Discussion

If 101×210 − 120×102 = 99×104 − □, then what is the number at □?

Answer: A

The number in the box is 1326.

Evaluate the left side first:

\[ \begin{aligned} 101 \times 210 &= 21210 \\ 120 \times 102 &= 12240 \\ 21210 - 12240 &= 8970 \end{aligned} \]

The right side is \(99 \times 104 = 10296\), so

\[ \begin{aligned} 10296 - \square &= 8970 \\ \square &= 10296 - 8970 = 1326 \end{aligned} \]

Check: \(10296 - 1326 = 8970\). Options 1327, 1329 and 1336 would make the two sides differ by 1, 3 and 10.

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