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The number 91 can be written as the sum of squares of 3 integers.

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The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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The number 91 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?

A. 2
B. 5
C. 7
D. 8
E. 9


[Reveal] Spoiler:
Spoiler ////

OA is height since it is the difference from 9 and 1. However, the question is not mentioning that the integers have to be positive. Therefore we could have -3 (still giving +9 once squared) and so a difference of 9 - -3 = +12.

Am I making this more complicated than it really is ?

Also, this was a question from the Economist free CAT. I got a 590 with a 28(!!!) on verbal (while on my previous CAT - Veritas - I got 38) even though I made only a few mistakes. I start to doubt of the reliability of the Economist CAT ... Any other experience with this CAT?

Thanks :)
[Reveal] Spoiler: OA

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Re: The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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New post 23 Nov 2014, 06:55
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MaximeU wrote:
The number 91 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?

A. 2
B. 5
C. 7
D. 8
E. 9


Spoiler ////

OA is height since it is the difference from 9 and 1. However, the question is not mentioning that the integers have to be positive. Therefore we could have -3 (still giving +9 once squared) and so a difference of 9 - -3 = +12.

Am I making this more complicated than it really is ?

Also, this was a question from the Economist free CAT. I got a 590 with a 28(!!!) on verbal (while on my previous CAT - Veritas - I got 38) even though I made only a few mistakes. I start to doubt of the reliability of the Economist CAT ... Any other experience with this CAT?

Thanks :)


Notice that the question asks which of the following could be the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-1, +/-3 and +/-9, so the difference could be 8, 10 or 12. Since only one of them is among the choices, then it must be the correct answer.

Answer: D.

Similar question to practice from GMAT Prep: the-number-75-can-be-written-as-the-sum-of-the-squares-of-125101.html

Hope it helps.
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Re: The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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New post 23 Nov 2014, 19:04
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Answer = D = 8

91 = 1 + 90

= 1 + 9 + 81

\(= 1^2 + 3^2 + 9^2\)

Difference = 9-1 = 8
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Re: The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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New post 11 Apr 2016, 12:35
91 can be expressed as sum of 3 squares as follows - (+/- 1)^2, (+/- 3)^2, (+/- 9)^2
I am considering both positive and negative numbers as integers can be both positive or negative,but the squares have to positive only
Possible differences between the numbers could be 8, 10 or 12
As the question asks for which could be the possible value for difference,the answer has to be 8
correct answer - D

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Re: The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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Re: The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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New post 09 Oct 2017, 10:58
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Hello Moderators,

I got this question as part of my Workbook recommendation. Do you think the highlighted portion of the question needs to be hidden? The highted test is giving away the answer to the question.

Thanking you in advance!

MaximeU wrote:
The number 91 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?

A. 2
B. 5
C. 7
D. 8
E. 9


Spoiler ////

OA is height since it is the difference from 9 and 1. However, the question is not mentioning that the integers have to be positive. Therefore we could have -3 (still giving +9 once squared) and so a difference of 9 - -3 = +12.

Am I making this more complicated than it really is ?

Also, this was a question from the Economist free CAT. I got a 590 with a 28(!!!) on verbal (while on my previous CAT - Veritas - I got 38) even though I made only a few mistakes. I start to doubt of the reliability of the Economist CAT ... Any other experience with this CAT?

Thanks :)

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Kudos [?]: 42 [1], given: 145

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42280

Kudos [?]: 132894 [0], given: 12391

Re: The number 91 can be written as the sum of squares of 3 integers. [#permalink]

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New post 09 Oct 2017, 11:05
susheelh wrote:
Hello Moderators,

I got this question as part of my Workbook recommendation. Do you think the highlighted portion of the question needs to be hidden? The highted test is giving away the answer to the question.

Thanking you in advance!

MaximeU wrote:
The number 91 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?

A. 2
B. 5
C. 7
D. 8
E. 9


Spoiler ////

OA is height since it is the difference from 9 and 1. However, the question is not mentioning that the integers have to be positive. Therefore we could have -3 (still giving +9 once squared) and so a difference of 9 - -3 = +12.

Am I making this more complicated than it really is ?

Also, this was a question from the Economist free CAT. I got a 590 with a 28(!!!) on verbal (while on my previous CAT - Veritas - I got 38) even though I made only a few mistakes. I start to doubt of the reliability of the Economist CAT ... Any other experience with this CAT?

Thanks :)

____________________
Done. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132894 [0], given: 12391

Re: The number 91 can be written as the sum of squares of 3 integers.   [#permalink] 09 Oct 2017, 11:05
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The number 91 can be written as the sum of squares of 3 integers.

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