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 Chinatown's problem (Posted on 2015-07-02)
x ≡ 0 mod 2
x ≡ 1 mod 3
x ≡ 2 mod 5
x ≡ 3 mod 7

a. What is the smallest x?
b. What is the largest 4-digit x?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 solution with some explanation | Comment 2 of 3 |
a.

x is even, 2 + 2k
x is 1 mod 3, so 4 + 6k
x is 2 mod 5, so 22 + 30k
x is 3 mod 7:
22 is 1 mod 7
30 is 2 mod 7

b.

10000 is
0 mod 2
1 mod 3
0 mod 5
4 mod 7

we need to subtract y

y is even, 2 + 2k
y is 0 mod 3, so 6 + 6k
y is 3 mod 5, so 18 + 30k
y is 1 mod 7:
18 is 4 mod 7
30 is 2 mod 7 so k is 2

answer is 10000 - (18 + 30*2)
= 10000 - 78 = 9922

Note: in each of these, of course, successive k's are not the same, but merely indicate separation of possible successive values.

Edited on July 2, 2015, 9:22 am
 Posted by Charlie on 2015-07-02 09:19:53

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