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How many multiples of 5 are there between 81 and 358?

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How many multiples of 5 are there between 81 and 358? [#permalink]

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New post 24 Nov 2010, 09:04
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How many multiples of 5 are there between 81 and 358?

A. 54
B. 55
C. 56
D. 57
E. 58

i tried this formula \(Sum = \frac{a1+an}{2}*n\)
[Reveal] Spoiler: OA

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Re: multiple of 5 [#permalink]

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shrive555 wrote:
How many multiples of 5 are there between 81 and 358?

54
55
56
57
58

i tried this formula \(Sum = \frac{a1+an}{2}*n\)


Check this: totally-basic-94862.html?hilit=multiple%20range

\(# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1\).

So we'll have: \(\frac{355-85}{5}+1=55\).

Answer: B.
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Re: multiple of 5 [#permalink]

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New post 24 Nov 2010, 09:15
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It should be ((355-85)/5)+1=55
This is explained beautifully in MGMAT books also.
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Re: multiple of 5 [#permalink]

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New post 24 Nov 2010, 09:18
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shrive555 wrote:
How many multiples of 5 are there between 81 and 358?

54
55
56
57
58

i tried this formula \(Sum = \frac{a1+an}{2}*n\)


How did you use this formula? We don't have the sum of all terms and we don't have n.

Focus on the logic here: Multiples of 5 between 81 and 358 are 85, 90, 95, 100.....350, 355
Question is: How many numbers are they?

85
90 = 85 + 1*5
95 = 85 + 2*5
100 = 85 + 3*5
.
.
.
355 = 85 + 54*5

Total 55 terms.

To get the 54 above, you would need to do the following: (355 - 85)/5
The point is, this is an arithmetic progression.
a, a + d, a + 2d, a + 3d ........ a + nd
Total number of terms = n + 1
The last term (355) is first term(85) plus n times the common difference(5).
355 = 85 + n*5
Solve this to get n as 54
Total number of terms = 54 + 1 = 55
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Re: multiple of 5 [#permalink]

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New post 25 Nov 2010, 04:51
Simple logic.

we know that every 5th # from 81, inclusive, is a multiple of 5
e.g. the first mult of 5 is 85

so, calculate how many #s are there between 81 and 358, inclusive
=358-81+1=278..and devide it by 5 as every 5th # from 81 is a multiple of 5
==> 273/5 =55.6 ==> 55 multiples of 5 between 81 and 358

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Re: How many multiples of 5 are there between 81 and 358? [#permalink]

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New post 14 May 2015, 22:00
Hi All,

This is an example of a "fence post" problem - in these types of questions, you have to be careful to include the first number in the set and the last number in the set. You'll notice that the answer choices are consecutive integers; if your math is "off", even a little bit, then you'll probably choose one of the wrong answers and not even know it....

There are a couple of different ways to approach this question. Since the numbers are relatively small, you COULD break the range into groups and do the math in pieces....

We're asked for the multiples of 5 from 81 to 358.

The 2-digit multiples of 5 here are: 85, 90 and 95 --> That's 3 multiples of 5

The 3-digit multiples that start with 1 are...100, 105, 110....195 --> That's 20 multiples of 5
The 3-digit multiples that start with 2 are...200, 205, 210....295 --> That's 20 multiples of 5

The 3-digit multiples that start with 3 are....300, 305, 310...355 --> that's 12 multiples of 5

3+20+20+12 = 55

Final Answer:
[Reveal] Spoiler:
B


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Re: How many multiples of 5 are there between 81 and 358? [#permalink]

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New post 24 Oct 2017, 05:08
shrive555 wrote:
How many multiples of 5 are there between 81 and 358?

A. 54
B. 55
C. 56
D. 57
E. 58


We can use the following formula:

(largest multiple of 5 in the set - smallest multiple of 5 in the set)/5 + 1

(355 - 85)/5 + 1 = 270/5 + 1 = 55

Answer: B
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Re: How many multiples of 5 are there between 81 and 358?   [#permalink] 24 Oct 2017, 05:08
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