Data Sufficiency

In 2003 Acme Computer's price for each of its computers was five times the price for each of its printers. What was the ratio of its gross revenue from computers to its gross revenue from printers in 2003?

(1) In the first half of 2003, Acme sold computers and printers in a ratio of 3:2; in the second half of 2003, Acme sold computers and printers in the ratio of 2:1.

(2) Acme's 2003 price for each of its computers was $1,000.

OA: E

I understand why B is out.

What I don't understand is the following:

Wanted: revenue computers/revenue printers = #computers x price computers / #printers x price printers = # computers x 5 /# printers.

Why is statement 1 insufficient? This statement tells us the ratio of numbers sold, which should be sufficient?!

In 2003 Acme Computer's price for each of its computers was five times the price for each of its printers. What was the ratio of its gross revenue from computers to its gross revenue from printers in 2003?

(1) In the first half of 2003, Acme sold computers and printers in a ratio of 3:2; in the second half of 2003, Acme sold computers and printers in the ratio of 2:1.

(2) Acme's 2003 price for each of its computers was $1000.

Plug in different combinations that satisfy both statements.

Statement 2 states that the computer price = 1000.
Since the computer price is 5 times the printer price, the printer price = 200.

Case 1:
First half of the year:
3 computers sold = 3*1000 = 3000.
2 printers sold = 2*200 = 400.

Second half of the year:
2 computers sold = 2*1000 = 2000.
1 printer sold = 1*200 = 200.

Computer revenue/Printer revenue = (3000+2000)/(400+200) = 5000/600 = 25/3.

Case 2:
Try to get a DIFFERENT RATIO.

Change the values for the first half of the year:
6 computers sold = 6*1000 = 6000.
4 printers sold = 4*200 = 800.

Don't change the values for the second half of the year:
2 computers sold = 2*1000 = 2000.
1 printer sold = 1*200 = 200.

Computer revenue/Printer revenue = (6000+2000)/(800+200) = 8000/1000 = 8.

Since the ratio can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.

we have to find C/P ratio.

Here C signifies revenue from computers sale
and P signifies revenue from Printers sale

say
cost of 1 comp is a
cost of 1 printer is b

1

first half the sold comp and printer in 3:2

so revenue for 1st half would be (3na)/(2nb)

Second half the sold comp and printer in 2:1

so revenue for 2nd half would be (2ma)/(1mb)


C/P = (3na + 2ma)/ (2nb + 1mb)

as we don't know n,m,a and b we can't tell the ratio of C/P

2. knowing the cost of Comp will not help as we can see from above equation.


combining two we still have 3 variables unknown - n,m and b. hence can't answer.

E is the correct answer.
here m and n are factor to get the actual no. of computer and printer sold in respective half