SAT Math Multiple Choice Practice Question 579: Answer and Explanation
15. If a – b = 119 and a – b = 7, what is the value of a ?
Correct Answer: B
B We've got some quadratic equations here. The expression a2 – b2 can be factored into (a + b)(a – b). The question tells us that a – b = 7, so we can replace that quantity in the factored equation: (a + b) × 7 = 119, so a + b = 17. We need to find the value of a, and we can use simultaneous equations. If we stack and add the equations, the b-values cancel out:
so a = 12, as seen in B.