Question

Below is a copy of a calendar of July 2015

Then the products of the diagonals of any 2 $\times$ 2 square are always ____ apart.

(Do it algebraically and choose the right answer)

• A. 4
• B. 7
• C. 9
• D. 11

Answer 1

The correct option is B

7

Let us consider any three dates in a row.

If we take the first number be x, then a 2 $\times$ 2 square with x in the top left box looks like:

$\begin{array}{cc}x& x+1\\ x+7& x+8\end{array}$

Then the products of the diagonals is given by x (x + 8) and (x + 1)(x + 7).

Now $x(x+8)=x^2+8x$ and $(x+1)(x+7)=x^2+7x+x+7=x^2+8x+7$

Now, $(x+1)(x+7)-x(x+8)=(x^2+8x+7)-(x^2+8x)=x^2+8x+7-x^2-8x=7$

Hence the products of the diagonals of any 2 $\times$ 2 square are always 7 apart.

So, the given statement is true.