How many integers between \[10\] and \[500\] begin and end in \[3\]? A). \[11\] B). \[12\] C). \[10\] D). \[13\] E). \[9\]
Hint: Here, in the given question, we are asked to find the number of integers between \[10\] and \[500\] that begin with \[3\] and end with \[3\]. First of all, we will understand about the integers, what the definition says and then accordingly calculate the required number of integers to get the final answer.
Complete step-by-step solution: Integers: Integers are all the real numbers but not the fractional ones. In simple words, integers include all the natural numbers, negatives of natural numbers and zero but no fraction allowed. Here, in the given question, we will take into consideration only the positive integers as there is no negative integer between \[10\] and \[500\]. Now, let us calculate the number of integers between \[10\] and \[500\] such that the number begins and ends with \[3\]. If we observe two digits, there is only \[1\] integer that fulfills the required condition and that integer is \[33\] only. And, if we observe three-digit numbers fulfilling the given condition, there are \[10\] integers in total. Starting from \[303\], if we change the tens unit from \[0\] to \[9\], we have \[10\] integers till \[393\]. Therefore, total integers between \[10\] and \[500\] begin and end in \[3\] = \[10 + 1\] \[ = 11\] Hence the option A. \[11\] is the correct option.
Note: In such types of questions, there is no need to apply any formula or anything. It is just the observation that we need to do to count all the required numbers. We may skip \[33\] in a hurry in the given question and mark the final answer as \[10\] which will be a wrong answer.