Functions and Custom Characters

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

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

Functions and Custom Characters

by swerve » Wed Mar 25, 2020 11:59 am

Timer

00:00

Your Answer

Global Stats

Let @x@ be defined as the number of positive perfect squares less than x
Let #x# be defined as the number of primes less than @x@
If #x# = 5, what is the value of #(@x@)#?

A. 7
B. 5
C. 4
D. 2
E. 1

The OA is E

Source: Magoosh

Quote

Source: Beat The GMAT — Problem Solving | Wed Mar 25, 2020 11:59 am

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

Re: Functions and Custom Characters

by Scott@TargetTestPrep » Fri Mar 27, 2020 6:10 am

swerve wrote: ↑
Wed Mar 25, 2020 11:59 am
Let @x@ be defined as the number of positive perfect squares less than x
Let #x# be defined as the number of primes less than @x@
If #x# = 5, what is the value of #(@x@)#?

A. 7
B. 5
C. 4
D. 2
E. 1

The OA is E

Source: Magoosh

Since #x# = 5, we see that there are 5 primes less than @x@. Since the 5th prime is 11 and the 6th prime is 13, we see that @x@ must be 12 or 13. Therefore, we have:

#(@x@)# = #12# or #13#

Since #12# is the number of primes less than @12@ and @12@ is the number of positive perfect squares less than 12, @12@ = 3 (since there are 3 perfect squares less than 12: 1, 4 and 9). Notice that since @13@ = 3 also, #13# is equal to the number of primes less than 3 as well.

So, #12# = #13# is the number of primes less than 3, and since there is only 1 prime (namely, 2) less than 3, the answer is 1.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]