A store purchased a Brand C computer for the same amount that it paid

Question

A store purchased a Brand C computer for the same amount that it paid for a Brand D computer and then sold them both at higher prices. The store's gross profit on the Brand C computer was what percent greater than its gross profit on the Brand D computer?

(1) The price at which the store sold the Brand C computer was 15 percent greater than the price at which the store sold the Brand D computer.

(2) The store's gross profit on the Brand D computer was $300.

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Official Answer

E

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KarishmaB · Accepted Answer

Cost price is same but selling price could be different.

We need  \frac{ProfitC - ProfitD}{ProfitD} * 100

So we need the value of ProfitC/ProfitD to get this.

(1) The price at which the store sold the Brand C computer was 15 percent greater than the price at which the store sold the Brand D computer.

SellingP of C is 15% more than SellingP of D. 
This says that  \frac{SellingC}{SellingD} = \frac{115}{100}

\frac{Cost + ProfitC}{Cost + ProfitD} = \frac{115}{100}

We cannot get ratio of profits from this.

(2) The store's gross profit on the Brand D computer was $300.

We know ProfitD now but not profitC. Not sufficient alone.

Using both,
 
  \frac{Cost + ProfitC}{Cost + 300} = \frac{115}{100}

We still can't find ProfitC.

Answer (E)

Abhishiek · Answer

Cost price of Brand C and Brand D = c

1. If Selling Price of D = x , SP of C = 1.15x
Profit of C = 1.15x - c
Profit of D = x - c
Insufficient.

Alternatively, you can put numbers. If D was sold for $100, and C was sold for $115, the profit ratio would change if cost was $10 vs if cost was $50.

2. We don't know anything about C.
Insufficient.

Both.
c-x = 300
c = 300-x

Profit on C = 0.15x - 300
Profit on D = 300
Still can't solve it.

Alternatively, you can understand this as:
D: sold for $4000, and C sold for $4600 on a cost price of $3700 vs
D: sold for $400, and C sold for $460 on a cost price of $100.
Both would have very different profit ratio.

E.

Luckisnoexcuse · Answer

(1) let the CP of Brand C and Brand D be 90 ; SP of Brand D = 100 ; SP of Brand C = 115
25-10/10 = 150%

let the CP of Brand C and Brand D be 190 ; SP of Brand D = 200 ; SP of Brand C = 230
40-10/10 = 300%

not sufficient

(2) No info abt Brand C SP..not sufficient

on combining 
let the CP of Brand C and Brand D be x; Profit from Brand D = 300 ; SP of Brand D = x+300
SP of brand C = 1.15(x+300); Profit from Brand C = 345+0.15x

No info abt CP of Brand C/D

not sufficient
E

gmathero911 · Answer

Bunuel Any other similar DS questions to this one?

nisen20 · Answer

profit = selling price - cost price

it's impossible to determine the difference between profits, if selling prices are only available factor.

sayan640 · Answer

A store purchased a Brand C computer for the same amount that it paid for a Brand D computer and then sold them both at higher prices. The store's gross profit on the Brand C computer was what percent greater than its gross profit on the Brand D computer?

(1) The price at which the store sold the Brand C computer was 15 percent greater than the price at which the store sold the Brand D computer.

(2) The store's gross profit on the Brand D computer was $300.

Solution :-

Brand D purchased for = X $
Brand C purchased for = X$

Using statement 1,
Brand D sold for = y $
Brand C sold for = 1.15y $
The store's gross profit on the Brand C computer :- 1.15Y - x 
The store's gross profit on the Brand D computer = y - x

Let , the store's gross profit on the Brand C computer was  ' P'  percent greater than its gross profit on the Brand D computer,
P= .15y / (y-x)   * 100

No info about y -x ; hence insufficient.

Using statement 2,
No info about Brand C , hence insufficient.

Together,

P = .15y / 300  * 100
Still we dont know about y and hence insufficient.

E is the answer.
 chetan2u   GMATinsight   KarishmaB

Usernamevisible · Answer

Here's the transferable rule that applies to many GMAT questions.

---

## TRANSFERABLE RULE #1: Never Assume Proportionality After Addition/Subtraction

If

A = B + k
or
A = B - k

then a percentage change in B does NOT imply the same percentage change in A.

Reason:
Adding or subtracting a constant changes ratios.

