
How many two digit numbers are divisible by 2?
Answer
537.6k+ views
1 likes
Hint: In this question use the concept that a two digit number which is divisible by 2 is from 10 to 98 and the series is 10, 12, 14, 16…………………….98. This forms an A.P so use the direct formula for the nth term of an A.P.
Complete step-by-step answer:
As we know all even numbers are divisible by 2.
So the even numbers are (2, 4, 6, 8, 10, 12, 14……………………………..)
Now we have to find out how many two digit numbers are divisible by 2.
So the first two digit number is (10), the second two digit number is (12) and the last two digit number is (98).
So the set of two digit numbers which are divisible by 2 are (10, 12, 14, 16, .... ,98)
Now as we see this set follows the trend of Arithmetic progression (A.P) with first term (a1 = 10) common difference (d) = (12 – 10) = (14 – 12) = 2 and the last term (an) = 98.
So according to the formula of last term of an A.P or nth term of an A.P
Where symbols have their usual meaning and n is the number of terms, so substitute the values in this equation we have,
Now simplify the above equation we have,
Now divide by 2 we have,
So this is the required number of two digit terms which are divisible by 2.
Hence option (C) is correct.
Note: Terms are said to be in A.P if the common difference that is the difference between the two consecutive terms remains constant all throughout the series. Another very frequently used series is that of G.P, in it the common ratio that is the ratio between two consecutive terms remains constant.
Complete step-by-step answer:
As we know all even numbers are divisible by 2.
So the even numbers are (2, 4, 6, 8, 10, 12, 14……………………………..)
Now we have to find out how many two digit numbers are divisible by 2.
So the first two digit number is (10), the second two digit number is (12) and the last two digit number is (98).
So the set of two digit numbers which are divisible by 2 are (10, 12, 14, 16, .... ,98)
Now as we see this set follows the trend of Arithmetic progression (A.P) with first term (a1 = 10) common difference (d) = (12 – 10) = (14 – 12) = 2 and the last term (an) = 98.
So according to the formula of last term of an A.P or nth term of an A.P
Now simplify the above equation we have,
Now divide by 2 we have,
So this is the required number of two digit terms which are divisible by 2.
Hence option (C) is correct.
Note: Terms are said to be in A.P if the common difference that is the difference between the two consecutive terms remains constant all throughout the series. Another very frequently used series is that of G.P, in it the common ratio that is the ratio between two consecutive terms remains constant.
Recently Updated Pages
Master Class 11 Physics: Engaging Questions & Answers for Success

Master Class 11 Chemistry: Engaging Questions & Answers for Success

Master Class 11 Biology: Engaging Questions & Answers for Success

Class 11 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Trending doubts
Difference Between Prokaryotic Cells and Eukaryotic Cells

1 ton equals to A 100 kg B 1000 kg C 10 kg D 10000 class 11 physics CBSE

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE

Give two reasons to justify a Water at room temperature class 11 chemistry CBSE
