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# The number of multiples of 3 between 102 and 729, inclusive

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The number of multiples of 3 between 102 and 729, inclusive [#permalink]  04 Apr 2018, 12:40
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64% (00:34) correct 35% (00:29) wrong based on 64 sessions

 Quantity A Quantity B The number of multiples of 3 between 102 and 729, inclusive $$\frac{729 - 102}{3}$$

A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
[Reveal] Spoiler: OA

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Re: The number of multiples of 3 between 102 and 729, inclusive [#permalink]  04 Apr 2018, 15:35
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A: The numbers of multiples of 3 between 102 and 729:
We should find the minimum and maximum multiples of 3 in this range of numbers.
102 is a multiple of 3 and the maximum multiple of 3 in this range is 729.
Multiples of 3: 102, 105, 108, …., 720, 723, 726, 729
How many numbers are there in this sequence? (Max - min)/ distance +1 = (729 - 102) / 3 + 1
As we see A is 1 value bigger than B and is the answer.

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Re: The number of multiples of 3 between 102 and 729, inclusive [#permalink]  24 Apr 2018, 16:17
1
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series formed will be:-
102,105......., 729
an = a+ (n-1)*d
729 = 102 + (n-1)*3
729-102
------- + 1 = n
3
Hence A is greater by 1
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Re: The number of multiples of 3 between 102 and 729, inclusive [#permalink]  28 May 2018, 22:49
I would take a small example to answer this.

3-9.

3-9 have 3 multiples of 3

9-3 / 3 = 2

So multiples inclusive of numbers will be 1 value greater than range by the number.

This is valid for any range. Hence the answer
Re: The number of multiples of 3 between 102 and 729, inclusive   [#permalink] 28 May 2018, 22:49
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