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If x is the sum of the first 10 positive multiples of 3 and y is the

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Bunuel
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If x is the sum of the first 10 positive multiples of 3 and y is the [#permalink] If x is the sum of the first 10 positive multiples of 3 and y is the   07 Dec 2022, 02:30
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If x is the sum of the first 10 positive multiples of 3 and y is the sum of the first 10 positive multiples of 2, which of the following is a factor of x – y?

A. 20
B. 35
C. 55
D. 75
E. 90

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C
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Re: If x is the sum of the first 10 positive multiples of 3 and y is the [#permalink] If x is the sum of the first 10 positive multiples of 3 and y is the   07 Dec 2022, 20:52
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Bunuel wrote:
If x is the sum of the first 10 positive multiples of 3 and y is the sum of the first 10 positive multiples of 2, which of the following is a factor of x – y?

A. 20
B. 35
C. 55
D. 75
E. 90



x=3+6+9+…..+30=3(1+2+3+….+10)
y=2+4+6+…..+20=2(1+2+3+….+10)

x-y= 3(1+2+3+….+10) - 2(1+2+3+….+10) = (1+2+3+….+10)
=\(\frac{10*11}{2} \)=55


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Re: If x is the sum of the first 10 positive multiples of 3 and y is the [#permalink] If x is the sum of the first 10 positive multiples of 3 and y is the   07 Dec 2022, 23:33
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Bunuel wrote:
If x is the sum of the first 10 positive multiples of 3 and y is the sum of the first 10 positive multiples of 2, which of the following is a factor of x – y?

A. 20
B. 35
C. 55
D. 75
E. 90


As the numbers are equally spaced, the sum = mean * number of terms

Mean of 10 positive multiples of 3 = \(\frac{15 + 18 }{ 2}\) = \(\frac{33}{2}\)

Mean of 10 positive multiples of 2 = \(\frac{10 + 12 }{ 2}\) = \(\frac{22}{2}\)

Difference = \(\frac{33 - 22}{ 2} * 10 \) = 11*5 = 55

Factor = 55

Option C
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Re: If x is the sum of the first 10 positive multiples of 3 and y is the [#permalink] If x is the sum of the first 10 positive multiples of 3 and y is the   08 Dec 2022, 12:09
3(1+2+3...10)-2(1+2+3+..10) = 3*11*10/2 - 2*11*10/2 = 55
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Re: If x is the sum of the first 10 positive multiples of 3 and y is the [#permalink] If x is the sum of the first 10 positive multiples of 3 and y is the   08 Dec 2022, 18:51
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Bunuel wrote:
If x is the sum of the first 10 positive multiples of 3 and y is the sum of the first 10 positive multiples of 2, which of the following is a factor of x – y?

A. 20
B. 35
C. 55
D. 75
E. 90



The sum the of the first 10 positive multiples of 3 is:

10 x (30 + 3)/2 = 10 x 33/2 = 5 x 33 = 165

The sum of the first 10 positive multiples of 2 is:

10 x (20 + 2)/2 = 10 x 11 = 110

Thus x - y = 165 - 110 = 55, and a factor of 55 is factor of 55.

Answer: C
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Re: If x is the sum of the first 10 positive multiples of 3 and y is the [#permalink]
08 Dec 2022, 18:51
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