Q.5 Find the missing number from the below options.
17 22
37
23
28
43
16 ? 36
Answers
Answer:
We are given that X and Y are two integers; both X and Y are greater than 1, X does not equal Y; and X+Y is less than 100. Foo and Bar are two talented course-18 undergrads. Foo is given the sum, and Bar is given the product of these numbers:
Bar says, "I cannot find the numbers."
Foo says, "I was sure that you could not find them."
Bar says, "Then, I found the numbers."
Foo says, "If you could find them, then I also found them."
What are the numbers?
We'll need a list of the prime numbers under 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97
From Bar's first statement, we can assume that X*Y cannot be prime, since both X and Y are greater than 1. Nor can it be the square of a prime, since X is not equal to Y. If X*Y had exactly two proper divisors, then Bar would know the answer, so this eliminates the product of two distinct primes.
From Foo's first statement, we know that X+Y cannot be the sum of two distinct primes. The prime sums under 100 are:
2+2=4, 2+3=5, 2+5=7, 2+7=9, 2+11=13, 2+13=15, 2+17=19, 2+19=21, 2+23=25, 2+29=31, 2+31=33, 2+37=39, 2+41=43, 2+43=45, 2+47=49, 2+53=55, 2+59=61, 2+61=63, 2+67=69, 2+71=73, 2+73=75, 2+79=81, 2+83=85, 2+89=91, 2+97=99, 3+2=5, 3+3=6, 3+5=8, 3+7=10, 3+11=14, 3+13=16, 3+17=20, 3+19=22, 3+23=26, 3+29=32, 3+31=34, 3+37=40, 3+41=44, 3+43=46, 3+47=50, 3+53=56, 3+59=62, 3+61=64, 3+67=70, 3+71=74, 3+73=76, 3+79=82, 3+83=86, 3+89=92, 5+2=7, 5+3=8, 5+5=10, 5+7=12, 5+11=16, 5+13=18, 5+17=22, 5+19=24, 5+23=28, 5+29=34, 5+31=36, 5+37=42, 5+41=46, 5+43=48, 5+47=52, 5+53=58, 5+59=64, 5+61=66, 5+67=72, 5+71=76, 5+73=78, 5+79=84, 5+83=88, 5+89=94, 7+2=9, 7+3=10, 7+5=12, 7+7=14, 7+11=18, 7+13=20, 7+17=24, 7+19=26, 7+23=30, 7+29=36, 7+31=38, 7+37=44, 7+41=48, 7+43=50, 7+47=54, 7+53=60, 7+59=66, 7+61=68, 7+67=74, 7+71=78, 7+73=80, 7+79=86, 7+83=90, 7+89=96, 11+2=13, 11+3=14, 11+5=16, 11+7=18, 11+11=22, 11+13=24, 11+17=28, 11+19=30
Step-by-step explanation:
use the formula of A.P.