baseball card

[j_shreyans]

The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plummeted by 50 percent. Over the same total time period, the value of another card B increased by 100%. At the end of ten years, the reduced value of A was what percent of the increased value of B?

1)Card A's initial value was $1000.

2)The initial value of A was four times that of B.

OAB

[GMATGuruNY]

The value of a rare baseball card A appreciated by 20 percent over a five year period; over the next five years, the value plummeted by 50 percent. Over the same total time period, the value of another card B increased by 100%. At the end of ten years, the reduced value of A was what percent of the increased value of B?

1)Card A's initial value was $1000.

2)The initial value of A was four times that of B.

OAB

Let the initial value of A = x.
After increasing by 20%, A = 1.2x
After decreasing by 50%, A = (0.5)(1.2)A = 0.6x.

Let the initial value of B = y.
After increasing by 100%, B = 2y.

(reduced A)/(increased B) = (0.6x)/(2y) = (0.3)(x/y).
Question stem, rephrased:
What is the value of x/y?

Statement 1: Card A's initial value was $1000.
Thus, x=1000.
No information about y.
INSUFFICIENT.

Statement 2: The initial value of A was four times that of B.
Thus, x = 4y.
Substituting x=4y into x/y, we get:
x/y = 4y/y = 4.
SUFFICIENT.

The correct answer is B.