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Set M consists of all positive integers that are multiples of 4. Set

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Set M consists of all positive integers that are multiples of 4. Set  [#permalink]

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New post 23 Mar 2018, 09:18
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Set M consists of all positive integers that are multiples of 4. Set N consists of all positive integers less than 100 that have a units digit of 8. How many integers do sets M and N have in common?


(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven

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Re: Set M consists of all positive integers that are multiples of 4. Set  [#permalink]

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New post 23 Mar 2018, 09:42
Bunuel wrote:
Set M consists of all positive integers that are multiples of 4. Set N consists of all positive integers less than 100 that have a units digit of 8. How many integers do sets M and N have in common?


(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven


IMO C.
Define the sets :-

M = { 4, 8, 12, 16, ...}
N = { 8, 18, 28, 38, ..., 88, 98}

M & N common will be all elements in N that are divisible by 4.

first element is divisible by 4. the next one is not ( as we add 10 to reach to next element)... a pattern is found -> every other element in set N is divisible by 4. ( adding 20 i.e 4*5 )

Hence # of elements common to M & N = # elements in N * 0.5 = 10 * 0.5 = 5.

Option (C).
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Re: Set M consists of all positive integers that are multiples of 4. Set  [#permalink]

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New post 23 Mar 2018, 10:31
Bunuel wrote:
Set M consists of all positive integers that are multiples of 4. Set N consists of all positive integers less than 100 that have a units digit of 8. How many integers do sets M and N have in common?


(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven


Essentially the question asks how may elements in set M are multiples of 4

So Set M={8,18,28...........,88,98}.

as there are only 11 elements in set M, we can actually count the numbers that are divisible by 4

they are 8,28,48,68 and 88 i.e. 5 elements. Hence Option C

----------------------------------

Alternatively, first number of set M that is divisible by 4 is 8, next number will be 28 and last number that is divisible by 4 is 88. This is an AP series with

\(a=8\), \(d=28-8=20\) and \(T_n=88\),

Hence, \(T_n=a+(n-1)*d=>88=8+(n-1)*20=>n=5\)
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Re: Set M consists of all positive integers that are multiples of 4. Set  [#permalink]

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New post 24 Mar 2018, 19:20
Bunuel wrote:
Set M consists of all positive integers that are multiples of 4. Set N consists of all positive integers less than 100 that have a units digit of 8. How many integers do sets M and N have in common?


(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven


set M consists of all the multiples of 4. on the other hand set N consists of all the digits having 8 as its unit digit.

i think it would be wiser to move on with se N. few numbers. so set N must include: 8 18 28 38 48 58 68 78 88 98. these are the elements of set N.
Now bk to the question. we have to find out common element : 1. multiple of 4 and unit digit 8.

from the listed numbers only : 8 28 48 68 88 are divisible by 4 and have unit digit of 8.

thus, our answer will be C
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Re: Set M consists of all positive integers that are multiples of 4. Set  [#permalink]

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New post 24 Mar 2018, 19:43
Bunuel wrote:
Set M consists of all positive integers that are multiples of 4. Set N consists of all positive integers less than 100 that have a units digit of 8. How many integers do sets M and N have in common?


(A) Three
(B) Four
(C) Five
(D) Six
(E) Seven


there are 10 positive integers <100 with a units digit of 8
half of them are multiples of 4
5
C
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Re: Set M consists of all positive integers that are multiples of 4. Set &nbs [#permalink] 24 Mar 2018, 19:43
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