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Sophie_A: I tried your method on a problem I made up (386 x 85 = 32810) but it doesn't seem to work on that one. I'm probably doing something wrong, because I don't think I've understood your method.
Your new problem is: 38? × 85 = 32810.
Start with 85 × ?. This ends with a 0, say X0. Write down 0 and carry the X. Next, 85 × 8 = 680. This plus the carried-over X must end with a 1, so X must be 1, 11, 21, 31, 41, 51, 61, 71. Hence 85 × ? must be 10, 110, 210, 310, 410, 510, 610, 710. Only one of these is divisible 85; divide it by 85.
It works perfectly fine for me.
Thanks guys! My method is as follows.
35 × ? is a number ending in 0, say X0. Write down the 0 and carry the X over. Then 35 × 7 = 245, and this added to the carried-over X is a number ending in 9. Thus X must be a number ending in 4, so it must be 4, 14, or 24. Therefore 35 × ? must be 40, 140, or 240. Only one of these is divisible by 35, namely 140 = 35 × 4. Hence ? = 4.
Does this make sense?
Find the digit represented by ? in the following problem: 37? × 35 = 13090. No calculators, please.
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