The question
A milk vendor mixes water with milk and sells the mixture at the same price per liter as if it were undiluted milk. The selling price per liter of the mixture is the vendor's cost per liter of the milk plus a markup of x%. The water costs the vendor nothing. If the vendor gets a 50% profit on the sale of the mixture, what is the value of x?
(1) If the vendor mixes half the intended quantity of water and sells every liter of the mixture at the cost price per liter of the undiluted milk, the vendor will get a 10% profit.
(2) The concentration of milk in the mixture after adding water is 5/6.
The Data Sufficiency answer choices
Every GMAT Data Sufficiency question uses the same five fixed choices. Memorize them so you never reread them on test day:
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER alone is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
The fast answer
The correct answer is D. The 50% profit condition collapses to one clean equation, (1 + r)(1 + x/100) = 1.5, where r is the water-to-milk ratio. So the only thing you need to nail down x is r. Statement (1) hands you r = 0.20 through a second profit scenario, and statement (2) hands you the same r = 0.20 through the milk concentration. Each statement alone fixes the ratio, so each alone gives x = 25%. The rest of this guide shows exactly why.
Step by step
Step 1: Name the quantities and write the profit equation
Data Sufficiency rewards clean notation. Let:
- C = the vendor's cost per liter of pure milk
- m = x/100, the markup as a decimal
- M = liters of milk in the batch
- W = liters of water added
- r = W / M, the water-to-milk ratio
The selling price per liter of the mixture is the milk cost per liter plus the markup, so SP per liter = C(1 + m). Because the vendor sells the whole mixture, the volume sold is M + W liters and revenue is:
Revenue = (M + W) × C(1 + m).
The key insight: water is free, so the only money the vendor spent is on the milk. Total cost = M × C. A 50% profit means revenue is 1.5 times cost:
(M + W) × C(1 + m) = 1.5 × (M × C).
Step 2: Collapse it to the ratio
Divide both sides by M × C. The cost per liter C cancels completely — prices never matter here — and M + W over M becomes 1 + r:
(1 + r)(1 + m) = 1.5.
This is the engine of the whole problem. The question asks for x = 100m, and this equation says m is pinned down the instant you know r. So the real question is no longer "what is x?" — it is "do we know the water-to-milk ratio r?" Each statement is just a different way of delivering r.
Step 3: Test statement (1)
Statement (1) describes a second, hypothetical scenario: use half the intended water (ratio r/2) and sell every liter at the plain milk cost C — that is, with no markup. Now the selling price per liter is just C, the volume is M + W/2 = M(1 + r/2), and the cost is still M × C (water is free). The profit in this scenario:
Profit = Revenue / Cost − 1 = [M(1 + r/2) × C] / (M × C) − 1 = (1 + r/2) − 1 = r/2.
We are told this profit is 10%, so:
r/2 = 0.10 ⟹ r = 0.20.
Now feed r = 0.20 into the master equation: (1.20)(1 + m) = 1.5, so 1 + m = 1.25, m = 0.25, and x = 25. Statement (1) is sufficient.
Step 4: Test statement (2)
Statement (2) says the concentration of milk in the mixture is 5/6 — that is, milk volume over total volume:
M / (M + W) = 5/6 ⟹ 6M = 5M + 5W ⟹ M = 5W ⟹ W / M = 1/5 = 0.20.
That is the very ratio the master equation needs: r = 0.20. Plug it in: (1.20)(1 + m) = 1.5, so m = 0.25 and x = 25. Statement (2) is sufficient.
Step 5: Choose the answer
Both statements alone deliver r = 0.20 and therefore x = 25. When each statement is independently sufficient, the Data Sufficiency answer is D — and notice both routes agree on the same number, which is the built-in consistency check the GMAT designers planted.
Statement (1): sufficient (x = 25). Statement (2): sufficient (x = 25). → Answer: D.
The GMAT theory behind the problem
This question is not really about milk. It is a profit-and-mixtures problem testing three ideas at once.
A free ingredient lowers the true cost per liter
Because water costs nothing, the batch's total cost stays at MC even as the volume sold rises to M + W. The vendor's real cost per liter of mixture is MC / (M + W) = C / (1 + r), which is below the milk price C. Selling at the milk price plus a markup stacks two profit sources on top of each other: the dilution and the markup. That is why a modest 25% markup can produce a 50% profit.
Profit depends on the ratio, not the prices or volumes
The cost per liter C and the absolute number of liters M both cancel when you divide revenue by cost. Everything reduces to the dimensionless ratio r = W/M. Whenever a GMAT profit or mixture problem looks like it is missing numbers, check whether the unknowns cancel — Data Sufficiency questions are frequently "sufficient" precisely because the messy quantities never survive the algebra.
