Russell Marsh

2022-09-30

Use a congruence modulo 9 to find the missing digit, indicated by a question mark: 89, 878*58,965=5299? 56270.

Amir Hanna

Beginner2022-10-01Added 6 answers

Notice that $$89,878\equiv 8+9+8+7+8\equiv 4(mod9),58,965\equiv 5+8+9+6+5\equiv 6(mod9)$$, and $$5,299,?56,270\equiv 5+2+9+9?+5+6+2+7+0\equiv ?(mod9)$$. Now, $$89,878\ast 58,965\equiv 4\ast 6\equiv 6\equiv ?(mod9)$$. Thus, as the question mark represents a single decimal digit, we get that ?=6

Result:

The missing digit indicated by the question mark is 6.

Result:

The missing digit indicated by the question mark is 6.

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