If W is the set of all the integers between 49 and 99, inclusive, that

Question

If W is the set of all the integers between 49 and 99, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?

A. 26
B. 32
C. 33
D. 34
E. 35

GmatKnightTutor · Answer

Interesting question. One of the main points to learn here is to subtract the "double counting" that the 6 brings into play. It may also be helpful to think of a way that works for you to figure out exactly how many even numbers for example exist within the range stated. You're dealing with answer choices that are very close, so approximate estimations can't work.

ZulfiquarA · Answer

First find the total number of elements - 49-99+1=51
No. of multiples of two - 51/2=25 elements
No. of multiples of three - 51/3=17 elements
Now note that there would be double counting between multiple of 3 & 2 such as 60, 66 etc.
No. of multiples of both 2 & 3 would be 51/2*3=51/6=8
No. of multiples of 2 & 3 = 25+17-8=34 (D)

RamseyGooner · Answer

Took me 2mins 10 secs, here it goes :

Elements with 2 : 50,.....,98 => number of elements : (last - first)/difference + 1= 25
Elements with 3 : 51,.....,99 => number of elements : (last - first)/difference + 1= 17

Now the tricky part,

Elements with 2*3(or 6) are the ones that are counted twice, lets deduct that from the total

Elements with 6 : 54,.....,96 => number of elements : (last - first)/difference + 1= (96-54)/6+1 = 8

Total = 25+17-8=34

Cheers!

CrackverbalGMAT · Answer

Solution:

The total number of numbers =99-49+1 =51 (We add 1 to include both 99 and 49 in the count)

Number of multiples of 2(50,52,..98) = 98-50/2 + 1 =48/2 +1 = 25 (We add 1 to include both 50 and 98 in the count)

Number of Multiples of 3 (51,99)=99-51/3 +1 = 16+1 = 17 (We add 1 to include both 99 and 51 in the count)

The common terms that are double counted are to be eliminated. They are multiples of 6(54,..96) = 96-54 / 6 + 1

(We add 1 to include both 54 and 96 in the count)

= 7+1

=8

Thus total count =25+17-8

= 34  (option d)

Devmitra Sen
GMAT SME

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If W is the set of all the integers between 49 and 99, inclusive, that

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If W is the set of all the integers between 49 and 99, inclusive, that

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