SAT Mathematics Practice Test 6

Let h be the riser height, in inches, and n be the number of the steps in the stairway. According to the architect’s design, the total rise of the stairway is 9 feet, or 9×12=108 inches. Hence,nh=108,and solving for n gives n=

108

h

,It is given that 7 < h < 8. It follows that

108

8

<

108

h

<

108

7

, or equivalently,

108

8

<n<

108

7

Since

108

8

<n<

108

7

.Since

108

8

<14 and

108

7

>15 and n is an integer, it follows that 14≤n≤15. Since n can be an odd number, n can only be 15; therefore h=

108

15

=7.2 inches. Substituting 7.2 for h in the riser-tread formula 2h+d=25 gives 14.4+d=25. Solving for d gives d=10.6 inches.
Choice A is incorrect because 7.2 inches is the riser height, not the tread depth of the stairs. Choice B is incorrect and may be the result of calculation errors. Choice D is incorrect because 15 is the number of steps, not the tread depth of the stairs.