If x and y are integers, which of the following CANNOT be th

Expert replies

Max@Math Revolution: 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 » Thu Jan 25, 2018 3:00 am

[GMAT math practice question]

If x and y are integers, which of the following CANNOT be the value of x^2+y^2?

A. 121
B. 122
C. 123
D. 125
E. 130

Math Revolution

The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]

Source: Beat The GMAT — Problem Solving | Thu Jan 25, 2018 3:00 am

DrMaths: Senior | Next Rank: 100 Posts; Posts: 82; Joined: Mon Jan 15, 2018 2:01 am

by DrMaths » Thu Jan 25, 2018 7:41 am

The smallest Pythagorean triples are:
(3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25)
None of these include 11
Answer A is 11^2 = 121

As 11 is not in the list of triples, then A is impossible.
All the other values are not squares, so non-integer solutions are possible.

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 25, 2018 9:27 am

DrMaths wrote:The smallest Pythagorean triples are:
(3, 4, 5) (5, 12, 13) (8, 15, 17) (7, 24, 25)
None of these include 11
Answer A is 11^2 = 121

As 11 is not in the list of triples, then A is impossible.
All the other values are not squares, so non-integer solutions are possible.

'

Be careful; if x = 0 and y = 11, then we get: 0² + 11² = 121
Eliminate A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jan 25, 2018 9:32 am

Max@Math Revolution wrote:[GMAT math practice question]

If x and y are integers, which of the following CANNOT be the value of x^2+y^2?

A. 121
B. 122
C. 123
D. 125
E. 130

Let's do this systematically:
0² = 0
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121

A. 121 = 0² + 11² ELIMINATE A
B. 122 = 1² + 11² ELIMINATE B
C. 123 = can't eliminate
D. 125 = 10² + 5² ELIMINATE D
E. 130 = 9² + 7² ELIMINATE E

Answer: C

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jan 25, 2018 11:02 am

Max@Math Revolution wrote:[GMAT math practice question]

If x and y are integers, which of the following CANNOT be the value of x^2+y^2?

A. 121
B. 122
C. 123
D. 125
E. 130

Eliminate the four answer choices that CAN be the value of x²+y², where x and y are integers.
A: 121 = 11² + 0²
B: 122 = 11² + 1²
D: 125 = 11² + 2²
E: 130 = 11² + 3²
Eliminate A, B, D and E.

The correct answer is C.

Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Max@Math Revolution: 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 Jan 28, 2018 5:39 pm

=>
Squares of even integers, (2k)^2 = 4k^2 have the remainder 0, when they are divided by 4.

Squares of odd integers, (2k+1)^2 = 4k^2 + 4k + 1 have the remainder 1, when they are divided by 4.

Hence, squares of integers can have remainders of 0 or 1 only, when they are divided by 4. So, the sum of two squares of integers cannot have the remainder of 3 when it is divided by 4.

Thus, 123 cannot be the value of x^2+y^2.
Therefore, the answer is C.
Answer: C

Jeff@TargetTestPrep: 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 Jan 29, 2018 9:42 am

Max@Math Revolution wrote:[GMAT math practice question]

If x and y are integers, which of the following CANNOT be the value of x^2+y^2?

A. 121
B. 122
C. 123
D. 125
E. 130

Let’s test our answer choices:

A) 121

121 = 0^2 + 11^2

B) 122

122 = 1^1 + 11^2

C) 123

There are no two perfect squares that sum to 123.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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

Featured schoolRound 2 closes Jan 7, 2027 53 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review