A craft store sold 40 handmade lamps. Each lamp was sold for either

Question

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.

M47-165

Bunuel · Accepted Answer

GMAT Club Official Solution:

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?

Before evaluating the statements, find the profit for each possible case.

For a $120 lamp:

25% markup:
120 = 1.25 * cost
cost = 96
profit = 120 - 96 = 24

50% markup:
120 = 1.5 * cost
cost = 80
profit = 120 - 80 = 40

For a $180 lamp:

25% markup:
180 = 1.25 * cost
cost = 144
profit = 180 - 144 = 36

50% markup:
180 = 1.5 * cost
cost = 120
profit = 180 - 120 = 60

So the possible profits are 24, 40, 36, and 60, depending on the selling price and markup.

(1) 16 lamps were sold for $120 each.

Then 24 lamps were sold for $180 each. But we do not know how many lamps in each price group were sold at a 25% markup and how many were sold at a 50% markup.

Not sufficient.

(2) 24 lamps were sold at a selling price that was 50% greater than cost.

Then 16 lamps were sold at a selling price that was 25% greater than cost. But we do not know how many lamps in each markup group were sold for $120 and how many were sold for $180.

Not sufficient.

(1)+(2) Even together, the statements are not sufficient.

For example, suppose all 16 lamps sold for $120 were sold at a 25% markup, and all 24 lamps sold for $180 were sold at a 50% markup.

Then the total profit would be:

16 * 24 + 24 * 60 = 1824

But suppose all 16 lamps sold for $120 were sold at a 50% markup. Then, since 24 lamps total were sold at a 50% markup, 8 of the $180 lamps were sold at a 50% markup and the remaining 16 were sold at a 25% markup.

The total profit would be:

16 * 40 + 8 * 60 + 16 * 36 = 1696

Both cases satisfy both statements, but they give different total profits.

Not sufficient.

Answer: E.

ankushsambare · Answer

Let:
 
 x = number of lamps sold for $120 
 y = number of lamps sold for $180  
We know:
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  
Be careful: profit is NOT 25% or 50% of selling price.
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  
  
We need total profit.
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  
Still not enough unless we verify carefully.
Case 1:
 
 All 24 of the $180 lamps had 50% markup 
 All 16 of the $120 lamps had 25% markup  
Profit:
 
 24 × (1/3 × 180) = 24 × 60 = 1440 
 16 × (0.2 × 120) = 16 × 24 = 384  
Total = 1824
Case 2:
 
 All 24 of the $120 lamps had 50% markup is impossible because only 16 lamps were sold at $120.  
So mix them:
Suppose:
 
 16 of the $120 lamps → 50% markup 
 Remaining 8 of the $180 lamps → 50% markup 
 Remaining 16 of the $180 lamps → 25% markup  
Profit:
 
 16 × 40 = 640 
 8 × 60 = 480 
 16 × 36 = 576  
Total = 1696
Different total profits are possible.
Therefore, even together the statements are NOT sufficient.
 Answer: E (Statements (1) and (2) together are not sufficient.)

BongBideshini · Answer

Statement (1): 
 
 16 lamps sold for $120 
 24 lamps sold for $180  
No information about the price
 Insufficient 
 Statement (2): 
 
 24 lamps had 50% markup 
 16 lamps had 25% markup  
No information about the price
 Insufficient

Statement (1)+(2):

The 16 lamps sold at $120 could be
 
 part of the 50% markup group
OR 
 part of the 25% markup group
OR 
 Split between both.

We only know the outside totals, not the inside split.
    
 $120 
 $180 
 Total 
 
  50% markup 
 ? 
 ? 
 24 
 
  25% markup 
 ? 
 ? 
 16 
 
  Total 
 16 
 24 
 40

The four inside cells can vary in many ways, so total profit cannot be uniquely determined.

Insufficient. 
 Ans E

SS990 · Answer

The answer is E

SP 
 number in CP25=SP/1.25 
 number in CP50=SP/1.5 
 total number 
 
  120

a 
 
  180

b

40

Given above info

To find: Profit of the sale of 40 lamps

1)16 were sold for 120$. But we know nothing of the CP. So this is insufficient

2) 24 were sold at CP50. But we know nothing of the split of this 24, in terms of CP. This is given since previous choice we lead us to 24 under 180$ sale. This is also insuffcient

Together, we know a=16, b=24 and we know some 24 lamps was from the CP50 category. But we know how much this 24 was sold to know profits from them or the rest. Hence insufficient.

krrishabh96 · Answer

https://gmatclub.com/forum/download/file.php?id=88524 We have 4 unknowns, 1 equation — we need 3 more independent equations to solve uniquely. Each statement gives us additional constraints. The question is whether those constraints pin down the profit uniquely even if individual variables aren't fully determined. Statement 1 "16 lamps were sold for $120 each." This tells us: a + c = 16 , and therefore b + d = 24 Now we have: a + c = 16 → $120 lamps b + d = 24 → $180 lamps But within each price group, we still don't know the markup split. For example: If a = 16, c = 0, b = 24, d = 0: Profit = 24(16) + 36(24) = 384 + 864 = $1,248 If a = 0, c = 16, b = 0, d = 24: Profit = 40(16) + 60(24) = 640 + 1,440 = $2,080 Different profits possible. Statement 1 alone: INSUFFICIENT Statement 2 "24 lamps were sold at 50% greater than cost." This tells us: c + d = 24, and therefore a + b = 16 But within each markup group, we don't know the price split: If c = 24, d = 0, a = 16, b = 0: Profit = 40(24) + 24(16) = 960 + 384 = $1,344 If c = 0, d = 24, a = 0, b = 16: Profit = 60(24) + 36(16) = 1,440 + 576 = $2,016 Different profits possible. Statement 2 alone: INSUFFICIENT https://gmatclub.com/forum/download/file.php?id=88525 the combinations give different profits ($1,824 vs $1,760 vs $1,696). That means even together, the statements are insufficient GMAT-Club-Forum-jm5pfac3.png GMAT-Club-Forum-y5escfho.png

A craft store sold 40 handmade lamps. Each lamp was sold for either

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SP	number in CP25=SP/1.25	number in CP50=SP/1.5	total number
120			a
180			b
			40

GMAT Data Sufficiency (DS) Questions

A craft store sold 40 handmade lamps. Each lamp was sold for either

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