A car dealer purchased a new car from the manufacturer for a percent

Question

A car dealer purchased a new car from the manufacturer for  a  percent more than the production cost, and then sold the car for  b  percent more than the price at which he purchased it. What was the production cost of the car?

(1) b = 5
(2) The difference between the price at which the car dealer bought the car and the price at which he sold the car was $2500.

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ManifestDreamMBA · Answer

Let production cost be P
CP = P(1+a/100)
SP = CP (1+b/100)

P=?

Statement 1
b= 5
We dont know SP, CP or a to find P
Insufficient

Statement 2
CP (1+b/100) - P(1+a/100) = 2500
Insufficient, we don't know any other variables

Combined, we have 5% of CP = 2500
But we still need a to calculate P, using CP = P(1+a/100)
Insufficient

Answer E

Sketchitesh · Answer

Production Cost = C
Purschase Price = P = (1+ a/100)*C
Selling price = S = (1+b/100)*P

What is the value of C? C = P/ (1+ a/100) = S / { ( (1+ a/100)* (1+b/100)} We need to know Either a,P or S,a,b

1. b= 5. 
Too many unknowns.
 Insufficient.  
2. S - P = 2500 . => P * (b/100) = 2500 Still  Insufficient

Together,   From 2 and b=5 from 1 we can deduce value of P, and S. Still a is unknown and required to calculate C.  Insuffucient.

E is the answer

NextstopISB · Answer

Question:
A car dealer purchased a new car from the manufacturer for a percent more than the production cost, and then sold the car for b percent more than the price at which he purchased it. What was the production cost of the car?

(1) b = 5 
(2) The difference between the price at which the car dealer bought the car and the price at which he sold the car was $2500.

Let’s assume:
Let the production cost = x 
Dealer's purchase price = x + (a/100)x = x(1 + a/100) 
Selling price =   * (1 + b/100)

We are asked to find x, the production cost.

Statement (1): 
Statement (1) tells us b = 5 
So selling price = purchase price * 1.05 
But we still don't know a or any monetary values, so we can't find x 
Statement (1) alone is not sufficient

Statement (2): 
We're told the dealer made a $2500 profit, i.e., 
Selling price - Purchase price = 2500

So: 
x(1 + a/100)(1 + b/100) - x(1 + a/100) = 2500 
Factor x(1 + a/100): 
x(1 + a/100)  = 2500 
x(1 + a/100)(b/100) = 2500

Still two unknowns: x and b 
We cannot solve for x without knowing b 
Statement (2) alone is not sufficient

Combining (1) and (2): 
From (1): b = 5 
Plug into the equation from (2):

x(1 + a/100)(5/100) = 2500 
Now we still have a and x as unknowns. Without knowing a, we cannot solve for x 
Even together, we have one equation and two unknowns 
Not sufficient

Answer: (E) – Statements (1) and (2) together are not sufficient

Dereno · Answer

Let the production cost be P

Car dealer purchase price is C = P(1+a/100)

Selling price by car dealer S = P * (1+a/100) * (1+b/100)

We need to calculate the Production cost P ?

We need the values of a, b and the difference between S and C.

STATEMENT 1:

(1) b = 5

Without knowing other values, P is not possible. Hence  NOT SUFFICIENT

STATEMENT 2:

(2) The difference between the price at which the car dealer bought the car and the price at which he sold the car was $2500.

GIVEN : S - C = $2500

P * (1+a/100) * (1+b/100) - { P(1+a/100)} = $2500

P * (1+a/100)   = $2500.

Hence  NOT SUFFICIENT .

Combining Statements 1 and 2, we get

P * (1+a/100)   = $2500

we don’t know value of a. Hence calculating P is  NOT POSSIBLE

OPTION E

bhargavhhhhhhhh · Answer

Let the production cost be P.

Dealer buys car at: P × (1 + a/100)
Dealer sells car at:   × (1 + b/100)

We are asked: What is the value of P?

Statement (1): b = 5
This gives us the profit margin the dealer used, but we don’t know the actual prices or what "a" is (the percent above production cost at which he bought it). Not sufficient.

Statement (2): The difference between purchase price and selling price is $2500

Selling price - Purchase price = $2500

So,
  × (1 + b/100) - P × (1 + a/100) = 2500

Factor out P × (1 + a/100):
P × (1 + a/100) ×   = 2500
P × (1 + a/100) × (b/100) = 2500

This equation has two unknowns (P and a) and one equation — not sufficient.

Now combine both statements:

From (1), b = 5. Plug this into the equation from (2):

P × (1 + a/100) × (5/100) = 2500

Now solve:
P × (1 + a/100) = 2500 × (100/5) = 50000

Still two variables (P and a) in one equation — we cannot uniquely determine P.

Therefore, even together, the statements are not sufficient.

Correct Answer: E. Statements (1) and (2) together are not sufficient.

A car dealer purchased a new car from the manufacturer for a percent

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GMAT Data Sufficiency (DS) Questions

A car dealer purchased a new car from the manufacturer for a percent

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