Who has the greater value ?

Number Theory Level 2

Which of the following is the largest?

A = 99999999 × 111111 B = 11111111 × 999999 C = 33333333 × 333333 \begin{array} { l l l l l } A & = & 99999999 \times 111111 \\ B & = & 11111111 \times 999999 \\ C & = & 33333333 \times 333333\\ \end{array}

A No Answer B A and C (Have the same value) B and C (Have the same value) A and B (Have the same value) A,B and C (Have the same value) C

Kadek Yuki Andika by Kadek Yuki Andika , 21, Indonesia

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1 solution

Alex Delhumeau
May 28, 2015

A = 99999999 ∗ 111111 = 9 ∗ 11111111 ∗ 111111 = 11111111 ∗ 999999 = B B = 11111111 ∗ 999999 = 11111111 ∗ 3 ∗ 333333 = 33333333 ∗ 333333 = C ⇒ A = B = C A = 99999999 * 111111 = 9 * 11111111 * 111111 = 11111111 * 999999 = B \\ B = 11111111 * 999999 = 11111111 * 3 * 333333 = 33333333 * 333333 = C \\ \Rightarrow \boxed{A = B = C}

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