A telephone number contains 10 digits, including a 3-digit area code. Bob remembers the area code and the next 5 digits

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Thu Sep 17, 2020 1:52 am

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A telephone number contains $10$ digits, including a $3$-digit area code. Bob remembers the area code and the next $5$ digits of the number. He also remembers that the remaining digits are not $0, 1, 2, 5,$ or $7.$ If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most $2$ attempts is closest to which of the following?

A. $\dfrac1{625}$

B. $\dfrac2{625}$

C. $\dfrac4{625}$

D. $\dfrac{25}{625}$

E. $\dfrac{50}{625}$

Answer: E

Source: Veritas Prep

Source: Beat The GMAT — Problem Solving | Thu Sep 17, 2020 1:52 am

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: A telephone number contains 10 digits, including a 3-digit area code. Bob remembers the area code and the next 5 dig

by swerve » Thu Sep 17, 2020 4:54 am

Gmat_mission wrote: ↑
Thu Sep 17, 2020 1:52 am
A telephone number contains $10$ digits, including a $3$-digit area code. Bob remembers the area code and the next $5$ digits of the number. He also remembers that the remaining digits are not $0, 1, 2, 5,$ or $7.$ If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most $2$ attempts is closest to which of the following?

A. $\dfrac1{625}$

B. $\dfrac2{625}$

C. $\dfrac4{625}$

D. $\dfrac{25}{625}$

E. $\dfrac{50}{625}$

Answer: E

Source: Veritas Prep

Here we have,

Last $2$ digit can be chosen out of $3, 4, 6, 8, 9$
means $5\times 5 = 25$ Numbers can be constructed. So,

Case 1: Bob able to dial the number in first attempt: $\dfrac{1}{25}$
Case 2: Bob able to dial the number in second attempt:

$\dfrac{24}{25} \times \dfrac{1}{24} = \dfrac{1}{25}$

Case $1 +$ Case $2 = \dfrac{2}{25}$ which is same as $\dfrac{50}{625}$.

Therefore, E

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