Problem Solving

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!

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!

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

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

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

[Here is a trend of getting (2^a)x - (2^a-1)y flowers after ath Dip]

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

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

x+y = 15 is one of the solutions

Answer: Option [spoiler]B[/spoiler]

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]

I didn't get why x + y be read as n + y here, while the question specifically mentions that Sabina started with x flowers in hands, not n. Although n is mentioned in the beginning just to introduce the nature of pool.

That was a silly reading mistake !!!

However, it doesn't change the answer.

n --> 2n --> 4n --> 8n ....

To find (x+y)

x --> 2x (Left=2x-y, shi=y) --> 4x-2y(Left 4x-3y, nan=y)---> 8x-6y(Left=8x-7y, Rashi=y)

8x-7y = 0
8x = 7y
if x=7 & y=8.. then this equation is possible.
So, 7+8 = 15
{B}