$1$.How many proper subset of $\{1,2,3,4,5,6,7\}$ contain the numbers $1$ and $7$ ?
Lets consider $\{1,7\}$ as a single element then the number of possible subset is $2^6$ and hence the number of proper subset is $62$.
$2$. A survey show that $63$% of the Americans like cheese where as $73$% like apples.If $x$% of Americans like both cheese and apples, then we have :
(A) $x \ge 39 $ (B) $x \le 63 $ (C) $39 \le x \le 63 $ (D) None of these
if $a$% and $b$% like only cheese and only apples then we have, $ a + x + x + b = 100 $ , $ a + x = 63 $ and $ b + x = 63 $ solving we get $x = 39%$. So (D) is my answer.
Am I correct?