2)
O=27
P=54
B=90-54-27=9

The number of black jelly beans are 9.
Sufficient.

Argo · Answer

I assume the answer is E as the question didn't specify the 'rest are black', but 'some are black'. Hence gems of one or more other color(s) may also exist.

Palpable · Answer

I have the same question - how are we assuming that 'some are black' would mean that the remaining are all black. Am I missing something?

Bunuel · Answer

The statement "A box contains 90 jelly beans, of which some are orange, some are purple, and some are black" implies the box only has jelly beans in those three colors.

A box contains 90 jelly beans, of which some are orange, some are purp

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A box contains 90 jelly beans, of which some are orange, some are purp

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