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# How many multiples of 4 are there between 16 and 260 ?

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Joined: 03 Jul 2013
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How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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02 Sep 2013, 12:46
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Difficulty:

55% (hard)

Question Stats:

55% (00:58) correct 45% (00:51) wrong based on 266 sessions

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How many multiples of 4 are there between 16 and 260 ?

A. 128
B. 64
C. 62
D. 61
E. 60

Any quick way of solving this ?
Math Expert
Joined: 02 Sep 2009
Posts: 64161
Re: How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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02 Sep 2013, 13:06
3
4
Dhairya275 wrote:
How many multiples of 4 are there between 16 and 260 ?

A. 128
B. 64
C. 62
D. 61
E. 60

It should be mentioned whether 16 and 260 are inclusive.

$$# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1$$ (check here: how-many-multiples-of-4-are-there-between-12-and-94862.html).

If 16 and 260 are inclusive, then the answer is (260-16)/4+1=62.
If 16 and 260 are NOT inclusive, then the answer is (256-20)/4+1=60.

Since OA is E, then we have NOT inclusive case.
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Re: How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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02 Sep 2013, 13:09
Bunuel wrote:
Dhairya275 wrote:
How many multiples of 4 are there between 16 and 260 ?

A. 128
B. 64
C. 62
D. 61
E. 60

It should be mentioned whether 16 and 260 are inclusive.

$$# \ of \ multiples \ of \ x \ in \ the \ range = \frac{Last \ multiple \ of \ x \ in \ the \ range \ - \ First \ multiple \ of \ x \ in \ the \ range}{x}+1$$ (check here: how-many-multiples-of-4-are-there-between-12-and-94862.html).

If 16 and 260 are inclusive, then the answer is (260-16)/4+1=62.
If 16 and 260 are NOT inclusive, then the answer is (256-20)/4+1=60.

Since OA is E, then we have NOT inclusive case.

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Hope it helps.
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Re: How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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19 Dec 2015, 10:46
1
yep, it's 60, did a different way:
16 is the 4th multiple
260 is the 65th multiple.
since we need to find the multiples between, without the 4th and 65th multiple, we need to find how many multiples are between 5th multiple and 64th multiple inclusive:
64-5+1=60.

E.
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Joined: 11 Sep 2015
Posts: 4879
GMAT 1: 770 Q49 V46
Re: How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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19 Dec 2015, 13:57
1
Dhairya275 wrote:
How many multiples of 4 are there between 16 and 260 ?

A. 128
B. 64
C. 62
D. 61
E. 60

Any quick way of solving this ?

If you're not good at remembering formulas, then another option is to look for a pattern.
So, we want to know how many terms are in the sequence 20, 24, 28, . . .. 252, 256

Notice that:
20 = 4(5)
24 = 4(6)
28 = 4(7)
32 = 4(8)
.
.
.
252 = 4(63)
256 = 4(64)

So, the number of terms in the sequence 20, 24, 28, . . .. 252, 256 is equal to the number of integers from 5 to 64 inclusive.

Well we have a formula (an easy formula) for finding this. We know that the number of integers from x to y inclusive is equal to y-x+1

So, the number of integers from 5 to 64 inclusive is equal to 64-5+1 = 60

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Re: How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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30 Nov 2016, 08:02
It's useful for these types of questions to figure out what multiple of 4 is already being represented by 16 and 260

16/4 =4
260/4 = 65

Thus we are looking for multiples of 4 from 5 to 64 --> 64-5+1=60

E.
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Re: How many multiples of 4 are there between 16 and 260 ?  [#permalink]

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07 Aug 2018, 06:47
Dhairya275 wrote:
How many multiples of 4 are there between 16 and 260 ?

A. 128
B. 64
C. 62
D. 61
E. 60

Any quick way of solving this ?

S = { 16, 20 , 24 ........260}

Or, S = 4{4,5...........64,65}

So, THe number of multiples of 4 is 65 - 4 + 1 = 60 , Answer must be (E)
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Re: How many multiples of 4 are there between 16 and 260 ?   [#permalink] 07 Aug 2018, 06:47