# SAT Math Multiple Choice Practice Question 579: Answer and Explanation

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**Question: 579**

**15.** If *a* – *b* = 119 and *a* – *b* = 7, what is the value of *a* ?

A. 5

B. 12

C. 14

D. 17

E. 21

**Correct Answer:** B

**Explanation:**

**B** We've got some quadratic equations here. The expression *a*^{2} – *b*^{2} 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.