Problem 1

Three problems

A

B

, and

C

were given on a mathematics olympiad. All 25 students solved at least one of these problems. The number of students who solved

B

and not

A

is twice the number of students who solved

C

and not

A

. The number of students who solved only

A

is greater by 1 than the number of students who, along with

A

, solved at least one other problem. Among the students who solved only one problem, half solved

A

. How many students solved only

B

Step 3 of 6: Translate the "one more" condition

Previous step Next step

In plain words

This condition only involves the region "only $A$ " and the merged region $e$ , so it converts directly into a one-line equation.

a=e+1

Detailed analysis

"The number of students who solved only $A$ is greater by 1 than the number who, along with $A$ , solved at least one other problem" translates directly to $a=e+1$ .