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Kate invested x dollars, where x ≥ 1,000, for one year in a new account that earned interest at an annual rate of r percent, compounded semiannually. Bob invested y dollars for one year in a new account that earned interest at an annual rate of 5 percent, compounded annually. If there were no other transactions to these accounts and if the sum consisting of the amount invested and the interest earned for the year was the same for both accounts, what was the value of r?
(1) y = 1.05x
(2) y = x + 100
GMAT-Club-Forum-g37xhtej.png [ 192.86 KiB | Viewed 4689 times ]
(1) y = 1.05x
(2) y = x + 100
Attachment:
GMAT-Club-Forum-g37xhtej.png [ 192.86 KiB | Viewed 4689 times ]
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24 Mar 2024, 06:23
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Bunuel
The value of Katie's investment after one year = \(x(1+\frac{r}{200})^2\)
The value of Bob's investment after one year = \(y(1+\frac{5}{100})\)
if the sum consisting of the amount invested and the interest earned for the year was the same for both accounts
\(x(1+\frac{r}{200})^2 = y(1+\frac{5}{100})\)
Statement 1
(1) y = 1.05x
\(x(1+\frac{r}{200})^2 = 1.05x(1+\frac{5}{100})\)
As \(x \neq 0\), we can divide both sides of the equation by x
\((1+\frac{r}{200})^2 = 1.05(1+\frac{5}{100})\)
We have one unknown, in the equation. Hence, we can solve the equation to obtain the value of \(r\).
The statement alone is sufficient and we can eliminate B, C, and E.
Statement 2
(2) y = x + 100
\(x(1+\frac{r}{200})^2 = (x+100)(1+\frac{5}{100})\)
We have two unknown variables in the equation \(x\) and \(r\). Hence, we can't find a unique value of \(r\) from this equation alone.
The statement alone is not sufficient to obtain the value of \(r\). Eliminate D.
Option A
Attachment:
GMAT-Club-Forum-4lbudj7m.png [ 192.86 KiB | Viewed 4645 times ]
General Discussion
29 Mar 2025, 14:18
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gmatophobia
After evaluating Statement 1, we are left with the quadratic equation with just one variable "r". However, how do we know, without solving, that the solution of "r" will not be two positive figures, which situation will imply that Statement 1 is not sufficient?
After evaluating Statement 1, we are left with the quadratic equation with just one variable "r". However, how do we know, without solving, that the solution of "r" will not be two positive figures, which situation will imply that Statement 1 is not sufficient?
