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Number Theory Level pending

The number $\overline{543ab}$ is a multiple of 2, 5 and 9. What is the number $\overline{ab}$ ?

Details and assumptions

$\overline{abc}$ means $100a + 10b + 1c$ , as opposed to $a \times b \times c$ . As an explicit example, for $a=2, b=3, c=4$ , $\overline{abc} = 234$ and not $2 \times 3 \times 4 = 24$ .

The answer is 60.

1 solution

Arron Kau Staff
May 13, 2014

Since it is a multiple of 2 and 5, and hence 10, we have $b = 0$ . Since it is a multiple of 9, hence $5+4+3+a+0$ is a multiple of 9. Since $a$ is a digit, thus $a = 6$ . Hence, $\overline{ab} = 60$ .

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The answer is 60.

1 solution

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