Two statements, one hidden variable
Statements (1) and (2) look completely different — one is a what-if profit scenario, the other a concentration fraction — yet both exist only to deliver r. Spotting that the question has a single hidden variable (the ratio) is what lets you evaluate each statement in seconds instead of grinding through full profit calculations twice.
How to avoid the GMAT traps
| Trap | What it tempts you to do | Why it is wrong |
|---|---|---|
| Hunting for the price or the volume | Decide you need the milk cost C or the number of liters before you can find x, then pick C or E. | C and M both cancel. The profit equation (1 + r)(1 + m) = 1.5 needs only the ratio r, so prices and volumes are never required. |
| Charging water to the cost | Treat the mixture's cost as covering all M + W liters, diluting the profit. | Water is free. Total cost is MC, not (M + W)C. Forgetting this understates profit and breaks the setup. |
| Misreading statement (1)'s scenario | Apply the x% markup again, or use the full water quantity, in the hypothetical. | Statement (1) changes two things: half the water (ratio r/2) and no markup (sell at C). The profit is simply r/2, which gives r directly. |
| Flipping the concentration fraction | Read 5/6 as W/(M + W) or as W/M, getting the wrong ratio. | Concentration of milk is milk over total: M/(M + W) = 5/6, which gives W/M = 1/5 = 0.20. Read the fraction carefully. |
| Stopping at "looks sufficient" | See statement (1) work, mark A, and never test statement (2). | Statement (2) also fixes r on its own. Each statement alone is sufficient, so the answer is D, not A. |
A reusable GMAT setup for mixture and profit Data Sufficiency
- Write profit as revenue ÷ cost. A 50% profit means revenue / cost = 1.5; a 10% profit means 1.10, and so on.
- Charge only what was actually paid for. A free ingredient adds volume but no cost — keep it out of the cost term.
- Divide to kill the prices and volumes. Cancel the per-unit cost and the base quantity so the equation lives entirely in ratios.
- Identify the single hidden variable. Here every statement exists to deliver the water-to-milk ratio r. Find what each statement is really pinning down.
- Judge each statement alone, then watch for D. If both independently fix the hidden variable, the answer is D — and the two values should agree.
Want a tutor to drill mixture and profit Data Sufficiency until the "cancel everything to a ratio" move is automatic? MBA House runs live GMAT Focus prep and private tutoring in New York built around clean reasoning, not memorized tricks.
Where this fits in your GMAT prep
Mixture, ratio, and profit Data Sufficiency questions are core GMAT Focus Quantitative Reasoning material, and they reward the habits MBA House teaches: translate the prompt into algebra, cancel away the noise, and evaluate each statement independently. If you want the full picture of the current exam, start with what the GMAT is and our breakdown of the GMAT Focus Edition. For more worked Quant, see our GMAT profit question with tiered costs and our percent error Data Sufficiency question, plus our sets from the Official Guide Quantitative Review 2026–2027 — including all 25 questions explained. To turn practice into a score, our GMAT Focus tutor NYC page explains how live classes and private tutoring work, and our guide to building GMAT and admissions strategy together ties your target score to your school list.
Preparing for the GMAT in New York? MBA House offers personalized GMAT Focus tutoring with proven score-improvement strategies and weekly live Quant practice.
GMAT mixture profit Data Sufficiency FAQs
What is the answer to the milk vendor mixture question?
The answer is D: each statement alone is sufficient. The markup obeys (1 + r)(1 + x/100) = 1.5, so x is fixed the moment you know the water-to-milk ratio r. Statement (1) gives r = 0.20 and statement (2) gives r = 0.20, so each alone forces x = 25%.
Why does free water change the cost per liter?
Water costs nothing, so the batch's total cost stays at MC while the volume sold grows to M + W. The true cost per liter of mixture is MC/(M + W) = C/(1 + r), below the milk price. Selling at the milk price plus a markup turns that hidden discount into extra profit.
How do you set up the milk-water profit equation?
Cost is MC, revenue is (M + W) × C(1 + m), and a 50% profit means revenue/cost = 1.5. Dividing by MC cancels the price and volume and leaves (1 + r)(1 + m) = 1.5, where r = W/M. Know r and you know m, hence x.
Why is statement (2) sufficient?
A 5/6 milk concentration means M/(M + W) = 5/6, so 6M = 5M + 5W, giving M = 5W and W/M = 1/5 = 0.20. That is the ratio r the equation needs. With r = 0.20, (1.20)(1 + m) = 1.5 gives x = 25%.
Is this a hard GMAT Data Sufficiency question?
It is medium-to-hard. The algebra is short, but it tests seeing that markup depends only on the ratio, handling a free ingredient that lowers the per-liter cost, and recognizing that two different-looking statements both deliver the same ratio — the skills GMAT Focus Data Sufficiency rewards.