4
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There is a number,
the second digit of which is smaller than the first digit by $4$, and if the number was divided by the digits' sum, the quotient would be $7$.

What is this number.

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5
  • $\begingroup$ The hint it leaves only 6 possible numbers. That is superfluous imho. $\endgroup$ – Florian F Jul 26 '20 at 11:21
  • $\begingroup$ @FlorianF Please tell me a better hint then. I didn't find one. $\endgroup$ – math Jul 26 '20 at 13:43
  • $\begingroup$ I would say the problem is already easy enough. No hint needed. $\endgroup$ – Florian F Jul 26 '20 at 13:55
  • $\begingroup$ @FlorianF Ok. edited. $\endgroup$ – math Jul 27 '20 at 7:47
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    $\begingroup$ I think it was better to mention that the number has two digits in total. $\endgroup$ – aminabzz Aug 6 '20 at 21:19
5
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Here is another answer

For number AB:

1. A - B = 4
2. (10A + B) ÷ (A + B) = 7

Rearrange 1. to A = B + 4

Substitute A into 2. -> (10[B + 4] + B) ÷ ([B + 4] + B) = 7

Simplify 2.
- (10B + 40 + B) ÷ (2B + 4) = 7
- 11B + 40 = 14B + 28
- 12 = 3B
- B = 4


A = B + 4 = 8

Number is 84

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2
  • $\begingroup$ @math Thanks. How do you use the spoiler feature? $\endgroup$ – asg Jul 26 '20 at 22:46
  • $\begingroup$ Visit spoilers in editing-help $\endgroup$ – math Jul 27 '20 at 7:44
1
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After some guess and check, the answer is,

84

Since

8 - 4 = 4
84 / 12 = 7

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2
  • $\begingroup$ Assuming that "second digit" and "first digit" are counted from left, it is actually possible to prove that this is the unique answer, even without the hint. $\endgroup$ – WhatsUp Jul 25 '20 at 18:50
  • $\begingroup$ It’s an algebra problem. The answer added by @asg gives the steps. $\endgroup$ – Damila Jul 26 '20 at 5:51

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