## x and y are positive integers and 5x + 4y = 240. If x is a multiple of 3, then y could be a multiple of which of the

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### x and y are positive integers and 5x + 4y = 240. If x is a multiple of 3, then y could be a multiple of which of the

by BTGmoderatorDC » Thu Mar 30, 2023 3:02 am

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x and y are positive integers and 5x + 4y = 240. If x is a multiple of 3, then y could be a multiple of which of the following?

I. 6

II. 9

III. 15

(A) I only
(B) II Only
(C) II & III
(D) I & III
(E) I, II, & III

OA E

Source: Magoosh

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### Re: x and y are positive integers and 5x + 4y = 240. If x is a multiple of 3, then y could be a multiple of which of the

by [email protected] » Thu Mar 30, 2023 5:01 pm
BTGmoderatorDC wrote:
Thu Mar 30, 2023 3:02 am
x and y are positive integers and 5x + 4y = 240. If x is a multiple of 3, then y could be a multiple of which of the following?

I. 6

II. 9

III. 15

(A) I only
(B) II Only
(C) II & III
(D) I & III
(E) I, II, & III

OA E

Source: Magoosh
Since we know x is a multipole of 3, we can say x = 3k. Thus, we have:

5(3k) + 4y = 240

15k + 4y = 240

4y = 240 - 15k

4y = 15(16 - k)

y = 15(16 - k)/4

We see that k can be 4, 8, or 12.

When k is 4, y is 45.

When k is 8, y is 30.

When k is 12, y is 15.

Thus, we see that y can be a mutlipole of 6, 9, and 15.