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GMATPrep Exam 3 Q12

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by Abhijit K » Sat Mar 14, 2015 8:36 pm
Each of the digits 7,5,8,9 and 4 is used only once 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.One
B.Two
C.Three
D.Four
E.Five
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by divyeshbatra » Sat Mar 14, 2015 11:58 pm
In order to make 555, we need _ _ 7 + _ 8 or _ _ 8 + _ 7
Now by hit and trial I get one pair as ( 497,58)

flipping the units and tens' digit I get ( 498,57) , (458,97), (457,98) and (497,58)

Thus 4 combinations.
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by GMATGuruNY » Sun Mar 15, 2015 2:25 am
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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