# SAT Math Multiple Choice Question 680: Answer and Explanation

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**Question: 680**

**5.** On a number line, the coordinates of points *P* and *R* are *p* and *r*, respectively, and *p* < *r*. If the point with coordinate *x* is closer to *p* than to *r*, then which of the following statements must be true?

- A.
- B.
- C. |
*x*-*p*|<*r* - D. |
*x*+*p*|<*r*-*p*

**Correct Answer:** B

**Explanation:**

**B**

**Algebra (expressing relationships) MEDIUM-HARD**

Draw a number line, and to show that *p* < *r*, place *p* to the left of *r* on the number line. The points that are closer to *p* than to *r* are all the points to the left of their midpoint. The midpoint is the average of the endpoints: , so if the point with coordinate *x* is closer to *p* than to *r*, then .