Michael bought 12 concert tickets at a price of a dollars per ticket.

Question

Michael bought 12 concert tickets, each at the same price. Later, he resold all 12 tickets for the same higher price per ticket and paid t percent tax on the profit from the resale. After paying the tax, what was Michael’s net profit from the resale?

(1) The resale price per ticket was 40 dollars more than the purchase price per ticket.
(2) If the tax rate had been 15 percentage points higher, then Michael’s net profit would have been 360 dollars.

Bunuel · Accepted Answer

GMAT Club Official Solution:

Michael bought 12 concert tickets, each at the same price. Later, he resold all 12 tickets for the same higher price per ticket and paid t percent tax on the profit from the resale. After paying the tax, what was Michael’s net profit from the resale?

Let purchase price per ticket be p and resale price per ticket be r.

Pre tax profit = 12 * (r - p)
Net profit after tax = 12 * (r - p) * (1 - t/100)

(1) The resale price per ticket was 40 dollars more than the purchase price per ticket.

This gives:

r - p = 40, so pre tax profit = 12 * 40 = 480.
But t is unknown, so net profit after tax is not fixed.

Not sufficient.

(2) If the tax rate had been 15 percentage points higher, then Michael’s net profit would have been 360 dollars.

Let pre tax profit be P. If the tax rate were t + 15, then net profit would be:

P * (1 - (t + 15 )/100 ) = 360.

This is 1 equation with 2 unknowns (P and t), so net profit after the original tax is not fixed.

Not sufficient.

(1)+(2): From (1), P = 480. Substitute into (2):
480 * (1 - (t + 15)/100) = 360
t = 10

So the actual net profit is:
480 * (1 - 10/100) = 480 * 0.9 = 432.

Sufficient.

Answer: C.

shwetakoshija · Answer

Question Stem Analysis: 
 
 Michael bought 12 concert tickets, each at the same price, say p. 
 Later, he resold all 12 tickets for the same higher price per ticket, say q. So, p < q. 
 He paid t% tax on the profit from the resale.   
 
To find:  Michael’s net profit from the resale after paying the tax.
 
 Gross profit = Revenue - Cost = 12q - 12p = 12(q - p) 
 Net profit = 12(q - p) - t% of 12(q - p) 
 = 12(q - p) - t% of 12(q - p) 
  = 12(q - p)(100 - t)/100   
There are 3 unknowns here. We need (q - p) and 't' to find the value of the required expression.

Statement 1 :  The resale price per ticket was 40 dollars more than the purchase price per ticket.
 
 This means that q = p + 40. 
 So, q - p = 40. 
 We still have no idea about 't'.

Statement 1 is insufficient alone.

Statement 2 :  If the tax rate had been 15 percentage points higher, then Michael's net profit would have been 360 dollars.
 
 The tax rate would then have been (t + 15)%. 
 So, Net profit = 12(q - p)(100 - t + 15)/100 ---- Replacing t by t + 15 in the Net Profit formula.  
 We are given that the net profit in this case is $360. 
 Thus, 12(q - p)(100 - t - 15)/100 = 360. 
 Or  12(q - p)(100 - t)/100 -  12(q - p)(15/100) = 360. 
 So,  12(q - p)(100 - t)/100  = 360 + 12(q - p)(0.15) 
  Net Profit  = 360 + 12(q - p)(0.15)

The value of the expression still depends on (q - p). 
Statement 2 is insufficient alone.

Statements 1 and 2 Together :  
 
 From 1, q - p = 40  
 From 2,  Net Profit  = 360 + 12(q - p)(15/100). 
 Combining, we have Net profit = 360 + 12(40)(0.15)

The value of the expression can now be found! The statements are sufficient together.

Correct Answer: C

Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years

Edskore · Answer

Great question to practice the core Data Sufficiency strategy: define exactly what you need before reading the statements.

Key concept being tested: Data Sufficiency — "What Information Is Actually Required?"

Step 1 — Build the formula first.
Net profit = Revenue − Cost − Tax
= 12q − 12p − t% of 12(q − p)
= 12(q − p) − (t/100) × 12(q − p)
= 12(q − p)(1 − t/100)
= 12(q − p)(100 − t) / 100

You have TWO unknowns: (q − p) and t. You need BOTH to get a specific dollar value.

Step 2 — Evaluate Statement 1.
Resale price was $40 more per ticket, so q − p = 40. This gives you one unknown but still no value of t. Net profit = 12(40)(100 − t)/100 = 480(100 − t)/100. This varies with t.
INSUFFICIENT alone.

Step 3 — Evaluate Statement 2.
If tax were 15 points higher, net profit would be $360.
So: 12(q − p)(100 − t − 15)/100 = 360
→ 12(q − p)(85 − t)/100 = 360
You have two unknowns (q − p) and t here. Plugging different values of (q − p) gives different values of t, so you can't pin down the original net profit.
INSUFFICIENT alone.

Step 4 — Combine both statements.
From S1: q − p = 40
Substitute into S2: 12(40)(85 − t)/100 = 360
→ 480(85 − t)/100 = 360
→ 85 − t = 360 × 100 / 480 = 75
→ t = 10

Now plug back: Net profit = 12(40)(100 − 10)/100 = 480 × 90/100 = 432

You get a unique value. SUFFICIENT together.

Answer: C

Common trap: Students often think S2 is sufficient on its own because it mentions a specific dollar amount ($360). But $360 is the net profit under a DIFFERENT tax rate — it's a hypothetical, not the actual answer. The trap is treating a conditional number as if it pins down the answer.

Takeaway: Whenever a DS problem gives you a hypothetical "what if X changed" statement, it gives you a relationship between variables — not a fixed value of the target expression. Always ask: how many independent equations do I have vs. how many unknowns?

Michael bought 12 concert tickets at a price of a dollars per ticket.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Michael bought 12 concert tickets at a price of a dollars per ticket.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards