SOLUTION: A number divided by 39 leaves reminder 20 the same number divided by 13 leaves reminder

Question 1005635: A number divided by 39 leaves reminder 20 the same number divided by 13 leaves reminder
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
, many possibilities for N and Q.

What if Q=1?

What is the remainder for ?
7
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.
A number divided by 39 leaves reminder 20. The same number divided by 13 leaves reminder ___ ?
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The first part of the condition, "A number divided by 39 leaves reminder 20." implies that
our number N can be presented in the form

N = 39*Q + 20.

Now ask yourself, what the remainder will be if to divide 39*Q + 20 by 13?

Clearly, the remainder will be the same as if you divide 20 by 13, i.e. 7.
Because 39 is multiple of 13.

Answer. The same number divided by 13 leaves reminder 7.

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