Question

Steven plans to visit his grandmother and his aunt for the summer vacation. His grandmother lives $125\frac{1}{2}$ miles west of Steven’s house, whereas his aunt lives $271\frac{1}{4}$ miles east of his grandmother’s house. Which of the following statement(s) is/are false?

• A. Steven’s aunt lives less than 125 mi away from him.
• B. Steven lives closer to his grandmother as compared to his aunt.
• C. Steven’s aunt lives further away from Steven as compared to his grandmother.
• D. Steven lives 145.75 mi away from his aunt.

Answer 1

The correct option is A Steven’s aunt lives less than 125 mi away from him.


Let Steven'ss position be at $O$
Steven’s distance from aunt $=OB=AB-OA$
$=271\frac{1}{4}-125\frac{1}{2}=\frac{1085}{4}-\frac{251}{2}=\frac{1085-2\times 251}{4}=\frac{583}{4}=145\frac{3}{4}mi$

Thus, option A is true.
Steven’s distance from his grandmother’s house $=OA=125\frac{1}{2}mi=125.5mi$
Steven’s distance from his aunt’s house $=OB=145\frac{3}{4}mi=145.75mi$
$125\frac{1}{2}<145\frac{3}{4}$
Thus, option B and C are true.
Steven’s distance from aunt $=OB=145\frac{3}{4}mi$
Thus, only option D is false.