SAT Math Multiple Choice Practice Question 173: Answer and Explanation

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Question: 173

19. Points E, F, G, and H lie on a number line, but not in that order (in either direction). If the distance EG = 23, GH = 11, and F is the midpoint of EH, then the distance FH must equal

A. 6
B. 11
C. 12
D. 17
E. 34

Correct Answer: A


A. Imagine that you started drawing the number line like this:

If you then tried to put F in as EH's midpoint, you'd be forced to put the letters in the order EFGH, which the question tells you isn't the case. Drawing the line backward doesn't solve your problem either, so you need to try drawing the line like this:

You can now see that the distance EH equals 12, which means F is 6 units from H.

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