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An alloy of copper and aluminum has 40% copper. An alloy of Copper and [#permalink]
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17 Sep 2016, 10:06
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An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take? A) 30% ≤ x ≤ 40% B) 32.5% ≤ x ≤ 40% C) 32.5% ≤ x ≤ 42% D) 33.33% ≤ x ≤ 40% E) 33.33 % ≤ x ≤ 42%
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and [#permalink]
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24 Sep 2016, 11:05
GMATantidote wrote: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?
A) 30% ≤ x ≤ 40%
B) 32.5% ≤ x ≤ 40%
C) 32.5% ≤ x ≤ 42%
D) 33.33% ≤ x ≤ 40%
E) 33.33 % ≤ x ≤ 42% Copper to Zinc ratio = 2/9 = 22.2 % Hence x  22.2 / 40  x = P / Q P Ration of and according to Question P > Q . Plug in the values a) only fits



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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and [#permalink]
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02 Oct 2016, 20:09
GMATantidote wrote: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?
A) 30% ≤ x ≤ 40%
B) 32.5% ≤ x ≤ 40%
C) 32.5% ≤ x ≤ 42%
D) 33.33% ≤ x ≤ 40%
E) 33.33 % ≤ x ≤ 42% X is the weighted average of \(\frac{2}{9}\) = ~20% and 40%. Since Zn < Al, weight given to 40% (Cu/Al) is more than the weight given to ~20% (Cu/Zn), which entails the average 'X' will be pulled closer to 40% than to ~20%. Also, the average will most certainly be greater than 30%, which is in the middle of 40% and 20%, but will be less than 40%. There can be any possibilities of X, depending on the weightage given. Hence I chose (A), which takes in values, all the way from the middle of 20% & 40% to the max of 40% : i.e. from 30% to 40%
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and [#permalink]
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03 Oct 2016, 03:44
GMATantidote wrote: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?
A) 30% ≤ x ≤ 40%
B) 32.5% ≤ x ≤ 40%
C) 32.5% ≤ x ≤ 42%
D) 33.33% ≤ x ≤ 40%
E) 33.33 % ≤ x ≤ 42% What is the source of this problem? It is certainly not GMAT specific because the numbers given are hard to work with. Also, the options are not accurate. "Range" means that we need to give the values that x does take. Option (A) covers extra values (like codomain) while option (B) doesn't cover all values. In a question like this, you cannot have an "approximate value" of x. Given: "in the overall alloy, there is more aluminum than Zinc," The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% < 40%. Minimum case: 60% of alloy A > (7/9) of alloy B A/B > 35/27 If the two alloys are mixed in this ratio, the copper concentration will be: Using weighted average: Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27) Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places) So x% > 32.26% Answer: 32.26 < x < 40
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An alloy of copper and aluminum has 40% copper. An alloy of Copper and [#permalink]
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06 Oct 2016, 10:37
VeritasPrepKarishma wrote: GMATantidote wrote: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?
A) 30% ≤ x ≤ 40%
B) 32.5% ≤ x ≤ 40%
C) 32.5% ≤ x ≤ 42%
D) 33.33% ≤ x ≤ 40%
E) 33.33 % ≤ x ≤ 42% What is the source of this problem? It is certainly not GMAT specific because the numbers given are hard to work with. Also, the options are not accurate. "Range" means that we need to give the values that x does take. Option (A) covers extra values (like codomain) while option (B) doesn't cover all values. In a question like this, you cannot have an "approximate value" of x. Given: "in the overall alloy, there is more aluminum than Zinc," The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% < 40%. Minimum case: 60% of alloy A > (7/9) of alloy B A/B > 35/27 If the two alloys are mixed in this ratio, the copper concentration will be: Using weighted average: Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27) Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places) So x% > 32.26% Answer: 32.26 < x < 40 VeritasPrepKarishmaThanks for the answer, I went through your posts on weighted average and scale on Veritasprep and really liked the approach. Can you pls explain  In this particular question, while calculating the maximum for Aluminum how are we using the statement that Aluminum can be no more than Zinc? TIA Also would be interested in getting answer to this question, since I learned Weighted average from your posts  so thought it will be good to understand your POV. apersoncanwalkataconstantrateof8mphandcanbikeatarateof215605.html#p1744545Thanks



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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and [#permalink]
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06 Oct 2016, 21:17
gauravk wrote: VeritasPrepKarishma wrote: GMATantidote wrote: An alloy of copper and aluminum has 40% copper. An alloy of Copper and Zinc has Copper and Zinc in the ratio 2:7. These two alloys are mixed in such a way that in the overall alloy, there is more aluminum than Zinc, and copper constitutes x% of this alloy. What is the range of values x can take?
A) 30% ≤ x ≤ 40%
B) 32.5% ≤ x ≤ 40%
C) 32.5% ≤ x ≤ 42%
D) 33.33% ≤ x ≤ 40%
E) 33.33 % ≤ x ≤ 42% What is the source of this problem? It is certainly not GMAT specific because the numbers given are hard to work with. Also, the options are not accurate. "Range" means that we need to give the values that x does take. Option (A) covers extra values (like codomain) while option (B) doesn't cover all values. In a question like this, you cannot have an "approximate value" of x. Given: "in the overall alloy, there is more aluminum than Zinc," The maximum aluminium you can have is when you mix copper and aluminium alloy (say alloy A) with infinitesimally small amount of copper and zinc alloy (alloy B). In that case, you will have almost 40% of copper in the mix (because alloy A has 40% of copper). So x% < 40%. Minimum case: 60% of alloy A > (7/9) of alloy B A/B > 35/27 If the two alloys are mixed in this ratio, the copper concentration will be: Using weighted average: Cavg = (2/5 * 35 + 2/9 * 27)/(35 + 27) Cavg = (14 + 6)/62= 20/62 = 32.26% (rounded to 2 decimal places) So x% > 32.26% Answer: 32.26 < x < 40 VeritasPrepKarishmaThanks for the answer, I went through your posts on weighted average and scale on Veritasprep and really liked the approach. Can you pls explain  In this particular question, while calculating the maximum for Aluminum how are we using the statement that Aluminum can be no more than Zinc? TIA Also would be interested in getting answer to this question, since I learned Weighted average from your posts  so thought it will be good to understand your POV. apersoncanwalkataconstantrateof8mphandcanbikeatarateof215605.html#p1744545Thanks When calculating maximum aluminium, we are practically taking only the aluminiumcopper alloy. We are mixing just an infinitesimally small amount of zinccopper alloy. Hence, the quantity of aluminium will certainly be more than the quantity of zinc which is what we require.
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