[Shashank Shekha]

Lets assume that she gets a,b,c and d chocolates respectively.
Then total no of swings in each step will be:
1st- a
2nd- a+b
3rd- a+b+c
4th- a+b+c+d

Hence total nos of swings= 4a+3b+2c+d
If we assume that she is given 7 chocolates each time, then minimum nos of times she is given chocolates:
(1+2+3+4+...+n)*7>= 99
Hence n>= 5
Now, according to question:
7x+3y= 99
x+y = (1+2+3+4+...+n) for n>=5 for which the value of x and y will be integer.
For x+y = 21 i.e 1+2+3+4+5+6, we get x= 9 and y= 12.
x=9 is possible in 5 different ways i.e {(6+3),(6+2+1),(5+4),(5+3+1),(4+3+2)}
Hence answer is 5.

[Aarav]

------------------------------------------------------------
Quantitative Question # 3
------------------------------------------------------------ Question:

Let f(x ,y) be a function satisfying f(x ,y)=f(2x + 2y, 2y -2x) for all x , y. Define g(x)=f(2^x , 0). What is the minimum positive integer p if g(x+p)=g(x) for all x?

(a) 4 (b) 6 (c) 8 (d) 12 (e) none of the foregoing

[krsh.vik]

Originally Posted by Aarav

------------------------------------------------------------
Quantitative Question # 3
------------------------------------------------------------ Question:

Let f(x ,y) be a function satisfying f(x ,y)=f(2x + 2y, 2y -2x) for all x , y. Define g(x)=f(2^x , 0). What is the minimum positive integer p if g(x+p)=g(x) for all x?

(a) 4 (b) 6 (c) 8 (d) 12 (e) none of the foregoing

f(4,0)=f(8,-=f(0,-32)=f(-64,-64)=f(-256,0)=f(-512,-512)=f(0,204=
f(4096,4096)=f(2*8192,0)
f(2^2,0)=f(2^14,0)
g(14)=g(2)
Hence p = 12

[Apple]

Answer (d) ..12.... not sure

[_lakshya]

option d) 12
g(x) is periodic with period p ie 12........

[sushane]

answer is d) 12

[innocent_123]

Solved by apple and me.
answer d =12.

f(x,0) = f(2x,-2x)
f(x,x) = f(4x,0)
f(0,x) = f(2x,2x)
------------------

using original and above 3

now f(x,0) = f(2x,-2x) =f(0,-8x) =f(-16x,16x) =f(-64x,0).

similarly f(-64x,0)= f(64*64x,0).

=>f(x,0)=f(2^12*x,0)

[sushane]

f(x,y) = f(2x+2y,2y-2x)
using the same relation again putting x = 2x+2y and y = 2y-2x we get
f(x,y) = f(4x+4y+4y-4x,4y-4x-4x-4y) = f(8y,-8x)
continuing in the same way x = 8y and y = -8x
f(x,y) = f(-64x,-64y)
again
f(x,y) = f(4096x,4096y)
therefore g(x) = f(2^x,0) = f(4096.2^x,0) = f(2^(x+12),0) = g(x+12)

hence p = 12

[vineet.nitd]

So puys, how does it feel after cracking this problem early morning

YOu all are performing beyond expectations , which is gr8 news

[maverickk_7]

We have g(x)=f(2^x , 0) & f(x ,y)=f(2x + 2y, 2y -2x)

Putting y=0 in f(x,y) we get g(x)=f(2^x+1,-(2^x+1))
Similarly g(x+p)=f(2^x+p+1,-(2^x+p+1))-----1

Now f(2^x+1,-(2^x+1))=f(0,-(2^x+3))=f(-(2^x+4),-(2^x+4))=f(-(2^x+6),0)=f(-(2^x+7),2^x+7)=f(0,2^x+9)=f(2^x+10,2^x+10)=f(2^x+1 2,0)=f(2^x+13,-2^(x+13))---2

From eq 1 & 2
We have p=12

Therefore ans is (d)

--Maverickk