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# Let x be a two-digit number. If the sum of the digits of x

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Senior Manager
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Let x be a two-digit number. If the sum of the digits of x [#permalink]

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25 May 2007, 11:56
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Let x be a two-digit number. If the sum of the digits of x is 9, then the sum of the digits of the number (x+10) is

A) 1
B) 8
C) 10
D) either 8 or 10
E) either 1 or 10
__________
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25 May 2007, 12:05
Hello Cass

number = AB = A*10+B

A+B = 9

so AB is devisable by 9

possible values are 18,27,36,45,54,63,73,81,90

A+B+1 = 9+1 = 10

exapt for 90 that will give the out come of 1 - (see ethan_casta post).

so 10 and 1

Last edited by KillerSquirrel on 25 May 2007, 15:34, edited 1 time in total.
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25 May 2007, 15:09
agreed. killer's method displays a deeper intrinsic understanding of math than mine.

i just thought of all the ways you could add 2 integers to make 9:

18,81,27,72,36,63,45,54,18,81 and added 10 to each set of numbers:

28 = 8+2 =10 73=7+3=10.... etc..
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25 May 2007, 15:17
x = _ _ . a two digit number

numbers:
18 ...sums to 9
27...sums to 9
36...sums to 9
45...sums to 9
81...sums to 9
72...sums to 9
63...sums to 9
54...sums to 9
90...sums to 9

all of the numbers above sum to 9, and when 10 is added, the digits sum to 10, except for 90.

when 10 is added to 90, the digits sum to 1, because 90 + 10 = 100.

so the answer should be 10 or 1.

let me know if you see a flaw in my work.
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25 May 2007, 15:31
ethan_casta wrote:
x = _ _ . a two digit number

numbers:
18 ...sums to 9
27...sums to 9
36...sums to 9
45...sums to 9
81...sums to 9
72...sums to 9
63...sums to 9
54...sums to 9
90...sums to 9

all of the numbers above sum to 9, and when 10 is added, the digits sum to 10, except for 90.

when 10 is added to 90, the digits sum to 1, because 90 + 10 = 100.

so the answer should be 10 or 1.

let me know if you see a flaw in my work.

No flaw here - you are correct, the answer is (E) and not (C)
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25 May 2007, 23:37
Yep! The OA is E.
It's a tricky because one can miss 90 and answer C instead
25 May 2007, 23:37
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