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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

If the sum of the squares of two positive integers is 106, w

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Fri Apr 20, 2018 12:43 am
[GMAT math practice question]

If the sum of the squares of two positive integers is 106, what is the sum of the two integers?

A. 13
B. 14
C. 15
D. 16
E. 17
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times

by Vincen » Fri Apr 20, 2018 2:40 am
Hello.

This is the way I would solve it:

Nº ---- (Nº)^2
1 ---- 1
2 ---- 4
3 ---- 9
4 ---- 16
5 ---- 25
6 ---- 36
7 ---- 49
8 ---- 64
9 ---- 81
10 ---- 100

The only two squared number whose sum is 106 are: 25 and 81.

Then the numbers are 5 and 9. Hence, 5+9=14.

The correct answer is B.

I'd like to know if is there another way to solve it?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Fri Apr 20, 2018 5:45 am
Vincen wrote:Hello.

This is the way I would solve it:

Nº ---- (Nº)^2
1 ---- 1
2 ---- 4
3 ---- 9
4 ---- 16
5 ---- 25
6 ---- 36
7 ---- 49
8 ---- 64
9 ---- 81
10 ---- 100

The only two squared number whose sum is 106 are: 25 and 81.

Then the numbers are 5 and 9. Hence, 5+9=14.

The correct answer is B.

I'd like to know if is there another way to solve it?
Your solution is perfect. I can't think of a different approach.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Sun Apr 22, 2018 5:22 pm
=>
x^2 + y^2 = 106.
We can plug-in the numbers from 1 to 10 to find the values of x and y that work.
We find that 9^2 + 5^2 = 81 + 25 = 106. So, the two numbers are 5 and 9, and their sum is 9 + 5 = 14.

Therefore, the answer is B.
Answer: B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:47 pm
Max@Math Revolution wrote:
If the sum of the squares of two positive integers is 106, what is the sum of the two integers?

A. 13
B. 14
C. 15
D. 16
E. 17
We can determine that 5^2 + 9^2 = 106, so the sum of the two numbers is 5 + 9 = 14.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1