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

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Bunuel
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How many positive integers less than 200 are there such that they are [#permalink] New post   04 Nov 2019, 04:17
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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

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C
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Himanshu453
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Re: How many positive integers less than 200 are there such that they are [#permalink] New post   04 Nov 2019, 04:39
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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] New post   04 Nov 2019, 04:44
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200÷12=~16
200÷13=~15
200÷156=~1
15+16-1=30

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nikhil553
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How many positive integers less than 200 are there such that they are [#permalink] New post   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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LevanKhukhunashvili
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How many positive integers less than 200 are there such that they are [#permalink] New post   13 Nov 2019, 07:47
Mohammadmo wrote:
200÷12=~16
200÷13=~15
200÷156=~1
15+16-1=30

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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 :(

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L
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chetan2u
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Re: How many positive integers less than 200 are there such that they are [#permalink] New post   14 Nov 2019, 00:16
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LevanKhukhunashvili wrote:
Mohammadmo 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

answer = 15+16-1=30

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] New post   17 Nov 2019, 20:18
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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

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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.

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

Answer: C
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Re: How many positive integers less than 200 are there such that they are [#permalink] New post   28 Mar 2020, 09:51
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


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

Multiples of 13 = {13,26,,,,195} = 15 numbers
Multiples of 12 = {12,24,,,,192} = 16 numbers
Multiples of 12*13 = 156 = 1 number

Number of positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 = 15 + 16 -1 = 30

IMO C
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Re: How many positive integers less than 200 are there such that they are [#permalink] New post   11 Jan 2022, 00:04
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