Math Problem Statement

1. Find all multiples of 40 that lie between 310 and 410. 2. Who am I? (a) I am a number less than 40. One of my factors is 7. The sum of my digits is 8. 3. I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 2.

Solution

Let's solve these questions step by step.

Question 1: Find all multiples of 40 that lie between 310 and 410.

Multiples of 40 between 310 and 410 are:

  • The first multiple of 40 greater than 310 is 320.
  • Adding 40 repeatedly: 320, 360, 400.

Thus, the multiples of 40 between 310 and 410 are: 320, 360, and 400.


Question 2: Who am I?

a. I am a number less than 40. One of my factors is 7. The sum of my digits is 8.

  • The factors of 7 under 40 are multiples of 7: 7, 14, 21, 28, 35.
  • Now, check the sum of the digits:
    • 7: 77 (not 8)
    • 14: 1+4=51 + 4 = 5 (not 8)
    • 21: 2+1=32 + 1 = 3 (not 8)
    • 28: 2+8=102 + 8 = 10 (not 8)
    • 35: 3+5=83 + 5 = 8.

Thus, the number is 35.


Question 3: I am a number less than 100. Two of my factors are 3 and 5. One of my digits is 2.

  • A number with factors 3 and 5 must be a multiple of 3×5=153 \times 5 = 15.
  • Multiples of 15 under 100 are: 15, 30, 45, 60, 75, 90.
  • Check which has a digit 2:
    • 15: No 2.
    • 30: No 2.
    • 45: No 2.
    • 60: No 2.
    • 75: No 2.
    • 90: No 2.

It seems there might be a mismatch in the question or no solution with the given conditions.

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Math Problem Analysis

Mathematical Concepts

Multiples and Factors
Basic Arithmetic

Formulas

Multiplication for finding multiples

Theorems

Basic properties of divisibility

Suitable Grade Level

Grades 5-7