VeritasPrepKarishma wrote:
farukqmul wrote:
Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 4 : 3
(E) 7 : 9
Responding to a pm:
When you need to find the average, it is better to use the formula in its original form: Avg = (C1*w1 + C2*w2)/(w1 + w2)
Avg = [(5/8)*4 + (1/3)*3]/(4+3) = 1/2
Ratio of the 2 elements in the mixture = 1:1
Obviously the formula will work in the other form too though it is best to use that when you need to find the ratio of the weights. Using the formula in the other form: w1/w2 = (A2 - Aavg)/(Aavg - A1)
element 1 in A = 5/8
element 1 in B = 1/3
element 1 in mixture = x
4/3 = (1/3 - x) / (x - 5/8)
4/3(x - 5/8) = 1/3 - x
(7/3)x = 7/6
x = 1/2
(You made a calculation error)
Ratio of elements in the mixture = 1:1
Responding to a pm:
Quote:
I am trying to understand the approach to the solution you posted to the Alloy-composition question above (I know it is quite a while ago..).
I understand how you get to the equation [5/8*4+1/3*3]/3+4 since 4 parts of the new mix need to contain 5/8 of element 1 from alloy A (correct?
) and the solution 1/2 but I don't understand what the 1/2 actually represent and how you the get to a ratio of 1:1.
Could you please help me and explain the reasoning?
I unfortunately also do not understand how you get to the equation 4/3 = (1/3 - x) / (x - 5/8) (ie. Why do you subtract x from 1/3 to represent alloy a?
)
We have a standard weighted average formula:
Avg = (C1*w1 + C2*w2)/(w1 + w2)
We can rearrange the terms in this formula to give us:
w1/w2 = (A2 - Aavg)/(Aavg - A1)
Both are the same formula. A is the quantity that you need to average. w1 and w2 are the weights in which this quantity is mixed.
We are given the following:
The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 2, respectively.
So we can say that the concentration of the first element is 5/(5+3) = 5/8 of alloy A and the concentration of the first element in alloy B is 1/(1+2) = 1/3 of alloy B.
We need to find the average concentration Aavg.
A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3.
The two allows are mixed in the ratio 4:3. So w1/w2 = 4/3
For more, check:
https://www.veritasprep.com/blog/2011/0 ... -averages/https://www.veritasprep.com/blog/2011/0 ... -mixtures/https://www.veritasprep.com/blog/2014/1 ... -averages/ _________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >