"A Dealer Originally Bought 100 Identical Batteries at a Total Cost of Q Dollars..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

A dealer originally bought 100 identical batteries at a total cost of $Q$ dollars. If each battery was sold at 50% above the original cost per battery, then, in terms of $Q$, for how many dollars was each battery sold?

(A) $\dfrac{3Q}{200}$

(B) $\dfrac{3Q}{2}$

(C) $150Q$

(D) $\dfrac{Q}{100}$

(E) $\dfrac{150}{Q}$

Try it before reading on.

Step 1: Label What Each Variable Represents

The most common error on this problem isn't the percent math. It's misreading what $Q$ represents. Before touching any numbers, write down:

• $Q$ = total cost of ALL 100 batteries
• 100 = number of batteries
• Asking for: selling price of ONE battery

That third line is where most people go wrong. The question asks for the price per battery, not the total selling price. If you miss that, you'll compute the right math on the wrong quantity.

Reread the problem after writing this down. Three seconds of double-checking catches the translation error before it costs you the question.

Step 2: Find the Original Cost Per Battery

If $Q$ dollars buys 100 batteries, the cost per battery is:

Write that down. Don't skip the step of writing it explicitly — the fraction $\frac{Q}{100}$ is where most of the wrong answers diverge from the right one.

Step 3: Apply the 50% Markup

Each battery is sold at 50% above the original cost per battery. A 50% increase means multiplying by $\frac{150}{100}$:

There are two ways to think about this step. Some people prefer the direct multiplier: $\frac{150}{100}$ means "150% of the original." Others prefer the addition method: take the original cost and add 50% of it:

Both produce the same result. Use whichever feels more natural. The key is that the markup applies to the cost per battery — $\frac{Q}{100}$ — not to $Q$ itself.

Step 4: Simplify the Fraction

Start with:

Cancel a 10 from the first fraction:

Then cancel a 5:

Now multiply across:

The answer is (A).

Why This Problem Matters

About 30% of test takers miss this problem — despite the math being a single percent increase on a fraction. The wrong answer distribution tells the story:

Choosing (B) — $\dfrac{3Q}{2}$: this is the most popular wrong answer, picked by about 14% of test takers. The math is right — a 50% increase gives you $\frac{3}{2}$ — but the $\frac{Q}{100}$ step was skipped. This happens when you think $Q$ is the cost per battery instead of the total cost. The label step (Step 1) prevents this.

Choosing (E) — $\dfrac{150}{Q}$: about 8% pick this. The likely mistake: reversing the given information, thinking there are $Q$ batteries purchased for $100 total. You'd increase 100 by 50% to get 150, then divide by $Q$ for the per-unit cost. The reread catches this — the problem clearly states 100 batteries at a total cost of $Q$ dollars.

Choosing (C) — $150Q$: about 5% pick this. The likely mistake: thinking $Q$ is the cost per battery, marking it up by 50%, then multiplying by 100 units to get total cost. Correct math, wrong interpretation of what's being asked.

Choosing (D) — $\dfrac{Q}{100}$: about 30% pick this. This is the cost per battery with no markup applied. The 50% increase was dropped somewhere between reading the problem and computing the answer. This one is common under time pressure — you read "50%," write it down, then forget to include it by the time you reach the calculation.

Every wrong answer maps to a specific translation error. The percent math itself is rarely the problem. The fix is the label-and-reread system: write what each variable means, write what's being asked, then reread before computing.

Want the full strategy behind this problem? Read: GMAT® Quant: Three Systems for Percent, Integer, and Sequence Problems

From Episode 24 of Real GMAT® Problems (The GMAT® Strategy Podcast).

Ready for the next one? "In an Increasing Sequence of 10 Consecutive Integers..." — GMAT® Worked Solution.