nave wrote:
Each of the digits 7, 5, 8, 9 and 4 is used only one to form a three digit integer and a two digit integer. If the sum of the integers is 555, how many such pairs of integers can be formed?
A. 1
B. 2
C. 3
D. 4
E. 5
Another method would be to start from the hundreds digit.
A three digit number and a two digit number add to give 555. So the three digit number must be greater than 455 but less than 500 since you do not have smaller digits to make one of the early 500 numbers such as 510. So the hundreds place of three digit number must have 4.
You are left with 5, 7, 8, 9
Next, the units digits must add to 15 and there is only one way of doing that: 7+8 = 15. The two digits, 7 and 8 can be arranged in either way - 4 __ 7 or 4 __ 8 so there are two ways to choose the units digit.
The leftover digits are 9 and 5 which need to go to tens places. Again, there are two ways of arranging them 4 9 __ or 4 5 __.
In all, there are 2*2 = 4 ways of making a 3 digit and a 2 digit number such that the sum is 555.
Answer (D)
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Karishma
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