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An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

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Originally posted by doomedcat on 07 Nov 2018, 08:47.
Last edited by chetan2u on 09 Nov 2018, 20:50, edited 1 time in total.
Corrected the OA
Math Expert V
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Posts: 7984
Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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doomedcat 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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

C:A = 40:60=2:3=2a:3a
C:Z=2:7=2b:7b....
Now 3a>7b.....a>7b/3
Also %of copper or C= (2a+2b)/(5a+9b)=x/100..

Now let us make use of choices...
If 42 fits in , A,B and C will get eliminated else D and E will get eliminated.
(2a+2b)/(5a+9b)=42/100......200a+200b=210a+378b......-10a=178b....
Negative value hence not possible, eliminate D and E as they contain 42%
Now let's try 33.33% or 100/3%
So (2a+2b)/(5a+9b)=100/100*3=1/3........6a+6b=5a+9b...a=3b >7b/3... possible
Or let X=30
(2a+2b)/(5a+9b)=30/100=3/10.....10a+10b=15a+27b.....-5a=27b... Not possible..
Eliminate A
Try a=33%
(2a+2b)/(5a+9b)=33/100.....200a+200b=165a+297b....35a=97b...a=97b/35.. possible
Eliminate B

Ans C
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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doomedcat 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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

Other way would be..
(2a+2b)/(5a+9b)=X/100

MAx Value of X ... Reduce denominator, do put b=0
Hence 2a/5b=x/100....X=40%

Min value
When a=7b/3, so (2*7b/3+2b)/(5*7b/3+9b)=20b/62b=20/62=10/31=X/100
x=1000/31 ~32.25

So range is 32.25% ≤ x ≤ 40%

C

OA is wrong, it has to be C
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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Let the quantity of 1st alloy be y -----> Cu:Al= (2/5)y : (3/5)y
Let the proportionality constant for second alloy be p ----> Cu:Zn = 2p:7p

The two alloys are mixed with condition : Al> Zn -----> 3/5y > 7p or 3/35y>p therefore max p can be 3/35y

Now, in the mixture the quantity of Cu is x%
-----> x = {Cu quantity / total quantity}*100 = {(2/5y + 2p) / ((2/5y + 2p)+3/5y + 7p)}*100= 20(2y+10p)/(y+9p).
or x= 20 + 20 (y+p)/ (y+9p).

Lets analyze (y+p)/ (y+9p). Max when p = 0 -----> x = 40 Min when p is max or p = 3/35y ------> x=32.5

Ans C
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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doomedcat 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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

GMATinsight : sir could you help in giving an alternate solution to this mixture problem..
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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Two mixtures can be written in units as:

1) 40% Copper + 60% Aluminum
i.e. 40 units Copper & 60 units Aluminum
2) 2:7 ratio
i.e. 22.22% Copper + 77.78% Zinc
i.e. 22.22 units Copper and 77.78 units Zinc

Now we need to calculate the ranges i.e. we need to calculate the two ends of the spectrum.

Since 1st mixture has less concentration of Aluminum when compared to the concentration of Zinc in the 2nd mixture. Hence we will need to mix more of mixture 1 to take up the % of aluminum in the final mixture.

One of the ranges is quite straightforward i.e. if we keep on adding more of the 1st mixture then the maximum concentration for copper can be 40% i.e. only A, B, C remain. (D & E are eliminated).

Next, for the lower range, let’s take the units of Aluminum just above the units of Zinc i.e. multiply the first mixture by 1.3 i.e:

1st Mixture = 40*1.3 & 60*1.4 i.e. 52 units of copper and 78 units of aluminum

By doing the above we take the units of aluminum (78) just above that of Zinc (77.78)

Now calculate the total concentration of copper in the final mixture = $$\frac{(52+22.22)}{(130+100)}$$ = $$\frac{74.22}{230}$$ ~ 32.25%

Hence 32.25% =< X =< 40%
i.e. the correct answer is C
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An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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doomedcat 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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

let a and b=respective weights of alloys
because aluminum must exceed zinc in mixture,
3/5*a>7/9*b
a/b>35/27
35/27=1.296
to ensure that aluminum barely exceeds zinc,
let a/b=1.3/1
let x=% of copper in alloy mixture
.4*1.3+(2/9)*1=x*(1.3+1)
x=32.26%
C

Originally posted by gracie on 15 Nov 2018, 16:11.
Last edited by gracie on 16 Nov 2018, 12:15, edited 1 time in total.
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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Archit3110 wrote:
doomedcat 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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

GMATinsight : sir could you help in giving an alternate solution to this mixture problem..

An alloy of copper and aluminum has 40% copper

i.e. Copper in first alloy = 40%
i.e. every 10 kg of alloy has 4 kg copper and 6 kg of Aluminium

An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7
i.e. Copper in Second alloy = (2/9)*100 = 22.22%
i.e. every 10 kg of alloy has 2.22 kg copper and 7.78 kg of Zinc

As question mentions "there is more aluminum than Zinc"
for first alloy to have 7.78 kg of aluminium the total weight of first alloy = 7.78(10/6) = 12.96 kg
i.e. first alloy must be more than 12.96 kg if weight of he second alloy is 10 kg
and weight of copper in 12.96 kg of first alloy = 5.19

i.e. If total weight of two alloys = 10+12.96 = 22.96 kg
then weight of copper = 5.19+2.22 = 7.4 kg

minimum percentage of copper in final alloy = (7.4/22.96)*100 = 32.25%

Also, Maximum percentage of copper can't exceed 40% even if the second alloy becomes 0%

i.e. 32.25 < x < 40

Although I don' think that Option C should include equal to sign alongwith < sign, but that seems the best answer available hence

Archit3110
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Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and  [#permalink]

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GMATinsight wrote:
Archit3110 wrote:
doomedcat 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)33.33% ≤ x ≤ 40%
C)32.25% ≤ x ≤ 40%
D)32.5% ≤ x ≤ 42%
E)35.5% ≤ x ≤ 42%

GMATinsight : sir could you help in giving an alternate solution to this mixture problem..

An alloy of copper and aluminum has 40% copper

i.e. Copper in first alloy = 40%
i.e. every 10 kg of alloy has 4 kg copper and 6 kg of Aluminium

An alloy of Copper and Zinc has Copper and Zinc in the ratio 2: 7
i.e. Copper in Second alloy = (2/9)*100 = 22.22%
i.e. every 10 kg of alloy has 2.22 kg copper and 7.78 kg of Zinc

As question mentions "there is more aluminum than Zinc"
for first alloy to have 7.78 kg of aluminium the total weight of first alloy = 7.78(10/6) = 12.96 kg
i.e. first alloy must be more than 12.96 kg if weight of he second alloy is 10 kg
and weight of copper in 12.96 kg of first alloy = 5.19

i.e. If total weight of two alloys = 10+12.96 = 22.96 kg
then weight of copper = 5.19+2.22 = 7.4 kg

minimum percentage of copper in final alloy = (7.4/22.96)*100 = 32.25%

Also, Maximum percentage of copper can't exceed 40% even if the second alloy becomes 0%

i.e. 32.25 < x < 40

Although I don' think that Option C should include equal to sign alongwith < sign, but that seems the best answer available hence

Archit3110

GMATinsight , sir thanks understood the working, but doing such a question under 2 mins is definitely a challenge .. Re: An alloy of copper and aluminum has 40% copper. An alloy of Copper and   [#permalink] 16 Nov 2018, 10:19
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