Each of the digits 7,5,8,9,4 is used only once to form a 3-digit integer and a 2 digit integer. If the sum of the integers is 555, how many such pairs of integers can be formed?
A - One
B - Two
C - Three
D - Four
E - Five
Let the 5 digits be A, B, C, D and E, as follows:
ABC
XDE
555
To yield a sum of 555, A=4:
4BC
XDE
555
Given the remaining digits 5, 7, 8, and 9, it is not possible that C+E = 5.
Thus, to yield a units digit of 5, C+E=15.
Implication:
Either C=7 and E=8 or C=8 and E=7.
Total options = 2.
For the tens place, only the digits 5 and 9 remain.
Thus, either B=5 and D=9 or B=9 and D=5.
Total options = 2.
To combine the options above, we multiply:
2*2 = 4.
The correct answer is
D.
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