Data Sufficiency

78. A manufacture produced x percent more video cameras in 1994 than in 1993 and y
percent more video cameras in 1995 than in 1994. If the manufacturer produced 1,000
video cameras in 1993, how many video cameras did the manufacturer produce in 1995?
1). xy=20
2). x+y+xy/100 = 9.2

ans is[spoiler] b[/spoiler

gmat prep - q ..cant figure out...thanks

deltaforce wrote:78. A manufacture produced x percent more video cameras in 1994 than in 1993 and y
percent more video cameras in 1995 than in 1994. If the manufacturer produced 1,000
video cameras in 1993, how many video cameras did the manufacturer produce in 1995?
1). xy=20

No useful info. x = 2%, y = 10%, or x = 4%, y = 5%

2). x+y+xy/100 = 9.2

1000 * (1 + x/100)(1 + y/100) = 1000 (1 + y/100 + x/100 + x*y/10,000) = 10 * (100 + x + y + x*y/100)

Let's call

C94 = number of cameras produced in 94

A manufacture produced x percent more video cameras in 1994 than in 1993 so C94 = (1+x/100)C93


y percent more video cameras in 1995 than in 1994

so C95 = (1+y/100)C94 ---> C95 = (1+y/100)(1+x/100)C93

you are given the value of C93, so in order to calculate the value of C95 you need to know (1+y/100)(1+x/100)

use FOIL in that expression

(1+y/100)(1+x/100) = 1 + (yx/10000) + y/100 + x/100 (1)

with this information take a look at the statements

statement I
xy=20

can you know the value of the expression just with that information? no
insufficient

statement II

compare the two expressions

x+y+xy/100 = 9.2

1 + (yx/10000) + y/100 + x/100

can you transform the first expression to get the second one?

divide everything by 100

x/100 + y/100 + xy/10000 = 9.2/100

sum 1 to both sides


if you compare now the both expressions

1 + (yx/10000) + y/100 + x/100

1 + x/100 + y/100 + xy/10000 = 1 + 9.2/100

you see that you have the information you need to answer the question

C95 = (1 + 9.2/100) *1000