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# How many integers between 100 & 150,inclusive,cannot be

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Manager
Joined: 20 Feb 2007
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How many integers between 100 & 150,inclusive,cannot be [#permalink]  22 Oct 2007, 21:29
How many integers between 100 & 150,inclusive,cannot be divided by 3 or 5?

Is there a easier way of doing this apart from counting the numbers?
VP
Joined: 08 Jun 2005
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[#permalink]  22 Oct 2007, 21:40
150/3- 102/3 = 16 ---> 17 numbers

150/5-100/5 = 10 ---> 11 numbers

150/15-105/15 = 3 --> 4 numbers

total

17+11-4 = 24 numbers

Manager
Joined: 20 Feb 2007
Posts: 81
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Kudos [?]: 2 [0], given: 0

[#permalink]  22 Oct 2007, 21:44
The answer is given as 27....is it wrong?
Manager
Joined: 20 Feb 2007
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[#permalink]  22 Oct 2007, 21:55
I get the number 150/3 - 102/3 = 16....do we have to add 1 to each cause its inclusive?
GMAT Club Legend
Joined: 07 Jul 2004
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[#permalink]  23 Oct 2007, 00:51
# of terms divisible by 3 --> (150-102)/3 + 1 = 17
# of terms divisible by 5 --> (150-100)/5 + 1 = 11
# of terms divsible by both 5 and 3 --> (150-105)/15 + 1 = 4

Drawing a venn diagram, you can solve for:

# of terms divisible by both 5 and 3 -> 4
# of terms divisible by 3 only -> 13
# of terms divisible by 5 only -> 7

Total = 7+4+13 = 24
GMAT Instructor
Joined: 04 Jul 2006
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[#permalink]  23 Oct 2007, 01:07
KillerSquirrel wrote:
150/3- 102/3 = 16 ---> 17 numbers

150/5-100/5 = 10 ---> 11 numbers

150/15-105/15 = 3 --> 4 numbers

total

17+11-4 = 24 numbers

Are you counting the number of integers that CAN be divided by 3 or by 5?
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

[#permalink]  23 Oct 2007, 01:08
kevincan wrote:
KillerSquirrel wrote:
150/3- 102/3 = 16 ---> 17 numbers

150/5-100/5 = 10 ---> 11 numbers

150/15-105/15 = 3 --> 4 numbers

total

17+11-4 = 24 numbers

Are you counting the number of integers that CAN be divided by 3 or by 5?

Haha... read it wrong =)

Answer should be ((150-100)+1)-24 = 27 =)
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 127 [0], given: 0

[#permalink]  23 Oct 2007, 11:54
ywilfred wrote:
kevincan wrote:
KillerSquirrel wrote:
150/3- 102/3 = 16 ---> 17 numbers

150/5-100/5 = 10 ---> 11 numbers

150/15-105/15 = 3 --> 4 numbers

total

17+11-4 = 24 numbers

Are you counting the number of integers that CAN be divided by 3 or by 5?

Haha... read it wrong =)

Answer should be ((150-100)+1)-24 = 27 =)

Yes ! I also fell to that trap.

[#permalink] 23 Oct 2007, 11:54
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# How many integers between 100 & 150,inclusive,cannot be

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