Problem Solving

The revenue from sales items in 1996 increases by x percent, compared in 1995 and the revenue in 1997 decreases by x percent, compared in 1996. If the revenue from sales items in 1997 decreases by 4 percent, compared in 1995, what is the value of x?

A. 10 B. 15 C. 20 D. 30 E. 35

==> If the revenue in creased by x% between 1995 and 1996, it is R --> R(1+x%). Since this decreased by x% in 1997, it becomes R(1+x%)(1-x%)=R(1-x^2%^2). However, this means 4% has been decreased in 1997 when compared to 1995, it becomes R --> R(1-4%). For these two be the same, x^2%^2=4%, x^2%=4 should kick in, and if you substitute %=1/100, you get x^2=400 and x=20. Therefore, the answer is C.

Answer: C

Max@Math Revolution wrote:==> If the revenue in creased by x% between 1995 and 1996, it is R --> R(1+x%). Since this decreased by x% in 1997, it becomes R(1+x%)(1-x%)=R(1-x^2%^2). However, this means 4% has been decreased in 1997 when compared to 1995, it becomes R --> R(1-4%). For these two be the same, x^2%^2=4%, x^2%=4 should kick in, and if you substitute %=1/100, you get x^2=400 and x=20. Therefore, the answer is C.

Answer: C

Can you show using example?

Max@Math Revolution wrote:The revenue from sales items in 1996 increases by x percent, compared in 1995 and the revenue in 1997 decreases by x percent, compared in 1996. If the revenue from sales items in 1997 decreases by 4 percent, compared in 1995, what is the value of x?

A. 10 B. 15 C. 20 D. 30 E. 35

Let the 1995 revenue = 100.
We can PLUG IN THE ANSWERS, which represent the value of x.
When the correct answer is plugged in, the percent decrease from 1995 to 1997 will be 4%.

D: x = 30%
1996:
After a 30% increase, the resulting revenue = 100 + (30% of 100) = 100+30 = 130.
1997:
After a 30% decrease, the resulting revenue = 130 - (30% of 130) = 130-39 = 91.
Percent decrease from 1995 to 1997 = 100-91 = 9%.
Here, the percent decrease is TOO GREAT.
Eliminate D.

B: x = 15%
1996:
After a 15% increase, the resulting revenue = 100 + (15% of 100) = 100+15 = 115.
1997:
After a 15% decrease, the resulting revenue = 115 - (15% of 115) = 115 - 17.25 = 97.75.
Percent decrease from 1995 to 1997 = 100 - 97.75 = 2.25%.
Here, the percent decrease is TOO SMALL.
Eliminate B.

Since B (15%) yields a percent decrease that is TOO SMALL, while D (30%) yields a percent decrease that is TOO GREAT, the correct answer must be BETWEEN 15% AND 30%.

The correct answer is C.