Number $N$ is randomly selected from a set of all primes between $10$ and $40,$ inclusive. Number $K$ is selecte

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Aug 15, 2021 8:44 am

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Number $N$ is randomly selected from a set of all primes between $10$ and $40,$ inclusive. Number $K$ is selected from a set of all multiples of $5$ between $10$ and $40$ inclusive. What is the probability that $N+K$ is odd?

(A) $\dfrac12$

(B) $\dfrac23$

(C) $\dfrac34$

(D) $\dfrac47$

(E) $\dfrac58$

Answer: D

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Sun Aug 15, 2021 8:44 am

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Re: Number $N$ is randomly selected from a set of all primes between $10$ and $40,$ inclusive. Number $K$ is sel

by Brent@GMATPrepNow » Sun Aug 15, 2021 2:28 pm

VJesus12 wrote: ↑
Sun Aug 15, 2021 8:44 am
Number $N$ is randomly selected from a set of all primes between $10$ and $40,$ inclusive. Number $K$ is selected from a set of all multiples of $5$ between $10$ and $40$ inclusive. What is the probability that $N+K$ is odd?

(A) $\dfrac12$

(B) $\dfrac23$

(C) $\dfrac34$

(D) $\dfrac47$

(E) $\dfrac58$

Answer: D

Source: Veritas Prep

Notice that there are 2 ways that the sum N+K can be ODD
1) N is ODD and K is EVEN
2) N is EVEN and K is ODD

However, N cannot be EVEN, since all of the primes between 10 and 40 are ODD (11, 13, 17, 19, . . . . 31, 37)
So, case 2 (above) is impossible

So, P(N+K is odd) = P(N is odd AND K is even)
= P(N is odd) x P(K is even)

------ASIDE-------
Possible values of N: (11, 13, 17, 19, . . . . 31, 37)
So, P(N is odd) = 1

Possible values of K: (10, 15, 20, 25, 30, 35, 40)
So, P(K is even) = 4/7
-----------------------------------------

So, P(N+K is odd) = P(N is odd AND K is even)
= P(N is odd) x P(K is even)
= 1 x 4/7
= 4/7
= D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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