Sabina took first dip

sanju09 wrote:An enchanted pool is such that if someone takes a dip into it with n flowers in hands, it becomes 2n flowers. Sabina took first dip into the pool with x flowers in her hands and given away y of the resulting number of flowers to Shivangi. She then took a second dip into the pool with the remaining flowers in her hands and again given away y of the resulting number of flowers to Nandini. She ultimately took a third dip into the pool with the remaining flowers in her hands and once again she given away y number of flowers to Rashika with no flower left in her hands. Which of the following is a possible value of x + y?
A. 12
B. 15
C. 18
D. 21
E. 24


Made Up!

GMATinsight wrote:

sanju09 wrote:An enchanted pool is such that if someone takes a dip into it with n flowers in hands, it becomes 2n flowers. Sabina took first dip into the pool with x flowers in her hands and given away y of the resulting number of flowers to Shivangi. She then took a second dip into the pool with the remaining flowers in her hands and again given away y of the resulting number of flowers to Nandini. She ultimately took a third dip into the pool with the remaining flowers in her hands and once again she given away y number of flowers to Rashika with no flower left in her hands. Which of the following is a possible value of n WHY? + y?
A. 12
B. 15
C. 18
D. 21
E. 24


Made Up!

x+y in question should be read as n+y

After First Dip in Pool:
Initial No. of Flowers in Hand = n, Flowers after Dip = 2n, Remaining after giving y flowers = 2n-y

After Second Dip in Pool:
Initial No. of Flowers in Hand = 2n-y, Flowers after Dip = 4n-2y, Remaining after giving y flowers = 4n-3y

After Third Dip in Pool:
Initial No. of Flowers in Hand = 4n-3y, Flowers after Dip = 8n-6y, Remaining after giving y flowers = 8n-7y

[Here is a trend o getting (2^x)n - (2^x-1)y flowers after xth Dip]

After Third Dip No. of Flowers = 0 = 8n-7y

i.e. 8n=7y
i.e. n=7 and y=8 is the first Integer Solution

n+y = 15 is one of the solutions

Answer: Option [spoiler]B[/spoiler]