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If the integer s is divided by 9, the remainder is 1.
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25 Jun 2020, 10:44
25 Jun 2020, 10:44
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If the integer s is divided by 9, the remainder is 1. If s is divided by 4, the remainder is 2. If s is between 30 and 90, what is one possible value of s ?
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46 or 82
Re: If the integer s is divided by 9, the remainder is 1.
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25 Jun 2020, 10:45
25 Jun 2020, 10:45
Expert Reply
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Re: If the integer s is divided by 9, the remainder is 1.
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25 Jun 2020, 17:07
25 Jun 2020, 17:07
1
Since the number we are looking for has remainder of 1 when its divided by 9. Lets find all multiples of 9 in this interval and add 1 to them.
Multiples of 9 in the interval: 36, 45, 54, 63, 72, 81, 90
Lets add 1 to these intervals and find the values that satisfy the condition.
37, 46, 55, 64, 73, 82, 91.
We can remove the odd integers since they give remainder of either 1 or 3 when divided by 4.
We are left with: 46, 64, 82
4 is a factor of 64, so we can cross it out.
We are left with 46 and 82.
46/4 = 11 remainder 2, and we know that it gives remainder 1 when divided by 9.
82/4 = 20 remainder 2, and we know that it gives remainder 1 when divided by 9.
Both of these numbers satisfy the conditions.
Multiples of 9 in the interval: 36, 45, 54, 63, 72, 81, 90
Lets add 1 to these intervals and find the values that satisfy the condition.
37, 46, 55, 64, 73, 82, 91.
We can remove the odd integers since they give remainder of either 1 or 3 when divided by 4.
We are left with: 46, 64, 82
4 is a factor of 64, so we can cross it out.
We are left with 46 and 82.
46/4 = 11 remainder 2, and we know that it gives remainder 1 when divided by 9.
82/4 = 20 remainder 2, and we know that it gives remainder 1 when divided by 9.
Both of these numbers satisfy the conditions.
