Grace makes an initial deposit of x dollars into a savings a

B.

B is sufficient due to the constraints in the problem. Since no number can be greater than 50 and Z is the same for both.

100y =zx

Basically says that X is larger than Y. The differences between annual and quarterly compounding of an identical interest rate over only one year will be fairly negligible. Assuming Z = 50 which is the most it can equal we are left with 2y = x. So we know that Grace is going to have more money than Georgia at the end of year 1.

Statement 2 is sufficient.

Hope that helps.

Responding to a pm:

Actually, u0422811's solution is perfect. That is exactly what went through my mind when I read this question.
Quarterly compounding yields more than annual compounding but the difference is minuscule in % terms.
e.g. if you invest $10 at 10% annual compounding, you get $11 at the end of the year.
but if you invest $10 at 10% quarterly compounding, you get $11.038 at the end of the year.
You get a small fraction of interest extra.

So x is invested at annual compounding and y at quarterly compounding. If x=y, the amount received from y will be a little more.

Statement 1 tells us z = 4. We need to compare x with y so this is not sufficient.

Statement 2 tells us 100y = zx
x/y = 100/z
Since maximum value of z is 50, x is at least twice of y.
If z% = 50%, amount obtained from x is 1.5x (= 3y) and that obtained from y is a little more than 1.5y.
Definitely an investment of $x results in a higher amount at the end of the year.

Answer (B)
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Hi Karishma,

taking B into consideration, we can have x=2, y=1, z=50.

so X after one year will be 3.

Y after one year and 4 interest bumps will be over 3....

Can you explain this?

How did you get that "Y after one year and 4 interest bumps will be over 3"?

If initial investment is $1 with an annual rate of 50% compounded quarterly, at the end of the year, the amount is 1(1 + 50/400)^4 = 1.608 i.e. somewhat above 1.5. How is it 3? Note that 50% is annual rate. If it is compounded quarterly, the quarterly rate becomes 50/4%
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look at choice 2
grace=x(1+Z/10)
Georga= y( 1+z/100*4)^4

from 2 we have, y=zx/100, plug this into condition 2.

Geogra= zx/100(1+z/100*4)^4
it is clear that this expression is smaller than x(1+z/100) even if z=50

One doubt : If we are assuming that z=50, for Statement 2, why can't we assume the same for Statement 1 :

I mean, at the final stage we need to compare "x" with "y", since given that "x", "y" and "z" are positive numbers no greater than 50, why can't "x" = "y" = 50?

(Even though Statement 1 doesn't tell us about "x" or "y", we can assume right? Just as we assume for "z" in Statement 2)

If we substitute as above, we find "y" > "x".

So either Statement "1" or Statement "2" is sufficient right?

Kindly enlighten me.

What I did was:
A) clearly not sufficient because we don't know X and Y, what if X is 49 and Y is 1 or vice versa? Interest rates won't make a difference;

B) 100y=zx, y=zx/100, which means y principal amount equals to the interests of z;
and since z<50, then the interest of y, which is <y*50%, is definitely less than y,
therefore the interest of y is definitely is less than the interest of z

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