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If a and b are the digits of the two-digit number X, what is

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Intern
Joined: 01 Dec 2007
Posts: 31
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Kudos [?]: 23 [0], given: 0

If a and b are the digits of the two-digit number X, what is [#permalink]

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01 Dec 2007, 21:56
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If a and b are the digits of the two-digit number X, what is the remainder when X is divided by 9?

(1) a + b = 11

(2) X + 7 is divisible by 9

What's the fastests way to solve this problem?
CEO
Joined: 17 Nov 2007
Posts: 3585
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 575

Kudos [?]: 3984 [0], given: 360

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01 Dec 2007, 22:20
D.

1. X(mod9)=(a+b)mod9=11(mod9)=2(mod9)
1. (X+7)mod9=0 ==> X+7=9n ==> X=9n-7 or X=9(n-1)+2 X(mod9)=2(mod9)
CEO
Joined: 17 Nov 2007
Posts: 3585
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 575

Kudos [?]: 3984 [0], given: 360

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01 Dec 2007, 22:33
applecrisp wrote:
What's mod9?

a(mod b)- reminder (a divided by b)

for example,
56(mod 11)=1(mod 11) ==> 56=11n+1
SVP
Joined: 05 Jul 2006
Posts: 1747
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Kudos [?]: 358 [0], given: 49

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02 Dec 2007, 03:38
applecrisp wrote:
If a and b are the digits of the two-digit number X, what is the remainder when X is divided by 9?

(1) a + b = 11

(2) X + 7 is divisible by 9

What's the fastests way to solve this problem?

FROM 1

A,B <10 THUS A,B = (9,2)OR (7,4) OR (5,6) OR (2.9) 0R (4,7)..ETC.......SUFF ALWAYS REMINDER WILL BE 2.

X+7 = 9K IE: X = 9K-7 , 9K - 7 / 9 RMINDER IS ALWAYS 2..SUFF

Re: DS Remainder   [#permalink] 02 Dec 2007, 03:38
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