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If M is the set of positive multiples of 2 less than 150 and N is the set of positive multiples of 9 less than 150, how many members are there in M n N?
- a)0
- b)8
- c)9
- d)18
- e)74
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If M is the set of positive multiples of 2 less than 150 and N is the ...
The only elements in both sets are multiples of 2 x 9 or 18. The multiples of 18 less than 150 are 18, 36, 54, 72, 90, 108, 126 and 144. These are the 8 elements that are in the intersection of both sets. Thus, B is the correct response.
a. (0) There are elements that are in both sets.
b. (8) Correct
c. (9) There are 8 elements in both sets, not 9.
d. (18) This is the number that the elements are multiples of.
e. (74) This is the number of multiples of 2 less than 150
a. (0) There are elements that are in both sets.
b. (8) Correct
c. (9) There are 8 elements in both sets, not 9.
d. (18) This is the number that the elements are multiples of.
e. (74) This is the number of multiples of 2 less than 150
Most Upvoted Answer
If M is the set of positive multiples of 2 less than 150 and N is the ...
Given, M is the set of positive multiples of 2 less than 150 and N is the set of positive multiples of 9 less than 150.
To find the intersection of M and N, we need to find the common multiples of 2 and 9 less than 150.
Method 1: Listing out the multiples of 2 and 9
Multiples of 2 less than 150: 2, 4, 6, 8, 10, 12, ...., 148
Multiples of 9 less than 150: 9, 18, 27, 36, ...., 144
Common multiples of 2 and 9: 18, 36, 54, 72, 90, 108, 126, 144
There are a total of 8 common multiples of 2 and 9 less than 150.
Method 2: Using LCM
The LCM of 2 and 9 is 18.
Multiples of 18 less than 150: 18, 36, 54, 72, 90, 108, 126, 144
There are 8 multiples of 18 less than 150, which are also common multiples of 2 and 9.
Therefore, the answer is option B) 8.
To find the intersection of M and N, we need to find the common multiples of 2 and 9 less than 150.
Method 1: Listing out the multiples of 2 and 9
Multiples of 2 less than 150: 2, 4, 6, 8, 10, 12, ...., 148
Multiples of 9 less than 150: 9, 18, 27, 36, ...., 144
Common multiples of 2 and 9: 18, 36, 54, 72, 90, 108, 126, 144
There are a total of 8 common multiples of 2 and 9 less than 150.
Method 2: Using LCM
The LCM of 2 and 9 is 18.
Multiples of 18 less than 150: 18, 36, 54, 72, 90, 108, 126, 144
There are 8 multiples of 18 less than 150, which are also common multiples of 2 and 9.
Therefore, the answer is option B) 8.
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