[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
3, 6, 9, 12, … are multiples of 3. How many multiples of 3
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- Max@Math Revolution
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$$? = \# \,\,{\rm{multiples}}\,\,{\rm{of}}\,\,3\,\,{\rm{between}}\,\,10\,\,{\rm{and}}\,\,200$$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
$$\left. \matrix{
12 = 3 \cdot 4 \hfill \cr
15 = 3 \cdot 5 \hfill \cr
\ldots \hfill \cr
195\left( { = 180 + 15} \right) = 3 \cdot 65\,\,\, \hfill \cr
198 = 3 \cdot 66 \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{fingers}}\,\,{\rm{technique}}} \,\,\,\,\,? = 66 - 4 + 1 = 63$$
This solution follows the notations and rationale taught in the GMATH method.
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The difference between the endpoints of the range = 200-10 = 190.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
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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- Max@Math Revolution
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=>
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
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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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: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
(198 - 12)/3 + 1 = 186/3 + 1= 62 + 1 = 63
Answer: D
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