Math Problem Statement

Terdapat tiga bilangan positif yang nilainya kurang dari 200. Masing-masing bilangan tersusun atas tiga angka yang habis dibagi 3 dan 5. Seluruh angka penyusun bilangan tersebut merupakan bilangan cacah. Misalkan angka kedua dan ketiga masing-masing bilangan merupakan bilangan prima kurang dari 7. Tentukanlah hubungan kuantitas yang tepat dari P dan Q sebagai berikut.

Solution

The image presents a math problem that involves three positive numbers less than 200. These numbers are described as having certain divisibility properties and are defined by certain relationships between their quantities, denoted as PP and QQ. Let's break down the problem.

Here’s a clearer restatement:

  • You are given three positive numbers less than 200.
  • The numbers are divisible by 3 and 5, and they are all odd numbers.
  • The second and third numbers are both prime numbers less than 7.
  • The goal is to determine the relationship between the quantities PP and QQ.

The table in the image is asking for the relationship between PP and QQ for the following conditions:

  1. The greatest common divisor (GCD) of the three numbers.
  2. The GCD between the smallest and largest numbers.

In the options, the relations between PP and QQ are given as:

  1. 12P=Q\frac{1}{2}P = Q
  2. P=2QP = 2Q
  3. 3P=2Q3P = 2Q
  4. 2P=Q2P = Q
  5. P=QP = Q

Next steps:

To better understand the problem, we need to figure out the exact numbers satisfying the conditions and then analyze how PP and QQ relate to each other.

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Math Problem Analysis

Mathematical Concepts

Divisibility
Prime Numbers
Greatest Common Divisor (GCD)

Formulas

GCD (Greatest Common Divisor)

Theorems

Euclidean algorithm for finding GCD

Suitable Grade Level

Grades 7-9