Number N is randomly selected from a set of consecutive inte

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Number N is randomly selected from a set of consecutive inte

by BTGmoderatorDC » Fri May 24, 2019 8:06 pm

Timer

00:00

Your Answer

Global Stats

Number N is randomly selected from a set of consecutive integers between 50 and 69, inclusive. What is the probability that N will have the same number of factors as 89?

a) 1/2
b 1/5
c) 0
d) 1/3
e) 1/4

OA B

Source: Manhattan Prep

Quote

Source: Beat The GMAT — Problem Solving | Fri May 24, 2019 8:06 pm

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 28, 2019 4:45 pm

BTGmoderatorDC wrote:Number N is randomly selected from a set of consecutive integers between 50 and 69, inclusive. What is the probability that N will have the same number of factors as 89?

a) 1/2
b 1/5
c) 0
d) 1/3
e) 1/4

OA B

Source: Manhattan Prep

The solution to this problem is straightforward if you know your prime numbers.

We need to determine the probability that a number, when randomly selected from the set of integers between 50 and 69, inclusive, will have the same number of factors as 89. Since 89 is prime and thus has only two factors, we need to determine the number of prime numbers between 50 and 69, inclusive. The prime numbers between 50 and 69, inclusive, are:

53, 59, 61, 67

We also know that there are 69 - 50 + 1 = 20 integers from 50 to 69, inclusive; thus, the probability that N will have the same number of factors as 89 is 4/20 = â…•.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]