Question

Twice my hat size is 3 times my shoe size. If my hat size is 18 more than my shoe size, then the sum of my hat size and shoe size together is:

A) 36 B) 54 C) 90 D) 108


What is the least 3-digit odd sum of two prime numbers
A) 101 B) 103 C) 105 D) 107

What is the greatest possible product of the ones digits of 4 numbers
A) 9 B) 105 C) 945 D) 6561




Please give a detailed and simple explanation please!

Answer 1

Q1. The sum of your hat size and shoe size is 54.

Q2. The correct answer is 101.

Q3. The correct answer is 6561.

Explanation:

Q1. Let's call the size of your hat H and the size of your shoe S. You can set up the following equation based on the given information:

H = 2S

H = S + 18

Substituting the first equation into the second equation, we get:

2S = S + 18

S = 18

Then, substituting this value back into the first equation, we get:

H = 2S

H = 2 * 18

H = 36

The sum of your hat size and shoe size is S + H = 18 + 36 = 54.

Q2. The least 3-digit odd sum of two prime numbers is 101, which can be achieved by adding the two prime numbers 2 and 99. Both 2 and 99 are prime numbers, and their sum is 101, which is a 3-digit odd number.

Q3. The greatest possible product of the ones digits of 4 numbers is 6561, which can be achieved by choosing the numbers 9901, 9911, 9921, and 9931. The ones digits of these numbers are 1, 1, 1, and 1, respectively, and their product is 6561.