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

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

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23 Nov 2014, 06:31
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25% (medium)

Question Stats:

78% (01:54) correct 22% (02:20) wrong based on 160 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
Joined: 02 Sep 2009
Posts: 59147
Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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23 Nov 2014, 06:55
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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Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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23 Nov 2014, 19:04
5
1

91 = 1 + 90

= 1 + 9 + 81

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

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

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

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09 Oct 2017, 10:58
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

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Joined: 02 Sep 2009
Posts: 59147
Re: The number 91 can be written as the sum of squares of 3 integers.  [#permalink]

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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.

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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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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17 Jun 2019, 19:36
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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