Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag. Afte

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag. Afte

by Vincen » Sun Dec 26, 2021 10:21 am

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Maria bought 4 black and a certain number of red and blue pencils at 15 cents each and carried them home in one bag. After Maria came home, she took out one pencil at random to write a note and then put the pencil back into the bag. Sometime later, she needed to write another note and again took out a pencil from the bag. If the probability that Maria wrote both her notes in black is 1/36, how much did she spend on all pencils?

A. $3
B. $3.2
C. $3.4
D. $3.6
E. $3.8

Answer: D

Source: Manhattan GMAT

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Source: Beat The GMAT — Problem Solving | Sun Dec 26, 2021 10:21 am

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Re: Maria bought 4 black and a certain number of red and blue pencils at 15 cents each an carried them home in one bag.

by swerve » Sun Dec 26, 2021 11:56 am

Vincen wrote: ↑
Sun Dec 26, 2021 10:21 am
Maria bought 4 black and a certain number of red and blue pencils at 15 cents each and carried them home in one bag. After Maria came home, she took out one pencil at random to write a note and then put the pencil back into the bag. Sometime later, she needed to write another note and again took out a pencil from the bag. If the probability that Maria wrote both her notes in black is 1/36, how much did she spend on all pencils?

A. $3
B. $3.2
C. $3.4
D. $3.6
E. $3.8

Answer: D

Source: Manhattan GMAT

If the total pencils are t, the probability of picking first as black $= \dfrac{4}{t}.$

As it is again replaced, the probability in next will also be the same $= \dfrac{4}{t}.$

$P$ to pick black pencil in both picks $=\dfrac{4}{t} \ast \dfrac{4}{t} = \dfrac{1}{36}$

$t^2=16\ast 36 \Longrightarrow t = 4 \ast 6 = 24$

Price of these $24$ pencils $= 15\ast 24 = \$3.6$

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