A certain stationary store arranges notebooks on display such that eac

Question

A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple?

(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2

(A) 1/49
(B) 1/8
(C) 1/7
(D) 2/7
(E) 1/2

GMATWhizTeam · Answer

Solution:
 • There is a total of  7  different colors.
 o They are arranged in a consecutive repeating pattern.
  The color of every 8th notebook is the same.  
• Now, 8 consecutive notebooks are selected.
 o This means there are exactly two notebooks of the same color. (For example, PWTOGRBP)
o There are seven different possibilities for selecting two notebooks of the same color. (Total cases) 
• If the first notebook is purple, then the last notebook will also be purple, this is the only favorable case.
 o Probability of selecting two purple notebooks =  \frac{1}{7}   
Hence, the correct answer is Option C.

v12345 · Answer

Total cases = 7 (seven colours notebook)
Favourable case = 1
Probability = 1/7
Hence, OA is (C).

Abulikabuli · Answer

I feel a better explanation is due. 
With the seven colors you get 7! arrangements.
Out of these only in the cases where Purple is the first are what we are concerned with as in those cases Purple repeats in the 8th place.
So total cases were purple is first is 6! 
So probability of getting Purple in 8th is 6!/7! =1/7

EshaFatim · Answer

could you please explain the 6! in detail?

EshaFatim · Answer

This could be a simpler way to think.

Out of 7 possible  starting positions (since the pattern repeats every 7 notebooks) , there is only 1 position where purple could appear twice in 8 consecutive notebooks.
Therefore, the probability of getting two purple notebooks in the selection of 8 consecutive notebooks is 1/7.

piermacabj · Answer

I solved it like this, looks a bit long but once you realize the pattern the answer comes pretty easily.

A certain stationary store arranges notebooks on display such that eac

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A certain stationary store arranges notebooks on display such that eac

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards