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There are 193 items that are members of set U. Of these items, 49 are 04 Dec 2019, 01:11
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35% (medium)

Question Stats:

74% (02:00) correct 26% (02:26) wrong based on 486 sessions

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There are 193 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?

(A) 72
(B) 85
(C) 94
(D) 98
(E) 108


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rajatchopra1994
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There are 193 items that are members of set U. Of these items, 49 are 04 Dec 2019, 01:25
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Bunuel
There are 193 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?

(A) 72
(B) 85
(C) 94
(D) 98
(E) 108


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Explanation:

Easy Question.
Total members of SET U = 193
Neither in SET A or SET B Members = 59
Left Member which are in either A or B or Both= 193-59 = 134
Total member in SET B = 49
In A&B= 23
In Set B only = 49-23 = 26
In Set A = 134-26 = 108
IMO-E

:please Please give kudos, if you find my explanation good enough :please
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There are 193 items that are members of set U. Of these items, 49 are 04 Dec 2019, 01:37
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2x2 matrix

---A---NA-- total U
B--23--26----49
NB--85--59----144
tota;--108--85--193
IMO E; 108


Bunuel
There are 193 items that are members of set U. Of these items, 49 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?

(A) 72
(B) 85
(C) 94
(D) 98
(E) 108


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There are 193 items that are members of set U. Of these items, 49 are 10 Sep 2026, 00:40
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193= 59 + 49 -23 + U&A Only; => U&A Only= 193-108 +23
U&A only= 108
therefore u and A and also B = 131 why are we calculating U&A but not including the B that might be inn the A?
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There are 193 items that are members of set U. Of these items, 49 are 10 Sep 2026, 11:34
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Hi!

I find an overlapping sets table to be a helpful way of understanding this problem. Based on the given information, we can set up this starting table. Note that everything in the table is a member of the larger set U, so the Totals Row and Totals Column should each add up to 193. I’ve highlighted our target: the total members of A, including those that overlap with B and those that don’t.



Next, we subtract the number in B from the total to find the number who are not in B, 144.


Then, we can subtract 144 - 59 to find the number who are in A, but not B, which is 85.


We can then add all the members of A, including those who are in B and those who are not, to get the total for group A, 108.






For more practice problems and teacher-written explanations, check out ManhattanPrep’s Free Starter Kit and QBank..
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