Word Problem - Data Sufficiency Test

Question

On average the number of dodger fans at home games one through four, inclusive, was 23,960. How many more dodger fans were at the 5th games of the season than were at the 1st game of the season?

(1) The average number of Dodger fans at home games two through five, inclusive, was 27, 670

(2) The sum of the fans at home games one through three equaled the sum of the fans at home games four and five.

Choices:

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

D. EACH statement ALONE is sufficient

E. Statement (1) and (2) TOGETHER are NOT sufficient

Answer 1

A is correct, that statement (1) alone is sufficient to calculate game 5 attendance, but (2) alone is not

(1) and (2) together lead to a different number for game 5

Let X= average attendance at games 1 to 4, Y = average attendance at games 2 through 5, and Z = attendance at game 5

Z= 4Y-3X for (1)

Z= 4(27,670) - 3(23960) =110680-71880= 38,800 for game 5

3X = Z+Y or Z =3X-Y for (2)

Z= 3(23,960) -27,670 = 71880-27670= 44,210 for game 5

Z=Z

4Y-3X = 3X-Y

5Y = 6X

5(27,670) = 6(23960)

138350 doesn't = 143760

The game 5 attendance is different under (1) and (2)