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03 Nov 2022, 12:43
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This is a weighted average question which can be easily solved under one minute using either of the two methods I tried:
1) the teeter-totter method in MGAMT word problems book:
As x, y are positive numbers, the weighted average has to be between 10 and 20, inclusive. Eliminate A and E.
If x=y, k is the average of 10 and 20 which is 15. We know this can't be the case given x < y. Eliminate C.
If x<y, x/(x+y) < y/(x+y), in other word, we are assigning more weight to 20 than 10. So the answer has to be greater than 15 (equal weight) but less than 20, which has to be D. Eliminate all others.
2) Smart Number
For the purpose of quick calculation, I tried the following x= 1, y=4 (x<y)
(1/(1+4))*10+(4/(1+4))*20=18
1) the teeter-totter method in MGAMT word problems book:
As x, y are positive numbers, the weighted average has to be between 10 and 20, inclusive. Eliminate A and E.
If x=y, k is the average of 10 and 20 which is 15. We know this can't be the case given x < y. Eliminate C.
If x<y, x/(x+y) < y/(x+y), in other word, we are assigning more weight to 20 than 10. So the answer has to be greater than 15 (equal weight) but less than 20, which has to be D. Eliminate all others.
2) Smart Number
For the purpose of quick calculation, I tried the following x= 1, y=4 (x<y)
(1/(1+4))*10+(4/(1+4))*20=18
17 Nov 2023, 03:42
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My intuition: it is a weighted average, where x/x+y (weight of 10) is lower than (y/x+y) weight of 20.
As x < y, k will be closer to 20 than to 10. Exclude A, B and C (C assumes x = y).
Exclude E (no sense).
It remains D.
As x < y, k will be closer to 20 than to 10. Exclude A, B and C (C assumes x = y).
Exclude E (no sense).
It remains D.
30 Nov 2024, 04:05
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Hi bunuel,
I solved the problem in following manner,
10x + 20y / x+ y = k
Therefore, 10x + 20y = kx+ ky
10x-kx = ky - 20y
x (10-k) = y (k-20).
Since, y>x , 10-k should be > k-20
10-k>k-20
30>2k
15>k
Please tell me where am i going wrong
I solved the problem in following manner,
10x + 20y / x+ y = k
Therefore, 10x + 20y = kx+ ky
10x-kx = ky - 20y
x (10-k) = y (k-20).
Since, y>x , 10-k should be > k-20
10-k>k-20
30>2k
15>k
Please tell me where am i going wrong
Bunuel
