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

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by Max@Math Revolution » Wed Oct 31, 2018 1:27 am

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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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by fskilnik@GMATH » Wed Oct 31, 2018 2:26 am
Max@Math Revolution 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
$$? = \# \,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,{\rm{between}}\,\,10\,\,{\rm{and}}\,\,200$$
$$\left. \matrix{
12 = 3 \cdot 4 \hfill \cr
15 = 3 \cdot 5 \hfill \cr
\ldots \hfill \cr
195\left( { = 180 + 15} \right) = 3 \cdot 65\,\,\, \hfill \cr
198 = 3 \cdot 66 \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{fingers}}\,\,{\rm{technique}}} \,\,\,\,\,? = 66 - 4 + 1 = 63$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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range

by GMATGuruNY » Wed Oct 31, 2018 3:38 am
Max@Math Revolution 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.

The correct answer is D.
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by Max@Math Revolution » Fri Nov 02, 2018 12:22 am
=>

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

Therefore, the answer is D.
Answer: D
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by Scott@TargetTestPrep » Sat Nov 03, 2018 5:00 pm
Max@Math Revolution 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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