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If a, b, and c are digits, is a + b + c a multiple of 9? A digit is on

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Joined: 02 Sep 2009
Posts: 51035
If a, b, and c are digits, is a + b + c a multiple of 9? A digit is on  [#permalink]

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29 Oct 2017, 00:59
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Difficulty:

35% (medium)

Question Stats:

80% (01:35) correct 20% (02:02) wrong based on 33 sessions

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If a, b, and c are digits, is a + b + c a multiple of 9? A digit is one of the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

(1) The three-digit number abc is a multiple of 9.
(2) (a * b) + c is a multiple of 9.

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Joined: 13 Apr 2010
Posts: 89
Re: If a, b, and c are digits, is a + b + c a multiple of 9? A digit is on  [#permalink]

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30 Oct 2017, 03:18
Bunuel wrote:
If a, b, and c are digits, is a + b + c a multiple of 9? A digit is one of the integers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

(1) The three-digit number abc is a multiple of 9.
(2) (a * b) + c is a multiple of 9.

Statement 1 : if a number is multiple of 9 or 3 then that number digits will be add to be a multiple of 9 or 3 .
Statement 1 is sufficient .
Ex. 111 is a multiple of 3 and digits will be add up to be a multiple of 3 .
Ex. 12123 is a multiple of 9 (9 * 1347) and its digits add up be a multiple of 9 and 3

Statement 2 : take a = b = 0 , c = 9 ; (a * b) + c = 0 + 9 = 9 (is a multiple of 9) and 0 + 0 + 9 = 9 (is a multiple of 9)
or
take a = b = 1 , c = 8 ; (a * b) + c = 1 + 8 = 9 (is a multiple of 9) but 1 + 1 + 8 = 10 (is NOT a multiple of 9)
Statement 2 is Insufficient .

Re: If a, b, and c are digits, is a + b + c a multiple of 9? A digit is on &nbs [#permalink] 30 Oct 2017, 03:18
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