Question

A test is divided into 4 sets of problems with the same number of problems in each set. Alice correctly solves 35 problems. How many problems are on the test if Alice solved more than 60 percent of the problems, but less that 65 percent of all problems? Give all possible answers.

Answer 1

The possible number of question are

232,228,224, and 220.

Explanation:

Given that Alice correctly solves 35 problems

From the statement, 35 represents between 60 and 65 percent of the whole problem.

Let x be the total number of questions and choose 61% as the percentage Alice solved then,

61% of x = 35

0.61x = 35

x = 35/0.61

= 57.37

Aproximately 57

The possible answer are 58, 57, 56, 55

Since this represent 1 part, the question on test are:

54 * 4 = 232

or

57 * 4 = 228

or

56 * 4 = 224

or

55 * 4 = 220

Answer 2

• 56 problems

Explanation:

The number is between

• 35/0.6 = 58.33

and

• 35/0.65 = 53.84

and

• is multiple of 4

Possible numbers are:

• 54, 55, 56, 57 and 58

Only one of the numbers, 56 is divisible by 4