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If 12x = 30y = 15z, and x, y, and z are all positive integers, which
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16 Dec 2021, 03:07
16 Dec 2021, 03:07
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If 12x = 30y = 15z, and x, y, and z are all positive integers, which of the following correctly orders them from least to greatest?
(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) y, z, x
(E) z, y, x
(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) y, z, x
(E) z, y, x
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Re: If 12x = 30y = 15z, and x, y, and z are all positive integers, which
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16 Dec 2021, 05:45
16 Dec 2021, 05:45
1
Carcass wrote:
If 12x = 30y = 15z, and x, y, and z are all positive integers, which of the following correctly orders them from least to greatest?
(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) y, z, x
(E) z, y, x
(A) x, y, z
(B) z, x, y
(C) y, x, z
(D) y, z, x
(E) z, y, x
Let's express all three variables in terms of x
Given: 12x = 30y
Divide both sides by 30 to get: y = 12x/30 = 2x/5 = 0.4x
Given: 12x = 15z
Divide both sides by 15 to get: z = 12x/15 = 4x/5 = 0.8x
Since x is positive, we know that 0.4x < 0.8x < x
Substitute to get: y < z < x
Answer: D
Re: If 12x = 30y = 15z, and x, y, and z are all positive integers, which
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17 Dec 2021, 01:38
17 Dec 2021, 01:38
1
given, 12x = 30y = 15z, dividing the entire equation by 3, we have: -
4x = 10y = 5z. Now, we can write x:y:z = 1/4 : 1/10 : 1/5. Converting fractions to whole numbers requires multiplication by LCM of their denominators
here LCM(4,10,5) = 20, so new ratio of x:y:z = 5 : 2 : 4,
rearranging ratio terms in ascending order => y:z:x = 2:4:5
Hence answer = D
4x = 10y = 5z. Now, we can write x:y:z = 1/4 : 1/10 : 1/5. Converting fractions to whole numbers requires multiplication by LCM of their denominators
here LCM(4,10,5) = 20, so new ratio of x:y:z = 5 : 2 : 4,
rearranging ratio terms in ascending order => y:z:x = 2:4:5
Hence answer = D
