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# How many positive three-digit positive integers are

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GMAT Instructor
Joined: 04 Jul 2006
Posts: 1268
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Kudos [?]: 149 [0], given: 0

How many positive three-digit positive integers are [#permalink]  19 Sep 2006, 12:43
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
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, 13:11, edited 1 time in total.
VP
Joined: 02 Jun 2006
Posts: 1267
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Kudos [?]: 42 [0], given: 0

(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

SVP
Joined: 05 Jul 2006
Posts: 1519
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Kudos [?]: 108 [0], given: 39

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
SVP
Joined: 05 Jul 2006
Posts: 1519
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Kudos [?]: 108 [0], given: 39

Kevin .. would u plz send OA...THANKS IN ADVANCE
Manager
Joined: 13 Sep 2006
Posts: 198
Schools: Olin Business School - Washington University
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Kudos [?]: 15 [0], given: 0

Got 7 too, but muscled thru it, not the most efficient way. I like your explanation Yezz...
SVP
Joined: 05 Jul 2006
Posts: 1519
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Kudos [?]: 108 [0], given: 39

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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