1.

Consider the set A of natural numbers n whose units digit is non-zero, such that if this units digit is erased, then the resulting number divides n. If K is the number of elements in the set A, then(a) K is infinite(b) K is infinite but K > 100(c) 25 ≤ K ≤ 10(d) K < 25

Answer»

Answer is : (d) K < 25

Let two digits number ab = 10a + b, b ≠ 0 if b is erased.

Then, the resulting number is a.

∴ ab is divisible by a if ab is multiple of c.

∴ Such number are 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 24, 26, 28, 33, 36, 39, 44, 48, 55, 66, 77, 88, 99.

∴ Total number are 23.

Hence, K < 25


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