(10x + 20 y)/(x+y) = k
10x + 20y = kx + ky
10x - kx = ky - 20y
x(10-k) = y (k-20)
x/y = (k-20)/(10-k)
Insert the values for k
A) 10----k cannot be 10 since denominator will be 0. Eliminate.
B) 12----
x/y = 4/1
4y=x, this cannot be possible since y>x and both the numbers are positive. Eliminate
C) 15----
x/y=1/1, x=y, same reason as above. Eliminate.
D) 18----
x/y=1/4, 4x=y, this is the only possible answer which satisfies all the above conditions.
E) 30----
x/y = -(10/20). x, y and k are all positive numbers, Eliminate.
Hence Answer is D.
Whats the OA?
Equations: if x, y, and k are positive numbers
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parallel_chase
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Ian Stewart
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The equation just represents a weighted average, and if y is larger than x, the answer must be closer to 20 than to 10. So 18 is the only possibility. I went into more detail here:
www.beatthegmat.com/tough-algebra-equation-t13568.html
www.beatthegmat.com/tough-algebra-equation-t13568.html
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pepeprepa
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That's clear there is an analogy with weighted average, but given I did not manage to use it to solve the question, I did that (parallel to Chase):
10x + 20y = (x+y)*k
A) 10
10y=0
That's wrong
B) 12
8y=2x
No because y>x
C) 15
5y=5x
No because y>x
D) 18
2y=8x
It seems nice, let's check if E is wrong
E) 30
-10y=20x
Impossible x>0 and y>0
That's D
10x + 20y = (x+y)*k
A) 10
10y=0
That's wrong
B) 12
8y=2x
No because y>x
C) 15
5y=5x
No because y>x
D) 18
2y=8x
It seems nice, let's check if E is wrong
E) 30
-10y=20x
Impossible x>0 and y>0
That's D