Examples:
Revenue = Cost + Profit
Profit = Selling Price - Cost
Age = Years + 18
Temperature = Celsius + 273

None of these are proportional.

---

## TRANSFERABLE RULE #2: Multiplication/Division Preserves Proportionality

If

A = kB

where k is constant,

then

A changes by the same percentage as B.

Examples:
Salary = 12 × Monthly Salary
Distance = Speed × 5 hours
Circumference = 2πr

If r increases 20%, circumference increases 20%.

---

## TRANSFERABLE RULE #3: Ask "Am I Adding/Subtracting or Multiplying?"

Whenever you see a percentage statement, immediately ask:

Is this quantity obtained by

1. Multiplying?
 Yes -> proportionality is preserved.

2. Adding/Subtracting?
 No -> proportionality is usually destroyed.

---

## GMAT Examples

1. Profit

Profit = SP - CP

15% higher SP
DOES NOT imply
15% higher profit.

2. Markup

SP = Cost × (1 + markup)

20% higher cost
DOES imply
20% higher SP if markup % is fixed.

3. Interest

Amount = Principal × (1 + r)

10% higher principal
DOES imply
10% higher amount.

4. Net Income

Net Income = Revenue - Expenses

10% higher revenue
DOES NOT imply
10% higher net income.

---

## Mental Checklist

Whenever you read:

"X is 20% more than Y."

Ask:

"What is the quantity I'm actually asked about?"

If that quantity equals

Target = X + constant
Target = X - constant

Stop. Do NOT transfer percentages.

If instead

Target = constant × X
Target = X / constant

The percentage transfers exactly.

---

## One-Line Memory Rule

Percentages transfer through multiplication and division, but they almost never transfer through addition or subtraction.

Rickooreo · Answer

Transferable DS rule

Whenever a percentage is applied to selling price or revenue but the question asks about profit, immediately ask: "Do I know the cost price?"

The reason is that profit = selling price - cost price. So a percentage change in selling price does not translate directly into the same percentage change in profit unless the relevant cost information is known.

More generally, whenever a question asks for a percentage change, first identify the base of that percentage. Then ask whether that base is known. A percentage statement about one quantity does not automatically give the same percentage change in another quantity derived from it.

Key learning from this question

The first key learning is that when two products have the same cost price, the difference in their gross profits is exactly equal to the difference in their selling prices. This is because Gross Profit = Selling Price - Cost Price, and the same cost price cancels out. Therefore, GP_C - GP_D = SP_C - SP_D.

The second key learning is that percentage comparison always requires the correct base. When the question asks, "C's profit was what percent greater than D's profit?", the calculation is (GP_C - GP_D) / GP_D x 100. Therefore, you need both the difference in profits and D's profit, because D's profit is the base.

Statement (2) gives D's profit as $300, so it gives us the denominator. However, statement (1) only tells us that C's selling price is 15% greater than D's selling price. It does NOT mean that C's profit is 15% greater than D's profit.

The reason is that the cost price is included in the selling price. When the selling price increases by 15%, the entire selling price increases by 15%, but only the portion above the cost price represents profit. Therefore, the percentage increase in profit depends on how large the original profit is relative to the cost price.

For example, suppose the common cost is $1,000. If D sells for $1,300, D's profit is $300. C sells for 15% more, so C's selling price is $1,495 and C's profit is $495. The increase in profit is $195, which is 65% of D's $300 profit.

Now suppose the common cost is $2,000. If D sells for $2,300, D's profit is still $300. C sells for 15% more, so C's selling price is $2,645 and C's profit is $645. The increase in profit is now $345, which is 115% of D's profit. Therefore, the same 15% increase in selling price can produce completely different percentage increases in profit.

---

Transferable DS rule

Whenever a percentage is applied to selling price or revenue but the question asks about profit, immediately ask: "Do I know the cost price?"

The reason is that profit = selling price - cost price. So a percentage change in selling price does not translate directly into the same percentage change in profit unless the relevant cost information is known.

More generally, whenever a question asks for a percentage change, first identify the base of that percentage. Then ask whether that base is known. A percentage statement about one quantity does not automatically give the same percentage change in another quantity derived from it.

A store purchased a Brand C computer for the same amount that it paid

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A store purchased a Brand C computer for the same amount that it paid

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