Quote:
Set A consists of five integers: 2, 4, 5, 6, and 7. X is a three digit number formed by using the digits from set A and Y is a two digit number formed by using the remaining digits from set A, such that all the digits are used only once. For example, X = 245 and Y = 67. If X + Y = 501, how many such pairs of integers can be formed?
A. None
B. One
C. Four
D. Six
E. Eight
X+Y= 501
So the last digits of X and Y have to be (4,7 or 7,4) and (5,6 or 6,5).
I) Using 4,7 or 7,4 leaves the numbers 2,5,6 for tens digit. Adding only 6 and 2 with the 1 carried over from units place gives 0 in the ten's place. But that will make the hundred's digit of the sum to be 6. Which is not possible. So 7,4 cannot be the units digits of the numbers X and Y.
II) Using 5,6 or 6,5 leaves the numbers 2,4,7 for tens digit. Adding only 2 and 7 with the 1 carried over from units place gives 0 in the ten's place. So with the remaining digit 4 we get 5 in the hundred's place.
So possible pairs of integers
i) X= 425 Y= 76
ii) X=426 Y=75
iii) X= 475 Y= 26
iv) X=476 Y=25
Hence. Ans C)