Tip:A–D to answerE for explanationV for videoS to reveal answer
The number of elements in the set {n∈N:10≤n≤100 and 3n−3 is a multiple of 7} is ________.
- A.
15
(Correct Answer) - B.
23
- C.
24
- D.
25
Explanation
Given that
{n∈N:10≤n≤100 and 3n−3 is a multiple of 7}
⇒3n−3=7k,k∈I,n∈N,n∈[10,100]
⇒n=1,7,13,20,…,97 which is an A.P.
Now,
but
Hence, number of possible values of n are 15.
Explanation
Given that
{n∈N:10≤n≤100 and 3n−3 is a multiple of 7}
⇒3n−3=7k,k∈I,n∈N,n∈[10,100]
⇒n=1,7,13,20,…,97 which is an A.P.
Now,
but
Hence, number of possible values of n are 15.
