Problem Solving

The number of singles that a baseball player hit increased 11 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 1 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?

(A) 1:3

(B) 9:11

(C) 1:1

(D) 2:1

(E) 11:3
.

Let singles be x and doubles be y.

x increased to 111x/100.

y decreased to 99y/100

111x/100 + 99y/100 = 102/100 (x + y)
111x + 99y = 102 (x + y)

9x = 3y
x:y = 1: 3

A?

RadiumBall wrote:The number of singles that a baseball player hit increased 11 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 1 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?

(A) 1:3

(B) 9:11

(C) 1:1

(D) 2:1

(E) 11:3
.

let singles hit in the first season be x and doubles hit in the first season be y.
total no. of singles and doubles that she hit=x+y;

singles hit increased by 11% in second season=1.11x;
doubles hit decreased by 1% in second season=.99y;
singles and doubles hit together increased by 2%=1.02(x+y);
1.11x+.99y=1.02x+1.02y;
.09x=.03y;
x/y=1/3; hence A

RadiumBall wrote:The number of singles that a baseball player hit increased 11 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 1 percent. If the total number of singles and doubles that she hit increased 2 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?

(A) 1:3

(B) 9:11

(C) 1:1

(D) 2:1

(E) 11:3
.

This is a weighted average question. Here is the question rephrased:

Solution X is 11% alcohol. Solution Y is -1% alcohol. X and Y are combined to yield a mixture that is 2% alcohol. What is the ratio of X to Y in the mixture?

The quickest approach is to look at the answers, which represent the ratio of singles to doubles.

The total increase of 2% is much closer to -1% (which is attributed to the number of doubles) than to 11% (which is attributed to the number of singles).
Thus, we need far more doubles than singles, and the ratio of singles:doubles must be very heavily weighted toward the number of doubles.

Eliminate B, C, D and E.

The correct answer is A.

We also could plug in the answers.
Recognizing that we need fewer singles than doubles, we could eliminate C, D and E and try either A or B.

Answer choice A: singles:doubles = 1:3.
Plug in 25 singles, 75 doubles.
Total hits = 25+75 = 100.
11% more singles = 25 + .11*25 = 27.75.
1% fewer doubles = 75 - .01*75 = 74.25.
New total = 27.75 + 74.25 = 102, an increase of 2%.

Yes OA: A