# SAT Math Multiple Choice Question 605: Answer and Explanation

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**Question: 605**

**5.**

Note: Figure not drawn to scale

A rectangular solid above has dimensions 3, *a*, and *b*, where *a* and *b* are integers. Which of the following CANNOT be the areas of three different faces of this solid?

- A. 15, 18, and 30
- B. 18, 24, and 48
- C. 12, 15, and 24
- D. 15, 24, and 40

**Correct Answer:** C

**Explanation:**

**C**

**Special Topics (three-dimensional geometry) MEDIUM**

On the drawing, we should first mark the areas of the three faces. The front and back faces both have an area of 3*a*. The left and right faces both have an area of 3*b*. The top and bottom faces both have an area of *ab*. We should now try to find integer values for *a* and *b* so that these areas match those given in the choices.

(A) 15, 18, and 30

This is possible if *a* = 5 and *b* = 6.

(B) 18, 24, and 48

This is possible if *a* = 6 and *b* = 8.

(C) 12, 15, and 24

This cannot work for any integer values of *a* and *b*.

(D) 15, 24, and 40

This is possible if *a* = 5 and *b* = 8.