Can guessing works here?

Set A A has 10 10 more elements than set B B . The two sets have 7 7 elements in common, and the total number of unique elements across both sets is 85. 85.

How many elements set A A have?

49 45 35 40 51

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1 solution

Hana Wehbi
Jun 24, 2017

A B = A + B A B |A \cup B| = |A|+ |B| - |A \cap B| .

Since A A consists of 10 10 more elements than set B B , then B = A 10 |B|= |A|-10 .

Since 7 7 elements are in common to both A A and B B , then A B = 7 |A \cap B|= 7 .

Since A A and B B have 85 85 unique elements A B = 85 \implies |A \cup B| = 85 .

A B = A + B A B |A\cup B| = |A |+| B |- |A \cap B|

85 = A + A 10 7 102 = 2 A A = 51 85 =| A |+ |A | -10 -7\implies 102 = 2|A| \implies |A|= 51 .

Set A A has 51 51 elements.

Note: S = |S|= number of elements in a set S S .

The first line of the solution already makes me scared about the solution

Mohammad Farhat - 2 years, 9 months ago

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I will try next time to make it simpler, no problem.

Hana Wehbi - 2 years, 9 months ago

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I look forward to it

Mohammad Farhat - 2 years, 9 months ago

I think I understand the solution

Mohammad Farhat - 2 years, 9 months ago

Hi. I'm slightly unsure about the solution. To get the total number of elements, shouldn't we add 14 instead of 7 to 85?

85 is the total number of unique elements. And each set has 7 more elements (albeit same). Hence |A| + |B| = 99.

Hence shouldn't the answer be none of the above?

Rahul Singh - 2 years, 4 months ago

The solution is correct.

Hana Wehbi - 2 years, 4 months ago

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