# SAT Math Multiple Choice Question 626: Answer and Explanation

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**Question: 626**

**11.**

If *s, t, u*, and *v* are the coordinates of the indicated points on the number line above, which of the following is greatest?

- A.
*|s*-*v*| - B.
*|s*-*t*| - C.
*|s*+*v*| - D.
*|u*+*v*|

**Correct Answer:** A

**Explanation:**

**A**

**Algebra (absolute values) MEDIUM-HARD**

First, we should notice that each choice can be interpreted as a distance between two points on the number line.

(A) |*s* - *v*| = the distance between *s* and *v*

(B) |*s* - *t*| = the distance between *s* and *t*

(C) |*s* + *v*| = |*s* - (-*v*)| = the distance between *s* and -*v*

(D) |*u* + *v*| = |*u* - (-*v*)| = the distance between *u* and -*v*

Thinking this way gives us a very straightforward way to solve the problem without doing any calculation. First we need to locate -*v* on the number line by just reflecting *v* over the origin at 0. (Recall that multiplication by -1 is equivalent to reflecting a point on the number line over the origin at 0.) This makes it easy to see the distances the problem is asking us to compare:

Clearly, the greatest of these distances is (A).