Question about Equation Rewrite

by **Guest** Sun Oct 14, 2007 1:08 pm

See bold portion below. I am confused as to why they ran rewrite the question as S = M + 3/8T -- it looks to me like it would be S = 3/8T - M.

Three business partners shared all the proceeds from the sale of their privately held company. If the partner with the largest share received exactly 5/8 of the total proceeds, how much money did the partner with the smallest share receive from the sale?

(1) The partner with the smallest share received from the sale exactly 1/5 the amount received by the partner with the second largest share.

(2) The partner with the second largest share received from the sale exactly half of the two million dollars received by the partner with the largest share.

We can rewrite the information in the question as an equation representing the T, the total dollar value of the sale:

L + M + S = T

L = the dollar amount received by the partner with the largest share
M = the dollar amount received by the partner with the middle (second largest) share
S = the dollar amount received by the partner with the smallest share

We are also told in the question that L = (5/8)T. Thus we can rewrite the equation as follows:

(5/8)T + M + S = T.

Since the question asks us the value of S, we can simplify the equation again as follows:

S = M + (3/8)T
Thus, in order to solve for S, we will need to determine the value of both M and T. The question can be rephrased as, what is the value of M + (3/8)T?

(1) NOT SUFFICIENT: The first statement tells us that S = (1/5)M. This gives us no information about T so statement one alone is not sufficient.

(2) SUFFICIENT: The second statement tells us that M = (1/2)L = $1 million. Additionally, since we know from the question that L = (5/8)T, then M must be equal to 1/2 of 5/8(T) or 5/16(T). We can therefore solve for T as follows:

M = $1,000,000 = 5

16
T

$3,200,000 = T

We can now easily solve for S:

L + M + S = T
2 million + 1 million + S = $3.2 million
S = .2 million

The correct answer is B.

by **StaceyKoprince** Mon Oct 22, 2007 8:54 pm

I've forwarded this to our curriculum director to check!