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A craft store sold 40 handmade lamps. Each lamp was sold for either $120 or $180. If for each lamp, the selling price was either 25% greater than its cost or 50% greater than its cost, what was the store’s total profit from the 40 lamps?
(1) 16 lamps were sold for $120 each.
(2) 24 lamps were sold at a selling price that was 50% greater than cost.
The OA will be automatically revealed on Sunday 24th of May 2026 07:00:14 PM Pacific Time Zone
(1) 16 lamps were sold for $120 each.
(2) 24 lamps were sold at a selling price that was 50% greater than cost.
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The OA will be automatically revealed on Sunday 24th of May 2026 07:00:14 PM Pacific Time Zone
ankushsambare
Joined: 13 Jun 2022
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Schools: ISB '27 Wharton '26 INSEAD Aug '26
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21 May 2026, 20:27
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Let:
x + y = 40
Also, each lamp was sold at either:
If selling price = 125% of cost:
Cost = Selling Price / 1.25
Profit = Selling Price − Cost = 20% of selling price
If selling price = 150% of cost:
Cost = Selling Price / 1.5
Profit = Selling Price − Cost = 1/3 of selling price
So:
Statement (1): 16 lamps were sold for $120 each.
Then 24 lamps were sold for $180 each.
But we still do not know which lamps had 25% markup and which had 50% markup.
Different assignments give different profits.
Not sufficient.
Statement (2): 24 lamps were sold at a selling price that was 50% greater than cost.
So 24 lamps had profit = 1/3 of selling price.
The remaining 16 lamps had profit = 20% of selling price.
But we do not know which selling prices correspond to which markup category.
Again, different totals are possible.
Not sufficient.
Now combine (1) and (2).
We know:
Case 1:
Case 2:
Suppose:
Different total profits are possible.
Therefore, even together the statements are NOT sufficient.
Answer: E (Statements (1) and (2) together are not sufficient.)
- x = number of lamps sold for $120
- y = number of lamps sold for $180
x + y = 40
Also, each lamp was sold at either:
- 25% greater than cost → profit = 25% of cost
- 50% greater than cost → profit = 50% of cost
If selling price = 125% of cost:
Cost = Selling Price / 1.25
Profit = Selling Price − Cost = 20% of selling price
If selling price = 150% of cost:
Cost = Selling Price / 1.5
Profit = Selling Price − Cost = 1/3 of selling price
So:
- For a lamp sold at 25% above cost:
- profit = 20% of selling price
- For a lamp sold at 50% above cost:
- profit = 1/3 of selling price
Statement (1): 16 lamps were sold for $120 each.
Then 24 lamps were sold for $180 each.
But we still do not know which lamps had 25% markup and which had 50% markup.
Different assignments give different profits.
Not sufficient.
Statement (2): 24 lamps were sold at a selling price that was 50% greater than cost.
So 24 lamps had profit = 1/3 of selling price.
The remaining 16 lamps had profit = 20% of selling price.
But we do not know which selling prices correspond to which markup category.
Again, different totals are possible.
Not sufficient.
Now combine (1) and (2).
We know:
- 16 lamps sold for $120
- 24 lamps sold for $180
- 24 lamps had 50% markup
- 16 lamps had 25% markup
Case 1:
- All 24 of the $180 lamps had 50% markup
- All 16 of the $120 lamps had 25% markup
- 24 × (1/3 × 180) = 24 × 60 = 1440
- 16 × (0.2 × 120) = 16 × 24 = 384
Case 2:
- All 24 of the $120 lamps had 50% markup is impossible because only 16 lamps were sold at $120.
Suppose:
- 16 of the $120 lamps → 50% markup
- Remaining 8 of the $180 lamps → 50% markup
- Remaining 16 of the $180 lamps → 25% markup
- 16 × 40 = 640
- 8 × 60 = 480
- 16 × 36 = 576
Different total profits are possible.
Therefore, even together the statements are NOT sufficient.
Answer: E (Statements (1) and (2) together are not sufficient.)
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