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A two-digit number \(\overline{ab}\) is called almost prime if one obtains a two-digit prime number by changing at most one of its digits a and b. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is
(a) 56
(b) 75
(c) 87
(d) 90
A two-digit number \(\overline{ab}\) is called almost prime if one obtains a two-digit prime number by changing at most one of its digits a and b. (For example, 18 is an almost prime number because 13 is a prime number). Then the number of almost prime two-digit numbers is
(a) 56
(b) 75
(c) 87
(d) 90
Answer is : (d) 90
Since in the group of first 10 two digit number 10-19, has atleast 1 prime number similarly in other groups of 10 two digits numbers
20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89 and 90-99 have almost 1 prime numbers.
So, the number of almost prime two-digit number is 90.