## Problem of the Week 3 – Largest Possible Value

Problem

The number $25ab$ where $a$ and $b$ are digits is divisible by $6$. What is the largest possible value of $a + b$?

Solution

A number is divisible by 6 if it is divisible by 2 and it is divisible by 3. For a number to be divisible by 2, it must be even. Therefore, $b$ must be even. So, the possible values of b are, 0, 2, 4, 6, and 8.

A number is divisible by 3 if the sum of the digits are divisible by 3. Therefore, we must be sure that in all the cases, the numbers are divisible by 3. Continue reading “Problem of the Week 3 – Largest Possible Value”

## Problem of the Week 2: Distance Between Two Houses

The second problem of the week was taken from the second set of MTAP Reviewers for Grade 5. We will discuss its solution below.

Problem of the Week 2

Amy’s house is 5/8 of a kilometer from school. Bryan’s house is 1/2 kilometers away from school. If Bryan’s house is between Amy’s house and the school, how far is Amy’s house from Bryan’s house? Continue reading “Problem of the Week 2: Distance Between Two Houses”

## 1st Problem Solved: The Bus Rent

This the first of the series of relatively hard problems for MTAP contestants. The problem below is probably good from Grade 4 to Grade 6.

Problem

The fee for a single person in Rideon Bus company is P1500 for a Metro Manila tour. If a 50-seater bus is rented out, the price for each person is reduced by 20%.

How many persons are needed for it to be a better deal to rent out the bus?

Solution

For each person, the discount is P1500 x 0.2 = P300.

Therefore, each person must pay P1500 – P300 = P1200 if 50 persons were to ride the bus.

Now, the price of the entire bus if 50 persons go is 1200 x 50 = P60,000.

Dividing 60,000 by the original price, we have 60,000/1500 = 40.

Meaning, 40 persons need to pay P60,000 which is the same as the price of renting out the entire bus.