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How many multiples of 4 are there between 16 and 260 ?
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Dhairya275
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How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  02 Sep 2013, 12:46
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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 ?
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Bunuel
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Re: How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  02 Sep 2013, 13:06
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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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Bunuel
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Re: How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  02 Sep 2013, 13:09
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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.


Similar questions to practice:
what-is-the-number-of-integers-from-1-to-1000-inclusive-126153.html
how-many-integers-from-1-to-200-inclusive-are-divisib-109333.html
how-many-multiples-of-5-are-there-between-81-and-105318.html
how-many-even-integers-n-where-100-n-200-are-divisib-103779.html
what-is-the-number-of-integers-from-1-to-1000-m07q14-75696.html
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what-is-the-total-number-of-positive-integers-that-are-less-128104.html

Hope it helps.
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Re: How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  19 Dec 2015, 10:46
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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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Re: How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  19 Dec 2015, 13:57
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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

Answer: E
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Re: How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  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] New post  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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How many multiples of 4 are there between 16 and 260 ? [#permalink] New post  14 May 2021, 23:13
First, note that we are looking for multiples of 4 “between” 16 and 260, so we are not counting the end-points (which are themselves multiples of 4)

If you lose track of the formulae, a method you can always fall back on:

(1st) list the multiples of 4 that we are looking for

20 ; 24 ; 28 ............. 252 ; 256

(2nd) subtract the first, smallest multiple so that it is zero. Subtract every number by that same constant

(20 - 20) ; (24 - 20) ; (28 - 20) ........ (252 - 20) ; (256 - 20)

0 ; 4 ; 8 ....... 232 ; 236

(3rd) now divide each number by the spacing. Here we are looking at multiples of 4, so divide each number by 4

(0/4) ; (4/4) ; (8/4)....... (232/4) ; (236/4)

0 ; 1 ; 2 .........58 ; 59


Now from 1 to 59 ———> 59 integers
And
Add + 1 more for the 0
_____________

60 multiples of 4

(E)

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