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# How many positive integers less than 200 are there such that they are

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Math Expert
Joined: 02 Sep 2009
Posts: 59622
How many positive integers less than 200 are there such that they are  [#permalink]

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04 Nov 2019, 04:17
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Difficulty:

65% (hard)

Question Stats:

56% (01:40) correct 44% (01:53) wrong based on 66 sessions

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How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12?

A. 28
B. 29
C. 30
D. 31
E. 32

Are You Up For the Challenge: 700 Level Questions

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Re: How many positive integers less than 200 are there such that they are  [#permalink]

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04 Nov 2019, 04:39
1
the two numbers are co prime ie 12,13, the lcm of the two is 156,

simply calculate the number of multiples independently.

200/13= 15.abc
200/12= 16.abc
subtract the common multiple that is counted twice in the list.
total number of multiples of 12, 13 under 200 = 15+16-1= 30
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Re: How many positive integers less than 200 are there such that they are  [#permalink]

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04 Nov 2019, 04:44
1
200÷12=~16
200÷13=~15
200÷156=~1
15+16-1=30

Posted from my mobile device
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How many positive integers less than 200 are there such that they are  [#permalink]

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04 Nov 2019, 11:32
n(aor b)=n(a)+n(b)-n(a&b)
n(a)=200/12 =~16; n(b)= 200/13= ~15; n(a&b)= 200/156=~1 (LCM 13X12=156)
n(a or b) = 16+15-1=30
ans:C
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Joined: 13 Feb 2018
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GMAT 1: 640 Q48 V28
How many positive integers less than 200 are there such that they are  [#permalink]

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13 Nov 2019, 07:47
200÷12=~16
200÷13=~15
200÷156=~1
15+16-1=30

Posted from my mobile device

Sir chetan2u is that correct approach above?

I have done tremendous calculations to reach those 15 and 16

$$\frac{(195-13)}{13}+1=15$$
$$\frac{(192-12)}{12}+1=16$$

Wasted precious time

Regards
L
Math Expert
Joined: 02 Aug 2009
Posts: 8289
Re: How many positive integers less than 200 are there such that they are  [#permalink]

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14 Nov 2019, 00:16
1
LevanKhukhunashvili wrote:
200÷12=~16
200÷13=~15
200÷156=~1
15+16-1=30

Posted from my mobile device

Sir chetan2u is that correct approach above?

I have done tremendous calculations to reach those 15 and 16

$$\frac{(195-13)}{13}+1=15$$
$$\frac{(192-12)}{12}+1=16$$

Wasted precious time

Regards
L

Hi,
the sign ~ is NOT correct..

$$200/13 = 15\frac{5}{13}$$.....So, you take only the integer 15...
$$\frac{200}{12}=16\frac{8}{12}$$. Here it is ~17, but you will take 16, as the integer portion is 16 and there are 16 multiples of 12

The above lists consists of repetition of common multiples of 12 and 13, so remove them..
LCM(12,13)=156
$$\frac{200}{156}=1\frac{44}{156}$$...so 1

Quote:
$$\frac{(195-13)}{13}+1=15$$

Where you would do this..
If the set of number does NOT begin from 1...
for example - Number of multiples of 12 from 100 to 200

But here we were looking for multiples in first 200 numbers...
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Re: How many positive integers less than 200 are there such that they are  [#permalink]

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17 Nov 2019, 20:18
Bunuel wrote:
How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12?

A. 28
B. 29
C. 30
D. 31
E. 32

Are You Up For the Challenge: 700 Level Questions

The number of multiples of 13 is:

(195 - 13)/13 + 1 = 15

The number of multiples of 12 is:

(192 - 12)/12 + 1 = 16

There is also one multiple of both 12 and 13, which is 12 x 13 = 156.

Thus, the number of multiples of 12 or 13 less than 200 is 15 + 16 - 1 = 30.

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# Scott Woodbury-Stewart

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Re: How many positive integers less than 200 are there such that they are  [#permalink]

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27 Nov 2019, 11:53
Bunuel wrote:
How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12?

A. 28
B. 29
C. 30
D. 31
E. 32

Are You Up For the Challenge: 700 Level Questions

The number of multiples of 13 is:

(195 - 13)/13 + 1 = 15

The number of multiples of 12 is:

(192 - 12)/12 + 1 = 16

There is also one multiple of both 12 and 13, which is 12 x 13 = 156.

Thus, the number of multiples of 12 or 13 that are also less than 200 is 15 + 16 - 1 = 30.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: How many positive integers less than 200 are there such that they are   [#permalink] 27 Nov 2019, 11:53
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