SajjadAhmad wrote:
A certain jar contains 20 jellybeans; each jellybean is either black, pink, or yellow. Does the jar contain more pink jellybeans than yellow jellybeans?
(1) The jar contains more black jellybeans than pink jellybeans.
(2) The jar contains 6 pink jellybeans.
Solution
Step 1: Analyse Question Stem
• Let us assume that b, p, and y are the number of black, pink and yellow jellybeans in the jar, respectively.
o \(b + p + y = 20 …………..Eq.(i)\)
• We need to find out if p > y
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The jar contains more black jellybeans than pink jellybeans.
• \(b > p\)
• We have no information about y. so we cannot find if p > y. For example:
o Case 1: b can be 10, p can be 6 and y can be 4, such that \(b + p + y = 20\) and \(b > p\)
In this case, \(p > y\)
o Case 2: However, b can be 10, p can be 4 and y can be 6, such that \(b + p + y = 20\) and \(b > p\)
• We are getting contradictory results.
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: The jar contains 6 pink jellybeans.
• According to this statement: \(p = 6\)
• However, this statement gives no information about b and y.
Hence, statement 2 is also NOT sufficient and we can eliminate answer Option B.
Step 3: Analyse Statements by combining.
From statement 1: \(b > p\)
From statement 2: \(p = 6\)
On combining we get,
• \(b > p\) and \(p = 6\)
• So, from above and equation (i), we can write,
o \(y = 20 – b – p ⟹ y < 20 – 6 – 6 ⟹ y < 8\)
o Therefore, y can be 7, in that case p < y
Also, y can be 5, in that case p > y
• We are still getting contradictory results.
Thus, the correct answer is
Option E.