Mathematics 2010 JAMB Past Questions - Question 24: If p and q are two non zero number and 18(p+q)=(18+p)q,which of the following must be true ?

Correct Answer

B

Explanation

18 (p+q) = (18+p)q18p + 18q = 18q +pqBy comparison:To determine which of the following statements must be true based on the equation 18(p+q) = (18+p)q, let's analyze the equation:18(p+q) = (18+p)qExpanding the equation, we get:18p + 18q = 18q + pqRearranging the terms, we have:18p = pqNow, let's consider the given statements:1. p = 02. q = 03. p = q4. p = 185. q = 18Analyzing each statement:1. If p = 0, then the equation becomes 0 = 0, which is true. However, this statement is not a must because there could be other values of p and q that satisfy the equation.2. If q = 0, then the equation becomes 18p = 0, which is true. However, similar to the previous statement, this statement is not a must because there could be other values of p and q that satisfy the equation.3. If p = q, then the equation becomes 18(2p) = (18+p)p, which simplifies to 36p = 18p + p². This equation is true, and it satisfies the given equation. Therefore, this statement must be true.4. If p = 18, then the equation becomes 18(18+q) = (18+18)q, which simplifies to 18(18+q) = 36q. This equation is not true for all values of q, so this statement is not a must.5. If q = 18, then the equation becomes 18(p+18) = (18+p)18, which simplifies to 18p + 324 = 18p + 18². This equation is true, and it satisfies the given equation. Therefore, this statement must be true.Based on our analysis, the statements that must be true are:- p = q- q = 18Please note that these are the specific conditions that satisfy the given equation, and other values of p and q may also exist that satisfy the equation.18p = 18q p = qAgain, 18 = pq or 18 = p which required.