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

Grade 6 MTAP Reviewer Set 2

This is the second set of Grade 6 reviewers for the MTAP Math challenge.

1.) What is the greatest common factor of 3 and 10?

2.) The sum of two numbers is 26, their difference is 12. What are the numbers?

3.) A large cube is formed using smaller cubes as shown below. In the figure, how many cubes cannot be seen?

rubix_cube

4.) Bimbo is twice as old as Miko. The sum of their ages is 54. How old is Miko? Continue reading

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

Grade 5 MTAP Reviewer Set 2

Below is the second set of MTAP reviewers for Grade 5 students. You may also use them for Grade 4 and Grade 6 students and possibly Grade 7 students. Good luck!

1.) Jim draw a triangle with one angle measuring 90 degrees. What could be the measures of the other two angles?

2.) What is 0.7 written as a fraction?

3.) What is the prime factorization of 36?

4.) Jasmine types 26 words per minute. At this rate, how many words can she type in 8.5 minutes? Continue reading

Grade 4 MTAP Reviewer Set 2

Here is the second set of MTAP reviewers for Grade 4. Of course, you can use this reviewer for Grade 3, 4, 5 and 6.

Grade 4 MTAP Reviewer Set 2

1.) What must be the largest value of N so that the number 97N is divisible by 2?

2.) If N – 3 = 6, what is N + 3?

3.) Fill in the blank: 7 hundreds = ____ ones

4.) What is 2345 rounded to the nearest hundreds?

5.) How many edges does a cube have? Continue reading