PSAT Math Multiple-Choice Question 4: Answer and Explanation

Question: 4

If x^yx⁶ = x⁵⁴ and , what is the value of y + z?

• A. 11
• B. 12
• C. 48
• D. 51

Correct Answer: D

Explanation:

D

The question asks for the value of an expression based on two equations involving exponents. When dealing with questions about exponents, remember the MADSPM rules. Take the two equations separately. The MA part of the MADSPM acronym indicates that Multiplying matching bases means to Add the exponents. If x^y × x⁶ = x⁵⁴, then x^{y + 6} = x⁵⁴. Therefore, y + 6 = 54. Subtract 6 from both sides to get y = 48. The PM part of the MADSPM acronym indicates that raising a base with an exponent to another Power means to Multiply the exponents. If (x³)^z = x⁹, then x^3z = x⁹. Therefore, 3z = 9. Divide both sides by 3 to get z = 3. Now you know that y = 48 and z = 3, so y + z = 51. The correct answer is (D).