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m2 + n2 = 17, where m and n are integers. What is the total number o
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17 Aug 2024, 05:02
17 Aug 2024, 05:02
Expert Reply
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Question Stats:
16% (00:25) correct
83% (01:23) wrong based on 6 sessions
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\(m^2 + n^2 = 17\), where m and n are integers. What is the total number of different values of \(m + n\)?
A. 1
B. 2
C. 3
D. 4
A. infinite values
A. 1
B. 2
C. 3
D. 4
A. infinite values
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Shorter GRE - Preparing for the Quantitative Reasoning Measure
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Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
Re: m2 + n2 = 17, where m and n are integers. What is the total number o
[#permalink]
17 Aug 2024, 21:25
17 Aug 2024, 21:25
Explanation please?
Re: m2 + n2 = 17, where m and n are integers. What is the total number o
[#permalink]
18 Aug 2024, 00:22
18 Aug 2024, 00:22
1
Expert Reply
This is more a logic question than a picking number one
You have two integers that raised to their square gives you 17 and you have to find the combination adding the two numbers. Moreover, you have to take into account also negative numbers because they raised to the power of two they are still positive.
17 is prime and the only combination to have 17 is 16+1 considering each number from 0 to 9
The only perfect square numbers are 4 and 1. \(1^2+4^2=1+16=17\). Also we have to consider -1 and -4
So we do have 4 numbers or two pairs of them : (1,4) and (-1,-4)
D is the answer
You have two integers that raised to their square gives you 17 and you have to find the combination adding the two numbers. Moreover, you have to take into account also negative numbers because they raised to the power of two they are still positive.
17 is prime and the only combination to have 17 is 16+1 considering each number from 0 to 9
The only perfect square numbers are 4 and 1. \(1^2+4^2=1+16=17\). Also we have to consider -1 and -4
So we do have 4 numbers or two pairs of them : (1,4) and (-1,-4)
D is the answer
