P is the set of positive integers, which are divisible by 2 and less

Question

P is the set of positive integers, which are divisible by 2 and less than 200. R be the set of positive integers, which are divisible by 5 and are less than 200. How many subsets of P are also subsets of R?

A. 2^18
B. 2^19 - 1
C. 2^19
D. 2^19 + 1
E. 2^20

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gurmukh · Accepted Answer

P = ( 2, 4 , 6 .... 198)
R = ( 5 , 10, 15, ....195)
Element of P which are also there in R are (10, 20, 30...190)
For subsets each of these have two choices either to take or not to take so total number of subsets of P which are also subsets of R are 2^19
Option C is the answer.

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yashikaaggarwal · Answer

P = {2,4,6..........198}

R = {5,10,15,20...........195}

Elements if subset of P and R = LCM of 2&5 = (10,20,30......190
An = A+(n-1)*d
190 = 10+(n-1)*10
180 = (n-1)*10
18 = n-1
19 = n -----------(1)

How many subsets of P are also subsets of R = Either taking one no. Or not = 2^19

Answer is C

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abhee84 · Answer

Can you please help me understanding in why we need to take 2^19?

ShaikhMoice · Answer

cian12 · Answer

Hello, it's because The number of subsets of a set with n elements is given by: 2^n. here n is the number of commun elements so n 19.

Sriesh · Answer

Hi
Can anyone explain when we include the empty set & full set in our answer? I remember a question where it said a subset does not involve an empty or full set. and hence in this I answered as  2^19 -1

Bunuel · Answer

Empty set is a subset of every set, and the set itself is also a subset of the set. So unless a question explicitly excludes them, both the empty set and the full set should be included when counting subsets. If you can share the link to the specific question you have in mind, I can point out exactly why those were excluded in that case.

Sriesh · Answer

I am not able to find the question, but now I think it mentioned "proper subset", which, on searching, I found is by definition meant to ignore the full set.

So
1) Improper subsets / Subsets -> Everything
2) Proper subset -> Everything - {Fullset}

Does this make sense? Don't want to mark a question wrong because of confusion

Bunuel · Answer

GMAT will not test you on such definitions, so a good GMAT question will clearly define what it wants you to find. Just remember that the subsets of a set include both the empty set and the set itself.

P is the set of positive integers, which are divisible by 2 and less

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P is the set of positive integers, which are divisible by 2 and less

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