GMATBaumgartner wrote:
Pamela and Joe invested some money at annual simple interest rates of 6% and 7% respectively. At the end of 2 years they found that together they received a sum of $354 as interest. Find the total money invested by them.
(1) One fourth of Pamela’s initial investment is equal to one-fifth of the money invested by Joe.
(2) Joe invested $300 more than the sum invested by Pamela.
Given: Pamela and Joe invested some money at annual simple interest rates of 6% and 7% respectively. At the end of 2 years they found that together they received a sum of $354 as interest. Let P = the amount of money Pamela invested
Let J = the amount of money Joe investedWhen it comes to simple interest, we have:
Interest earned = (annual interest rate)(number of years)(principle)So, Pamela's interest = (6%)(2)(P) = (0.06)(2)(P) =
0.12PAnd Joe's interest = (7%)(2)(J) = (0.07)(2)(J) =
0.14JWe can now write:
0.12P + 0.14J = 354Target question: What is the value of P + J Statement 1: One fourth of Pamela’s initial investment is equal to one-fifth of the money invested by Joe. We can write: (1/4)P = (1/5)J, which is the same as
0.25P = 0.2J, which means we now have the following system of equations:
0.12P + 0.14J = 3540.25P = 0.2JSince we have a system of two different linear equations with two variables, we COULD solve the system for P and J, which means we COULD determine
the value of P + J - although we would never waste valuable time on test day actually solving the systemSince we could answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: Joe invested $300 more than the sum invested by Pamela.We can write:
J = P + 300, which means we now have the following system of equations:
0.12P + 0.14J = 354J = P + 300Once again, we could solve this system for P and J, which means we COULD determine
the value of P + JSince we could answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
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