SAT Math Problem

Question

Billy has been spending a half an hour each night using a cell phone app to help keep his brain stimulated. In the app, he is presented with 100 words with which he must correctly identify the definition from four answer choices. When the round is done, Billy's score is calculated by the number of incorrect definitions that he chose. The goal is to get a score of zero. Billy had a score of 64 on his third night and a score of 48 on his seventh night. If Billy's score reduces by the same amount each night, on which of the following nights will Billy receive a perfect score of zero?

 

A. the 4th night

B. the 10th night

C. the 19th night

D. the 20th night

 

 

Answer 1

Using arithmetic sequence:

a₇ = a₃ + (4)d

48 = 64 + 4d

-16 = 4d

-4 = d

 

0 = 48 + (n)(-4)

-48 = -4n

12 = n

 

Twelve nights after the seventh night, or the 19th night.

 

 

Answer 2

C. the 19th night

 

We need to identify the pattern, and if he has 64 points on the 3rd night and 48 points on the 7th night, he is improving his score by 4 points (less) each night.  48 divided by 4 is 12, so he will need 12 more nights to get to zero, and 12 + 7 is 19.