Problem Solving

Hi,

could someone please help solving these 3 questions from an old published GMAT Test?


Q.1: Last year Department Store X had a sales total for December that was 4 times the average (arithmetic mean) of the monthly sales totals for January through November. The sales total for December was what fraction of the sales total for the year?

A. 1/4
B. 4/15
C.1/3
D. 4/11
E. 4/5

Correct B.


Q.2: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 15, and 18 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?

A. 4/11
B. 1/2
C. 15/22
D. 22/15
E. 23/270

Correct D.

Comment: I know there are already a couple work and rate related topics posted, but this one doesn't seem to work with the usual formula...(at least not with me)


Q.3: In 1985 a company sold a brand of shoes to retailers for a fixed price per pair. In 1986 the number of pairs of the shoes that the company sold to retailers decreased by 20 percent, while the price per pair increased by 20 percent. If the company's revenue from the sale of the shoes in 1986 was $3.0 million, what was the approximate revenue from the sale of the shoes in 1985?

A. 1.3 million
B. 1.9 million
C. 2.4 million
D. 3.1 million
E. 3.6 million

Correct D.

Comment: I've tried two different (both obviously wrong) approaches and got 1.9 million and 3.6 million but not the correct answer :S

Thank you for your help in advance,
E.

Hi,
Q1)Let x be the average of the monthly sales totals for January through November.
So, sales totals for January through November = 11*x = 11x
Give that sales total for December = 4x
So, fraction of December sales total is 4x/(11x+4x) = 4/15

Q2)if t is the time taken for Y and Z working together, 1/t = 1/y+1/z = 1/15 + 1/18 = (6+5)/90
So, x:t = x/t = 12*11/90 = 22/15

Q3)Let x be the rate per pair and 'n' be the number of pairs in 1985
So, 1.2x is the rate per pair and 0.8n is the number of pairs in 1986
Revenue in 1985 is n*x = nx
Revenue in 1986 is (0.8n)*(1.2x) = 0.96nx
Given that 0.96nx = 3
So, nx = 3/0.96 = 3*100/96 = 25/8 = 3.125million