"If Candy Bars That Regularly Sell for 40 Cents Each Are on Sale at Two for 75 Cents..." — GMAT® Worked Solution

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

If candy bars that regularly sell for 40 cents each are on sale at two for 75 cents, what is the percent reduction in the price of two such candy bars purchased at their sale price?

(A) $2\dfrac{1}{2}\%$

(B) $6\dfrac{1}{4}\%$

(C) $6\dfrac{2}{3}\%$

(D) $8\%$

(E) $12\dfrac{1}{2}\%$

Try it before reading on.

Step 1: Write What's Given and What's Asked

Before plugging anything into a formula, write down the information clearly.

Given:

• Regular price: $0.40 per candy bar
• Sale price: 2 for $0.75

Asked: Percent reduction in the price of TWO candy bars at the sale price.

The question asks about two candy bars, not one. This is the most important detail in the problem, and it's easy to miss under time pressure.

Step 2: Identify Old and New Values

The percent change formula requires an old value and a new value:

$\frac{\text{new} - \text{old}}{\text{old}} \times 100 = \text{percent change}$

The old value is the price before the change, and the new value is the price after.

• Old value (regular price for 2 candy bars): 2 × $0.40 = $0.80
• New value (sale price for 2 candy bars): $0.75

The old value is the regular price for two bars, not one. Doubling the regular price is the step that most people miss.

Step 3: Plug Into the Formula

$\frac{0.75 - 0.80}{0.80} \times 100$

$\frac{-0.05}{0.80} \times 100$

Step 4: Simplify the Fraction

Decimals inside a fraction are error-prone, so multiply the top and bottom by 100 to clear them:

$\frac{-5}{80} \times 100$

Write 100 as $\dfrac{100}{1}$ to make the cross-canceling easier to see:

$\frac{-5}{80} \times \frac{100}{1}$

Cross-cancel a 10 from 80 and 100:

$\frac{-5}{8} \times \frac{10}{1}$

Cross-cancel a 2 from 8 and 10:

$\frac{-5}{4} \times \frac{5}{1} = \frac{-25}{4}$

Step 5: Convert to a Mixed Number

$\frac{-25}{4} = -6.25 = -6\dfrac{1}{4}\%$

The negative sign indicates a decrease. Since the problem asks for a "reduction," the answer is expressed as a positive percentage:

$6\dfrac{1}{4}\%$

The answer is (B).

Why This Problem Matters

About 23% of test takers miss this problem. Two wrong answers account for most of the misses, and each one reveals a different setup error.

Answer (C): $6\dfrac{2}{3}\%$. This is what you get if you swap the old and new values in the formula. Instead of $\dfrac{0.75 - 0.80}{0.80}$, you compute $\dfrac{0.80 - 0.75}{0.75} = \dfrac{5}{75} = \dfrac{1}{15} \approx 6\dfrac{2}{3}\%$. The math is correct, but the values are reversed. The sale price is the new value because it's the result of the discount. The regular price is the old value because it's what the price was before the change.

Answer (E): $12\dfrac{1}{2}\%$. This is what you get if you compute the percent change for one candy bar instead of two. The discount is 5 cents per bar, and the old price of one bar is 40 cents, so $\dfrac{5}{40} = 12.5\%$. The formula is right, but the quantity is wrong. The problem asks about two bars, not one.

Both errors produce answers that match wrong answer choices, which is why the GMAT® includes those choices. The test is designed to reward correct setup, not just correct computation. A quick double-check of two things, whether you're increasing or decreasing, and whether you're computing for the right quantity, catches both errors before they cost you points.

Want the full strategy behind this problem? Read: GMAT® Quant: Three Systems for Exponents, Primes, and Percent Change

From Episode 27 of Real GMAT® Problems (The GMAT® Strategy Podcast).