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If the sum of 5 consecutive positive multiples of a prime number is 105, what is the sum of the first 5 positive multipl

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If the sum of 5 consecutive positive multiples of a prime number is 105, what is the sum of the first 5 positive multipl

by VJesus12 » Fri Jul 10, 2020 3:29 am

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If the sum of 5 consecutive positive multiples of a prime number is 105, what is the sum of the first 5 positive multiples of that prime number?

A) 30
B) 45
C) 75
D) 105
E)Can’t be determined

[spoiler]OA=E[/spoiler]

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Re: If the sum of 5 consecutive positive multiples of a prime number is 105, what is the sum of the first 5 positive mul

by deloitte247 » Sat Jul 11, 2020 6:46 am
Let the prime number = p and multiple = m
Sum of 5 consecutive positive multiples of p = 105
=> (p * m) + [p * (m+1)] + [p * (m+2)] + [p * (m+3)] + [p * (m+4)]
=> pm + pm+p + pm+2p + pm+3p + pm+4p
$$=>5pm+10p=105$$
$$=>\frac{5p\left(m+2\right)}{5}=\frac{105}{5}$$
$$=>p\left(m+2\right)=21$$
This equation has 2 unknown variables which cannot be evaluated with 1 equation so the answer to the question cannot be determined

Answer = E
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