nikhilsrl wrote:A bag of coins contains only nickels, dimes and quarters. There are 38 coins in all. What is the total value of all the coins in the bag?
1. Quarters account for half the value of the coins in the bag.
2. The value of all the dimes equals the value of all the nickels.
This is a Kaplan GMAT Premier question (Pg 476, Qn 38). I did not understand the solution provided. Any help really appreciated.[/list]
Let n = nickels, d= dimes, q = quarters.
What is value of 5n + 10d + 25q?
Generally, to solve for
n variables, we need
n different linear equations. Since in this problem we have 3 variables, 3 different linear equations will allow us to solve for each variable. The question stem tells us that n + d + q = 38. Given this equation, 2 more linear equations will give us sufficient information to solve for each variable.
Statement 1:
The value of all the quarters = the value of all the nickels and dimes.
Thus, 25q = 5n + 10d.
Statement 1 gives us a 2nd linear equation, but we need a 3rd in order to solve.
Insufficient.
Statement 2:
The value of all the dimes = the value of all the nickels.
Thus, 10d = 5n.
Statement 2 gives us a 2nd linear equation, but we need a 3rd in order to solve.
Insufficient.
Statements 1 and 2:
3 variables, 3 different linear equations.
Sufficient.
The correct answer is
C.
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