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# The integers between 1 and 100, inclusive, are put in list A if they a

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Math Expert
Joined: 02 Sep 2009
Posts: 59674
The integers between 1 and 100, inclusive, are put in list A if they a  [#permalink]

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22 Nov 2019, 03:42
00:00

Difficulty:

45% (medium)

Question Stats:

50% (01:51) correct 50% (01:49) wrong based on 40 sessions

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The integers between 1 and 100, inclusive, are put in list A if they are divisible by 2 and in list B if they are divisible by 3. How many integers in list A are not in list B?

(A) 11
(B) 16
(C) 25
(D) 33
(E) 34

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Re: The integers between 1 and 100, inclusive, are put in list A if they a  [#permalink]

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22 Nov 2019, 04:27
Bunuel wrote:
The integers between 1 and 100, inclusive, are put in list A if they are divisible by 2 and in list B if they are divisible by 3. How many integers in list A are not in list B?

(A) 11
(B) 16
(C) 25
(D) 33
(E) 34

A= 50
B = 33
common set = LCM = 6 ; 16
so A has 34 less not in B
IMO E
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Re: The integers between 1 and 100, inclusive, are put in list A if they a  [#permalink]

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23 Nov 2019, 10:28
# of items in list A = $$\frac{100-2}{2}$$+1 = 50. For list B, it is $$\frac{99-3}{3}$$+1 = 33. LCM of 2 and 3 is 6, factors of 6 ($$\frac{96-6}{6}$$+1 = 16) will be in list A and B ==> 50 - 16 = 34 are in A but not in B. The answer is D
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Re: The integers between 1 and 100, inclusive, are put in list A if they a  [#permalink]

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23 Nov 2019, 15:00
Bunuel wrote:
The integers between 1 and 100, inclusive, are put in list A if they are divisible by 2 and in list B if they are divisible by 3. How many integers in list A are not in list B?

(A) 11
(B) 16
(C) 25
(D) 33
(E) 34

List A would have all the multiples of 2 i.e 2,4,6,8,10 and so on. Easy way to calculate multiples of a number within a range of numbers is $$\frac{(last multiple)-(first multiple)}{number}$$ +1. $$\frac{100-2}{2}$$ +1 = 50

Similarly with List B, all multiples of 3 and that would be 33 in size ( not required but in a hurry we tend go with the question stem and even get this number but we won't use it )

All the numbers - common numbers = Uncommon numbers

common numbers= common multiples of 2 and 3 = 2X3 = 6 so multiples of 6. There are 16 multiples of 6

50 - 16 = 34 is the answer
Re: The integers between 1 and 100, inclusive, are put in list A if they a   [#permalink] 23 Nov 2019, 15:00
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