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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The number 91 can be written as the sum of squares of 3 integers.

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Intern  Joined: 12 Nov 2014
Posts: 3
The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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4 00:00

Difficulty:   25% (medium)

Question Stats: 78% (01:54) correct 22% (02:19) wrong based on 163 sessions

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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

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 Math Expert V
Joined: 02 Sep 2009
Posts: 59720
Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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1
4
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.

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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Joined: 27 Dec 2012
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Location: India
Concentration: General Management, Technology
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Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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5
1

91 = 1 + 90

= 1 + 9 + 81

$$= 1^2 + 3^2 + 9^2$$

Difference = 9-1 = 8
##### General Discussion
Manager  G
Joined: 12 Jun 2016
Posts: 205
Location: India
WE: Sales (Telecommunications)
Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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1
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.

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 _________________
My Best is yet to come!
Senior Manager  G
Joined: 24 Nov 2015
Posts: 480
Location: United States (LA)
Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 59720
Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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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.

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.
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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] 17 Jun 2019, 19:36
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