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# How many positive three-digit positive integers are

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GMAT Instructor
Joined: 04 Jul 2006
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How many positive three-digit positive integers are [#permalink]

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19 Sep 2006, 13:43
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How many positive three-digit positive integers are multiples of 6, 9 and 7?

(A) 3 (B) 4 (C) 6 (D) 7 (E) 8

Last edited by kevincan on 19 Sep 2006, 14:11, edited 1 time in total.

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VP
Joined: 02 Jun 2006
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19 Sep 2006, 14:06
(D) 7

I am presuming multiples of 6 & 7 & 9, not independently.

LCM (6,7,9) = 126

Three digit +ve integers... {100... 999}

First multiple of 126 after 100 = 126

Last multiple of 126 < 999 = 882

# of multiples = (882-126)/126 +1 (inclusive)
= 7-1 +1 = 7

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Retired Moderator
Joined: 05 Jul 2006
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20 Sep 2006, 05:31
How many positive three-digit positive integers are multiples of 6, 9 and 7?

(A) 3 (B) 4 (C) 6 (D) 7 (E) 8

the intiger will be in the form of LCM OF (6,9,7)*K WHERE K IS ANY POSITIVE INTIGER

lcm = 7*3^2*2 = 126

now lets name our intiger K

126 < 126K<999
1< K <7.9...K COULD ONLY BE INTIGER , THUS 1=<K=<7
NUMBER OF MULTIPLES IS THUS 7-1+1 = 7

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1749

Kudos [?]: 443 [0], given: 49

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20 Sep 2006, 22:34
Kevin .. would u plz send OA...THANKS IN ADVANCE

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Manager
Joined: 14 Sep 2006
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Schools: Olin Business School - Washington University

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20 Sep 2006, 23:38
Got 7 too, but muscled thru it, not the most efficient way. I like your explanation Yezz...

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Retired Moderator
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21 Sep 2006, 02:13
Die Gmat....thanks man..........i had no clue about this way before joining our forum here so thanks to Gmat club and each and every member in it.

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21 Sep 2006, 02:13
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# How many positive three-digit positive integers are

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