eybrj2 wrote:
What is the number of integers that are common to both set S and set T ?
(1) The number of integers in S is 7, and the number of integers in T is 6.
(2) U is the set of integers that are in S only or in T only or in both, and the number of integers in U is 10.
DS41402.01
Let,
\(x\) \(=\) Elements in S only
\(y\) \(=\) Elements in T only
\(z\) \(=\) Elements in both S and T (The question asks us to find the value of \(z\))
Statement - I (Insufficient)1. \(x + z = 7\) and \(y + z = 6\)
2. We cannot solve for \(z\) since the we have \(2\) equations and \(3\) variables
Statement - II (Insufficient)1. \(x + y + z = 10\)
2. Again, we cannot solve for \(z\) since the we have \(1\) equation and \(3\) variables
Combined (Sufficient)1. Add the \(2\) equations from statement-I -> \(x + y + 2z = 13\)
2. From the equation from statement-II we have \(x + y = 10 - z\)
3. Plugging in \(2\) into \(1\) -> \(10 - z + 2z = 13\) -> \(z = 3\)
Ans.
C _________________
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