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# If set S consists of all positive integers that are multiples of both

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Joined: 02 Sep 2009
Posts: 53063
If set S consists of all positive integers that are multiples of both  [#permalink]

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28 Jan 2019, 01:49
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Difficulty:

35% (medium)

Question Stats:

55% (01:33) correct 45% (02:40) wrong based on 14 sessions

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If set S consists of all positive integers that are multiples of both 2 and 7, how many numbers in set S are between 140 and 240, inclusive?

A. 6
B. 7
C. 8
D. 9
E. 10

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Re: If set S consists of all positive integers that are multiples of both  [#permalink]

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28 Jan 2019, 02:38
1
Bunuel wrote:
If set S consists of all positive integers that are multiples of both 2 and 7, how many numbers in set S are between 140 and 240, inclusive?

A. 6
B. 7
C. 8
D. 9
E. 10

7*2 =14.

S consists of the integers that are multiple of 14.

140 to 240

140 = 14*10

238 = 14*17

Total number of multiples = 17 -10 +1 = 8.

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If set S consists of all positive integers that are multiples of both  [#permalink]

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28 Jan 2019, 02:49
1
Bunuel wrote:
If set S consists of all positive integers that are multiples of both 2 and 7, how many numbers in set S are between 140 and 240, inclusive?

A. 6
B. 7
C. 8
D. 9
E. 10

IMO C

Multiples of both 7 and 2, multiples of 14, will be an AP of those terms

First Term = 140, Last Term = 238

n = number of term

Last term = First term + (n-1) common difference
238 = 140 + (n-1) 14
98 /14 = n-1
7 + 1 = n

n = 8
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If set S consists of all positive integers that are multiples of both  [#permalink]

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28 Jan 2019, 04:47
Bunuel wrote:
If set S consists of all positive integers that are multiples of both 2 and 7, how many numbers in set S are between 140 and 240, inclusive?

A. 6
B. 7
C. 8
D. 9
E. 10

lcm would be 14
so
140/14 = 10
240/14 = ~17
total no 17-10+1 = 8
IMO C
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If set S consists of all positive integers that are multiples of both   [#permalink] 28 Jan 2019, 04:47
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