SOLUTION: 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 t

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Question 1174877: 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 all problems, but less than 65 percent of all problems? Give all possible answers.
Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the total number of problems in the test.


Alice solved more than 0.6x problems, but less than 0.65x problems.


From the condition, you have this compound inequality


    0.6x < 35 < 0.65x


It implies   


    x < 35%2F0.6 = 58.3 (rounded)   and   x > 35%2F0.65 = 53.8 (rounded).


So, the integer values of x are among the values  54, 55, 56, 57 and 58.


Of them, only the value of 56 is a multiple of 4.


ANSWER.  The number of questions in the test was 56.

Solved.