Question

One week, you tell two of your friends a secret. The next week, each of them tell two people the secret, and the next week, each of those people tell two more people. So the first week, two new people know the secret; the second week, four new people know the secret; the third week, eight new people know the secret, etc. How many people find out the secret on the sixth week?

A. 32
B. 64
C. 128
D. 256

Answer 1

B. 64 people.

Explanation:

Each week the number who know the secret doubles so in the 4th week 8*2 = 16 ( = 2^4) new people know.

The number who find it out in the 6th week is 2^6 = 64 people.

Answer 2

B. 64

Explanation:

The trick here is to recognize that the number of new people who learn this information each week is in powers of 2.

Week 0: 2^0 = 1

Week 1: 2^1 = 2

Week 2: 2^2 = 4 (2*2)

Week 3: 2^3 = 8 (2*2*2)

So following this pattern, we can just plug in 6 for week 6 and see what our answer is:

Week 6: 2^6 = 64 (2*2*2*2*2*2)

* A quick note in calculating powers:

calculating 2*2 six times is a lot of work. You know what isn't? 2*2*2 (8). You know what also isn't? 8*8. That's right, 8*8 is also 64! So instead of calculating 2*2*2*2*2*2, you can just calculate 2^3*2^3, or 8*8. :)