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Math Revolution GMAT Instructor V
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3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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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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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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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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Top Contributor
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.

Posted from my mobile device
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3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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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?

$$A. 54$$
$$B. 57$$
$$C. 60$$
$$D. 63$$
$$E. 66$$

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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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8017
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between  [#permalink]

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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 $$\frac{( 198 – 12 )}{3 + 1} = \frac{186}{3} + 1 = 62 + 1 = 63$$

Therefore, the 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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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

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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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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 Re: 3, 6, 9, 12, … are multiples of 3. How many multiples of 3 lie between   [#permalink] 03 Nov 2018, 18:39
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