Re: HOT Competition: Set A consists of five integers: 2, 4, 5, 6, and 7. X
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24 Aug 2020, 08:45
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--> correct
D. Six
E. Eight
Detail Solution:
A = {2, 4, 5, 6, 7} & X+Y =501,
unit digit combo of (4+7) & (5+6) can give us unit digit of X+Y = 1
let's say for unit digit combo of (4+7)
X=__4
Y= _7
A = {2, 4, 5, 6, 7} --> we are left with 2,5, & 6 and we can't add any of the two make the sum = 9 (10-1) --> so this combination(4+7) of unit digit is not possible
Next let's say for unit digit combo of (5+6)
X=__5
Y= _6
A = {2, 4, 5, 6, 7} --> we are left with 2,4, & 7 and we can add (2+7) to get the sum = 9 (10-1)
so hundred position of X=4, ten position can have 2/7, & unit position can have 5/6 => so total number of combinations = 1*2*2=4
details:
X=475 --> 425 --> 476 --> 426
Y= 26 --> 76 --> 25 --> 75
-----------------------------
->501 --> 501 --> 501 --> 501
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