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

Question

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

Bunuel · Accepted Answer

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: https://gmatclub.com/forum/how-many-mult ... 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.

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/what-is-the-n ... 26153.html https://gmatclub.com/forum/how-many-inte ... 09333.html https://gmatclub.com/forum/how-many-mult ... 05318.html https://gmatclub.com/forum/how-many-even ... 03779.html https://gmatclub.com/forum/what-is-the-t ... 28104.html https://gmatclub.com/forum/for-any-posit ... 27817.html https://gmatclub.com/forum/if-x-is-equal ... 27276.html Hope it helps.

mvictor · Answer

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.

BrentGMATPrepNow · Answer

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

law258 · Answer

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.

Abhishek009 · Answer

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)

Fdambro294 · Answer

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)

Posted from my mobile device

rickygo01 · Answer

The question is asking how many multiples of 4 are there between 16 and 260----> this means 16 and 260 are not included.

We know that the first term which satisfies the request is therefore 20 and the last one is 256

That's enough to use the formula of the sequences in order to find the number of terms n in a sequence

256=20+(n-1)4-----> ... 
n=60

Answer E

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

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

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