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22 Apr 2015, 02:05
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
59% (02:31) correct
41%
(02:35)
wrong
based on 98
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When integer A divided by 9 remainder is X, when integer B divided by 9 the remainder is Y. What is \(|X-Y|\)?
1) When \(A + B\) divided by 9 remainder is 6
2) When \(A * B\) divided by 9 remainder is 8
Source: self-made
1) When \(A + B\) divided by 9 remainder is 6
2) When \(A * B\) divided by 9 remainder is 8
Source: self-made
22 Apr 2015, 07:21
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When integer A divided by 9 remainder is X, when integer B divided by 9 the remainder is Y. What is |X−Y|?
1) When A+B divided by 9 remainder is 6
2) When A∗B divided by 9 remainder is 8
stmt 1: A=9(m+n)+ (x+y) x+y is the remainder so x+y = 6. But that could be 5+1,4+2 etc not suff
stmt 2: A= (9m+x) * (9n+y) after using foil xy is the remainder which equals 8. But that could be 2*4 or 8*1 not suff
Both: we see that 2 and 4 satisfy both stmt 1 and stmt 2 and because the we are looking for the absolute of x-y (and remainders must be positive) this is suff
1) When A+B divided by 9 remainder is 6
2) When A∗B divided by 9 remainder is 8
stmt 1: A=9(m+n)+ (x+y) x+y is the remainder so x+y = 6. But that could be 5+1,4+2 etc not suff
stmt 2: A= (9m+x) * (9n+y) after using foil xy is the remainder which equals 8. But that could be 2*4 or 8*1 not suff
Both: we see that 2 and 4 satisfy both stmt 1 and stmt 2 and because the we are looking for the absolute of x-y (and remainders must be positive) this is suff
26 Aug 2015, 15:00
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Harley1980
I believe the correct answer to this question is E.
Since X and Y are remainders when divided by 9, they must each be less than 9. X<9 and Y<9, therefore X+Y<18 and X*Y<81.
X+Y = 9k + 6 and X*Y= 9z + 8. The only values that X+Y can take in this problem are 6 and 15. The only values that X*Y can take in this problem are 8,17,26,35,44,53,62,71, and 80. There is no such solution for sum equal 6 that satisfies X+Y = 9k + 6 and X*Y= 9z + 8. For sum equal to 15 there are 4 solutions that satisfy both X+Y = 9k + 6 and X*Y= 9z + 8, which are (2,13), (13,2), (4,11) and (11,4). The absolute difference can be either 11 or 7.
