$5000 is invested in one account that pays x percent simple interest p

Question

$5000 is invested in one account that pays x percent simple interest per year, and $6000 is invested in a different account that pays y percent simple interest per year. If the amount of money in each account is equal after one year, what is the value of x?

(1) x − y = 22

(2) If $6000 had been invested at x percent simple interest, and $5000 had been invested at y percent simple interest, after one year one account would have contained $2420 more than the other

ThatDudeKnows · Answer

Translating the question stem gives us 5000(1+x)=6000(1+y) and asks for the value of x. We can't cancel out y from the given equation, so we need to derive a second (non-equivalent equation) so we can set up simultaneous equations and solve for x. Note that we converted from x% and y% to both in decimal form. Just in case we need it later, let's simplify the given equation as follows.
5000+5000x=6000+6000y
5+5x=6+6y
5x=6y+1
x=1.2y+0.2

Evaluating statement (1) alone:
x-y=0.22 (again converting both to decimal form)
That's a second equation that is non-equivalent to the first. We COULD solve the simultaneous equations, but we don't need to for Data Sufficiency!
Does statement (1) alone give us enough information to find the value of x? Yes. AD

Evaluating statement (2) alone:
This one is a little tricky. The statement provides us two options:
A) 6000(1+x)=5000(1+y)+2420
B) 6000(1+x)+2420=5000(1+y)

Both of those may LOOK like they'd work as simultaneous equations with the equation that we already have from the question stem, but B would result in negative values for x and y and the question is about earning simple interest, so x and y must be positive. That means B doesn't apply and we are left with only the equation from the question stem and A. Those are non-equivalent simultaneous equations, so we can solve for both variables...but we don't need to actually do it.
Does statement (2) alone give us enough information to find the value of x? Yes. D

Answer choice D.

GMATGuruNY · Answer

The $5000 account begins $1000 behind the $6000 account.
Implication:
For the two accounts to end with the same amount, the interest earned by the $5000 investment must be $1000 greater than the interest earned by the $6000 investment:
 \frac{x}{100} * 5000 = \frac{y}{100} * 6000 + 1000 
 50x = 60y + 1000 
 5x = 6y + 100 
Note:
The resulting equation implies that x > y.

Statement 1: 
Since we have two variables (x and y) and two distinct linear equations (5x=6y+100 and x-y=22), we can solve for the two variables.
Thus, the value of x can be determined.
SUFFICIENT.

Statement 2:
Since the prompt requires that x>y, the percentage applied here to the $5000 investment (y) is less than the percentage applied to the $6000 investment (x).
Implication:
It is not possible for the $5000 account to surpass the $6000 account by $2420.
The resulting amount for the $6000 investment must thus be $2420 greater than the resulting amount for the $5000 investment.

Since the $6000 investment begins $1000 ahead of the $5000 investment, a difference of $2420 will be yielded if the interest earned by the $6000 investment is $1420 greater than the interest earned by the $5000 investment:
 \frac{x}{100} * 6000 = \frac{y}{100} * 5000 + 1420 
 60x = 50y + 1420 
 6x = 5y + 142

Since we have two variables (x and y) and two distinct linear equations (5x=6y+100 and 6x=5y+142), we can solve for the two variables.
Thus, the value of x can be determined.
SUFFICIENT.

D

SkyBulb · Answer

Hi, is it always a case that simple interest is positive in gmat?

Bunuel · Answer

If an account “ pays  x percent simple interest,” x is normally understood to be a positive interest rate unless the problem explicitly indicates otherwise.

So you should not consider negative interest rates in a typical GMAT interest problem unless the wording gives you a reason to do so.

$5000 is invested in one account that pays x percent simple interest p

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