I = V/RThe formula above is Ohm's law for an electric circuit with current I, in amperes, potential difference V,...
GMAT Algebra : (Alg) Questions
\(\mathrm{I = \frac{V}{R}}\)
The formula above is Ohm's law for an electric circuit with current \(\mathrm{I}\), in amperes, potential difference \(\mathrm{V}\), in volts, and resistance \(\mathrm{R}\), in ohms. A circuit has a resistance of \(\mathrm{500}\) ohms, and its potential difference will be generated by \(\mathrm{n}\) six-volt batteries that produce a total potential difference of \(\mathrm{6n}\) volts. If the circuit is to have a current of no more than \(\mathrm{0.25}\) ampere, what is the greatest number, \(\mathrm{n}\), of six-volt batteries that can be used?
1. TRANSLATE the problem information
- Given information:
- Formula: \(\mathrm{I = V/R}\) (Ohm's law)
- Resistance: \(\mathrm{R = 500}\) ohms
- Each battery: 6 volts
- n batteries total: \(\mathrm{V = 6n}\) volts
- Constraint: current \(\mathrm{\leq 0.25}\) ampere
- What we need: Greatest whole number value of n
2. INFER the solution approach
- Since we have Ohm's law and know R, we can express current in terms of n
- The constraint gives us an inequality to solve
- We'll substitute into Ohm's law, then solve the inequality
3. TRANSLATE the constraint into mathematics
- "No more than 0.25 ampere" means \(\mathrm{I \leq 0.25}\)
- Using Ohm's law: \(\mathrm{I = V/R = 6n/500}\)
- Therefore: \(\mathrm{6n/500 \leq 0.25}\)
4. SIMPLIFY the inequality algebraically
- Multiply both sides by 500: \(\mathrm{6n \leq 125}\)
- Divide both sides by 6: \(\mathrm{n \leq 20.833...}\)
5. APPLY CONSTRAINTS to select final answer
- Since n represents number of batteries, it must be a whole number
- The greatest whole number less than or equal to 20.833 is 20
Answer: 20
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students may misinterpret "no more than 0.25 ampere" as an equality (\(\mathrm{I = 0.25}\)) rather than an inequality (\(\mathrm{I \leq 0.25}\)).
When they solve \(\mathrm{6n/500 = 0.25}\), they get exactly \(\mathrm{n = 20.833}\), then might round this to 21 instead of recognizing they need the constraint to be satisfied. This leads to confusion about whether the answer should be 20 or 21.
Second Most Common Error:
Inadequate APPLY CONSTRAINTS reasoning: Students correctly solve the inequality to get \(\mathrm{n \leq 20.833}\) but fail to recognize that n must be a whole number representing actual batteries.
They might give the answer as 20.833 or 20.8, not realizing that you can't use a fraction of a battery in a real circuit.
The Bottom Line:
This problem tests whether students can properly set up and solve an inequality from a word problem constraint, then apply real-world limitations to select the appropriate answer. The key insight is recognizing that "no more than" creates an inequality, not an equation.