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

Redeem

If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represents

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pm
Thanked: 6 times
Followed by:5 members

If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represents

by Vincen » Wed Jul 22, 2020 12:46 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represents the first term such that \(a_n > 500?\)

A. 13
B. 22
C. 33
D. 46
E. 78

[spoiler]OA=B[/spoiler]

Source: Magoosh
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

Re: If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represen

by Jay@ManhattanReview » Wed Jul 22, 2020 10:39 pm
Vincen wrote: ↑
Wed Jul 22, 2020 12:46 pm
 If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represents the first term such that \(a_n > 500?\)

A. 13
B. 22
C. 33
D. 46
E. 78

[spoiler]OA=B[/spoiler]

Source: Magoosh
So we have \(n^2+n+\sqrt{n+3} > 500\)

We have to find out the minimum positive integer value of n such that \(\sqrt{n+3}\) is an integer, and \(n^2+n+\sqrt{n+3} > 500\). By hit and trial, we find that n = 22 serves the purpose as at n = 13, though \(\sqrt{n+3}\) is an integer, \(n^2+n+\sqrt{n+3} < 500\).

Correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Prep Indianapolis | LSAT Prep Atlanta | GRE San Antonio | SAT Prep Detroit | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top

GMAT/MBA Expert

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

Re: If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represen

by Scott@TargetTestPrep » Sat Jul 25, 2020 2:15 pm
Vincen wrote: ↑
Wed Jul 22, 2020 12:46 pm
 If the sequence \(a_n\) is defined as \(a_n=n^2+n+\sqrt{n+3},\) then which of the following values of \(n\) represents the first term such that \(a_n > 500?\)

A. 13
B. 22
C. 33
D. 46
E. 78

[spoiler]OA=B[/spoiler]

Solution:

The best way to solve this problem is to try the answer choices out. Since the terms n and √(n + 3) are much smaller than n^2, we can assume a(n) = n^2.

A. If n = 13, a(13) = 13^2 = 169. This is a lot less than 500, so A can’t be the correct answer.

B. If n = 22, a(22) = 22^2 = 484. This is about 500, so let’s use the actual formula for a(n):

a(22) = 22^2 + 22 + √(22 + 3) = 484 + 22 + 5 = 511

This is greater than 500, so B is the correct answer.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1