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Math Revolution GMAT Instructor V
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How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

First multiple of 33 in the range : 132 (33*4)

Last Multiple in the range : 990 (33*30)

No. of multiple in the range : (30-4) + 1 = 27.

GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4542
GMAT 1: 770 Q49 V46
Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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Top Contributor
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

Some positive multiples of 33 are: 33, 66, 99, 132, 165, 198,. . . , 957, 990, 1023
So, we want the number of multiples of 33 from 132 to 990 inclusive

Observe:
132 = (33)(4)
165 = (33)(5)
198 = (33)(6)
.
.
.
957 = (33)(29)
990 = (33)(30)

We can see that the number of multiples of 33 from 132 to 990 inclusive is the SAME as the number of integers from 4 to 30 inclusive.

To determine the above, we can apply the following rule: the number of integers from x to y inclusive equals y - x + 1
So, the number of integers from 4 to 30 inclusive = 30 - 4 + 1 = 27

Cheers,
Brent
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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Top Contributor
2
MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

Another approach is to apply the following rule:

If x and y are multiples of k, then the number of multiples of k from x to y inclusive = [(y-x)/k] + 1
So, for example, the multiples of 3 from 6 to 21 inclusive = [(21 - 6)/3] + 1 = [15/3] + 1 = 6

So, the number of multiples of 33 from 132 to 990 inclusive = (990 - 132)/33 + 1
= 858/33 + 1
= 26 + 1
= 27

Cheers,
Brent
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

Since 1000 - 101 ≈ 900 -- and the answer choices are a bit spread out -- we can count the multiples of 33 simply by dividing 33 into 900:
900/33 = 300/11 = a bit more than 27.
Thus, there are 27 multiples of 33 between 101 and 1000.

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How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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MathRevolution wrote:
[Math Revolution GMAT math practice question]

How many multiples of $$33$$ lie between $$101$$ and $$1,000,$$ inclusive?

$$A. 24$$
$$B. 27$$
$$C. 33$$
$$D. 36$$
$$E. 48$$

One of our students´ most-loved mottos is: let the "Queen of Sciences" (Mathematics) do the weight-lifting for you!

$$101 < 33M < 1000$$

$$? = M\,\,\,\left( {\operatorname{int} } \right)$$

$$\left( {99 + 33 = } \right)\,\,\,132 \leqslant 33M \leqslant 990\,\,\,\,\left( { = 30 \cdot 33} \right)$$

$$4 \leqslant M \leqslant 30\,\,\,\, \Rightarrow \,\,\,\,? = 30 - 4 + 1 = 27$$

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

Regards,
fskilnik.

P.S.: that´s EXACTLY Selim´s solution, only a bit more "structured". Congrats, Selim!!
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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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=>
Consider the arithmetic sequence $$132, 165, …, 990$$ of multiples of $$33$$.
The number of terms in this sequence is $$\frac{(990-132)}{33} + 1 =\frac{858}{33} + 1 = 26 + 1 = 27.$$

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Re: How many multiples of 33 lie between 101 and 1,000, inclusive?  [#permalink]

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_________________ Re: How many multiples of 33 lie between 101 and 1,000, inclusive?   [#permalink] 08 Feb 2020, 19:49
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