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

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

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New post 22 Nov 2019, 03:42
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A
B
C
D
E

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Question Stats:

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

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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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New post 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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New post 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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New post 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 :tongue_opt1 :tongue_opt3 )

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
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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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