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Bunuel
The digits of a four-digit positive integer have a sum of 19. If the ten's digit is twice the units digit and the hundreds digit is 8/3 the units digit, what is the number?

A. 863
B. 1842
C. 2863
D. 8263
E. 9820

We can let a, b, c, and d be the units, tens, hundreds, and thousands digits, respectively; thus:

a + b + c + d = 19

and

b = 2a

and

c = 8a/3

We see that the units digit must be a multiple of 3, and since the tens digit is twice the units digit, the only option for the units digit is 3, and thus the tens digit must be 6. Now we can determine c:

c = 8(3)/3 = 8

Finally, we can determine the thousands digit:

3 + 6 + 8 + d = 19

d = 2

Thus, the number is 2,863.

Answer: C
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