Mbawarrior01 wrote:
A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly x new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?
(A) 5^1/12
(B) 3^11 * 5^11
(C) 3^12 * 5^12
(D) 3^11 * 5^12
(E) 60^12
I found it difficult and tricky.
Started with previous week= m,
first week= m+5,
second week = m+5+5x, then got stuck.
It is a very tricky question. Though it seems easy in the first instance but when we start solving it, the question gets tougher because of the unknown x. The questions asks which of the options could be y. That means we will have to somehow eliminate the options apart from correct one.
So. Lets start solving
The number of members added at the end of 1st week = 5
Total members = m+5 ( Let me be the members during the start of 1st week)
New members = 5
There on after at the end of each week, no. of members added = x times the new members last week.
2nd week : total members = m + 5 + 5x ; New members = 5x
3rd week : total members = m+ 5+5x + 5x^2 ; New members = 5X^2
..
..
12th week : Total members = m + 5+ 5x+ 5x^2 +..... +5x^11 ; New members = 5x^11.
Now as explained above we will have to check option for integral value of x (As x is an integer.)
Option 1 : 5^1/12 = 5 X^11 => x^11 = 5^(1/12 -1)= 5^(-11/12) (x is not an integer)
Option 2 : 3^11 * 5^11 = 5 X^11 => 3^11 *5^10 = x^11 (x is not an integer)
Option 3 : 3^12 * 5^12 = 5 X^11 => 3^12 * 5^11 = x^11 (x is not an integer)
Option 4 : 3^11 * 5^12 = 5 x^11 => 3^11 * 5^11 = x^11 => x = 15 (x is an integer)Option 5 : 60^12 = 5 X^11 => 12 * 60^12 = x^11 (x is not an integer)
So Option D gives us an integral value of X
Answer D