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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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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Since we know x is a multipole of 3, we can say x = 3k. Thus, we have:BTGmoderatorDC wrote: ↑Thu Mar 30, 2023 3:02 amx 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
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.
Answer: E
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