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NeilWatson: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Wed Oct 30, 2013 7:54 amFollowed by: 1 member

by NeilWatson » Sun Apr 06, 2014 6:14 pm

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?
A) 17
B) 16
C) 15
D) 14
E) 13

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Source: Beat The GMAT — Problem Solving | Sun Apr 06, 2014 6:14 pm

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 » Sun Apr 06, 2014 6:32 pm

The number 75 can be written as the sum of the squares of 3 diff positive integers. What is the sum of these 3 integers?
a) 17
b) 16
c) 15
d) 14
e) 13

75 = the sum of three PERFECT SQUARES.
List the perfect squares less than 75.
Ask yourself the following:
Which perfect square will the average test-taker forget to consider?
Answer:
1Â² = 1.
Don't be an average test-taker.
Be sure to include 1Â² = 1 in your list:
1Â² = 1.
2Â² = 4.
3Â² = 9.
4Â² = 16.
5Â² = 25.
6Â² = 36.
7Â² = 49.
8Â² = 64.

The sum of the 3 values in red is 75:
1Â²+ 5Â² + 7Â² = 1 + 25 + 49 = 75.

Thus, the sum of the 3 integers = 1+5+7 = 13.

The correct answer is E.

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NeilWatson: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Wed Oct 30, 2013 7:54 amFollowed by: 1 member

by NeilWatson » Mon Apr 07, 2014 2:50 pm

Thanks! But is there a mathematical way to solve this? Or is the only way through brute strength?

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon Apr 07, 2014 10:44 pm

NeilWatson wrote:Thanks! But is there a mathematical way to solve this? Or is the only way through brute strength?

No, there is no mathematical way to answer such questions. This is "Just Do It" kind of question in which the answer choices may be taken as help.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
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www.manyagroup.com

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