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3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between

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3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 31 Oct 2018, 01:46
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[Math Revolution GMAT math practice question]

\(3, 6, 9, 12, …\) are multiples of \(3\). How many multiples of \(3\) lie between \(10\) and \(200\), inclusive?

\(A. 54\)
\(B. 57\)
\(C. 60\)
\(D. 63\)
\(E. 66\)

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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 31 Oct 2018, 02:07
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(3, 6, 9, 12, …\) are multiples of \(3\). How many multiples of \(3\) lie between \(10\) and \(200\), inclusive?

\(A. 54\)
\(B. 57\)
\(C. 60\)
\(D. 63\)
\(E. 66\)



Between 10 and 200 , inclusive.

First multiple of 3 in the range : 12 =3*4

Last Multiple of 3 in the range : 198 = 3*66

Total no. of multiple in the range : 66 - 4 + 1 = 63.

The best answer is D.
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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 31 Oct 2018, 02:20
number of integers : 200-10=190 integers.
every third integer is a multiple of 3 so 190/3=63
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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 31 Oct 2018, 02:46
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The multiples are 12,15....198

Thus, Nth= a1+ (n-1)d
198= 12 + (n-1)d
198= 12 + (n-1)3
N= 63 ans.

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3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 31 Oct 2018, 03:41
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(3, 6, 9, 12, …\) are multiples of \(3\). How many multiples of \(3\) lie between \(10\) and \(200\), inclusive?

\(A. 54\)
\(B. 57\)
\(C. 60\)
\(D. 63\)
\(E. 66\)


The difference between the endpoints of the range = 200-10 = 190.
Since neither endpoint is a multiple of 3, we can count the multiples of 3 simply by dividing 3 into 190:
190/3 ≈ 63


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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 02 Nov 2018, 00:31
=>

\(12\) is the smallest multiple of \(3\) and \(198\) is the largest multiple of \(3\) between \(10\) and \(200\), inclusive.
Thus, the number of multiples of \(3\) between \(10\) and \(200\), inclusive is \(\frac{( 198 – 12 )}{3 + 1} = \frac{186}{3} + 1 = 62 + 1 = 63\)

Therefore, the answer is D.
Answer: D
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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 03 Nov 2018, 17:08
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(3, 6, 9, 12, …\) are multiples of \(3\). How many multiples of \(3\) lie between \(10\) and \(200\), inclusive?

\(A. 54\)
\(B. 57\)
\(C. 60\)
\(D. 63\)
\(E. 66\)


The smallest multiple of 3 within the range is 12 and the largest is 198. So the number of multiples of 3 within the range is:

(198 - 12)/3 + 1 = 186/3 + 1= 62 + 1 = 63

Answer: D
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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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New post 03 Nov 2018, 17:39
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(3, 6, 9, 12, …\) are multiples of \(3\). How many multiples of \(3\) lie between \(10\) and \(200\), inclusive?

\(A. 54\)
\(B. 57\)
\(C. 60\)
\(D. 63\)
\(E. 66\)


Last digit- First/spacing between digits + 1

198-12/3 +1
62+1=63
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Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between &nbs [#permalink] 03 Nov 2018, 17:39
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3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between

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