Answer
Verified
482.4k+ views
Hint- This question can be solved by writing all composite numbers on the higher side i.e. from $90$ onwards.
In order to write seven consecutive composite numbers between $1$ and $100$ we have to consider the numbers of the higher side in counting because if we take smaller numbers there is more probability of prime numbers.
For example: If we start from first prime number i.e.
$2$ and $3$ are prime numbers followed by $5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$.
When we see these numbers we get, composite numbers
$
4,6,8,9,10,12,14,15,16,18,20,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50, \\
51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90, \\
91,92,93,94,95,96,98,99. \\
$
On seeing these numbers we find that we are not able to get $5$ consecutive composite numbers from $4$ to $88$ . And when we start from $90$ to $96$ we get seven consecutive composite numbers.
Note- Whenever we face such types of questions the key concept is that we have to locate composite numbers in the top series i.e. $90$ onwards . Like we did in this question. We can’t find consecutive seven composite numbers from $4$ to $88$.
In order to write seven consecutive composite numbers between $1$ and $100$ we have to consider the numbers of the higher side in counting because if we take smaller numbers there is more probability of prime numbers.
For example: If we start from first prime number i.e.
$2$ and $3$ are prime numbers followed by $5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97$.
When we see these numbers we get, composite numbers
$
4,6,8,9,10,12,14,15,16,18,20,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50, \\
51,52,54,55,56,57,58,60,62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90, \\
91,92,93,94,95,96,98,99. \\
$
On seeing these numbers we find that we are not able to get $5$ consecutive composite numbers from $4$ to $88$ . And when we start from $90$ to $96$ we get seven consecutive composite numbers.
Note- Whenever we face such types of questions the key concept is that we have to locate composite numbers in the top series i.e. $90$ onwards . Like we did in this question. We can’t find consecutive seven composite numbers from $4$ to $88$.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE