Question

The integers P,Q,R and S shown on the number line above are all equally spaced. If R and S are equal to $7^{12}$ and $7^{13}$, respectively, what is the value of P?

• A. 7¹⁰
• B. 7¹¹
• C. -7¹³
• D. 7⁹
• E. none of these

Answer 1

The correct option is E none of these

Solution

The distance between R and S is $7^{13}-7^{12}=7^{12}\left(6\right)$

The distance between and two consecutive points is constant

Value of $Q=7^{12}-6\times 7^{12}=-5\times 7^{12}$

Value of $P=-5\times 7^{12}-6\times 7^{12}=-11\times 7^{12}$

The correct answer is option (e).