Test: Sale And Purchase- 1 - GRE MCQ

Steps 1 & 2: Understand Question and Draw Inferences

The company manufactured and sold 1,200 motorcycles during its fiscal year. The question is whether it made a profit, so you need to know the revenue and expenses.

Step 3: Analyze Statement 1

(1)          For each motorcycle sold, the company’s revenue was $10,000

Statement 1 tells you that the company’s revenue was $12,000,000 during its fiscal year. However, without knowing its expenses, you don’t know whether the company made a profit.

Statement 1 is not sufficient.

Step 4: Analyze Statement 2

(2)          The company’s expenses comprise a fixed expense of $2,000,000 per quarter and an additional $3,500 for each motorcycle.

Statement 2 tells you that the company’s annual expenses were $8,000,000 fixed plus $4,200,000 ($3,500 × 1,200), for a total of $12,200,000. However, without knowing the revenue, you don’t know whether the company made a profit.

Statement 2 is not sufficient.

Step 5: Analyze Both Statements Together (if needed)

Taken together, if the revenues were $12.0m and the expenses were $12.2m, you know that the company did not make a profit.

With these, you are able to answer the question, even though the answer is no.

Answer: Option (C)

Step 1: Question statement and Inferences

The station purchased g gallons of petroleum for d dollars per gallon, and then added e gallons of ethanol at f dollars per gallon.

The total volume of the mixture = (g + e) gallons

Step 2: Finding required values

The cost price of g gallons of petroleum = dg dollars

The cost price of e gallons of ethanol = ef dollars

So, the total cost price of the mixture = (dg + ef) dollars

The cost per gallon of the mixture = 

Step 3: Calculating the final answer

Profit per gallon is given by Selling price per gallon – cost price per gallon.

We know that the selling price per gallon is h dollars, thus, profit is as shown:

Answer: Option (D)

Steps 1 & 2: Understand Question and Draw Inferences

The electronics store marked up all of its 500 tablets. The question is how many were sold at a 40% markup? You can infer that the tablets were marked up either 20% or 40%, but no other percentage.

Let the number of tablets marked up at 20% be x.

Therefore, the number of tablets marked up at 40% will be 500 – x.

The selling price (SP) of and the profit made upon the sale of each 20% marked up and the 40% marked up tablet is calculated as below:

We need to find the value of 500 – x. For this, we need to know the value of x.

We will now determine if Statements 1 and 2, alone or together, are sufficient to give us the value of x.

Step 3: Analyze Statement 1

(1)   Had the store sold all the tablets at a markup of 30%, its gross profit would have been 6.25% lower.

Gross profit in the scenario given in the question statement

= 30x + 60(500 – x)

= 30x + 30,000 – 60x

= 30,000 – 30x

Let’s now consider the scenario given in Statement 1:

SP = $150 + 30% of $150

Profit per tablet = SP – CP = ($150 + 30% of $150) -$150 = 30% of $150 = $45

Gross profit upon the sale of 500 tablets = 45(500) = $22,500

Per Statement 1,

22,500 = (30,000 – 30x) – 6.25% of (30,000 – 30x)

Thus, Statement 1 gives us a linear equation with only one unknown.

Therefore, upon solving this equation, we will be able to get a unique value of x.

Statement 1 alone is therefore sufficient.

Step 4: Analyze Statement 2

(2)  The gross profit from the 40% lot were three times the gross profit from the 20% lot.

Representing this mathematically, 

Again, we get a linear equation with only one unknown. Upon solving this equation, we will be able to find a unique value of x

Statement 2 is sufficient.

Step 5: Analyze Both Statements Together (if needed)

You get a unique answer in steps 3 and 4, so this step is not required

 Answer: Option (D)

Steps 1 & 2: Understand Question and Draw Inferences

Let the marked price of item A be a dollars,

The marked price of item B be b dollars, and

The marked price of item C be c dollars

So, had she not shopped at the budget store, she would have bought these three items at their marked price.

So, she would have spent a total of (a+b+c) dollars to buy these three items.

At the budget store,

Let the selling price of item A be a’

=> a’ = a – 40% of a  = 0.6a

Let the selling price of item B be b’

=> b’ = b – 20% of b = 0.8b

Let the selling price of item C be c’

=> c’ = c – 10% of c = 0.9 c

So, the money actually paid by Jamie for the three items = (0.6a + 0.8b + 0.9c)

Money saved by her by shopping at the budget store = (Money she would have otherwise spent to buy these 3 items) – (Money she spent at the budget store to buy these three items)

=> Money saved = (a + b + c) – (0.6a + 0.8b + 0.9c)

=> Money saved = 0.4a + 0.2b + 0.1c

% Moneysaved= 

% Moneysaved=

Thus, in order to find the % Money saved, we need to know the values of a, b and c.

Step 3: Analyze Statement 1 independently

Statement 1 states that:

The marked price of item B is 75% of the marked price of item A and 200% more than the marked price of item C

Also,

Substituting Equation 3 in Equation 2:

3c = 0.75 a

⇒ c = 0.25a   ..... Equ 4

Substituting Equations 2 and 4 in Equation 1:

We see that if we divide the numerator and denominator by a, we will get a tangible number. We don’t need to actually solve this expression, since this is a DS question and not a PS question. But we do know that we will be able to get a unique value for % Money Saved.

Therefore, Statement 1 alone is sufficient to arrive at a unique answer.

Step 4: Analyse Statement 2 independently

Statement 2 states that:

The marked price of item A is 400% of the marked price of item C

=>  a = 400% of c

=> a = 400/100 * c

=> a = 4c

However, Statement 2 gives us no idea of the value of b.

So, we will not be able to solve Equation 1 to determine a unique value of % Money Saved.

Therefore, Statement 2 is not sufficient.

Step 5: Analyse both statements together

This step is not required since we do get a unique solution in Step 3.

Correct answer = Option A.

Steps 1 & 2: Understand Question and Draw Inferences

We are given that the original marked price (say P) of an electric vehicle is $50,000. In 2012, this product was being sold at a discount of n%.

 P = $50,000

So, the selling price Q of the product in 2012:

In 2013, the demand for the electric vehicle increased and its prices was raised by m% over its discounted price in 2012. Let’s say its new selling price is R:

By simplifying the above expression, we get:

By plugging in the value of P in the above equation,

So, we need to find the value of m and n to answer the question “What is the final price of the vehicle?”

Step 3: Analyze Statement 1

Statement I says: m = 10     

This statement gives us the value of m only. We still don’t have the value of n.  So, we can’t determine the value of R.

Hence, statement I alone is not sufficient to answer the question: “What is the final price of the vehicle?”    

Step 4: Analyze Statement 2

Statement 2 says: (100-n)(100+m)=2200    

The expression given in this statement can directly be used in equation (2) to find the value of R.

So, statement II alone is sufficient to answer the question: “What is the final price of the vehicle?” 

Step 5: Analyze Both Statements Together (if needed)

Since step 4 provides a unique answer to the question, we don’t need to perform this step. 

 Answer: Option (B)

Step 1: Question statement and Inferences

Both chairs have the same cost price but different selling prices. We need to find the price at which each chair sells, in order to calculate the total profit made by selling the two chairs.

Step 2: Finding required values

Stuart purchased two chairs for $60

So, Cost price of one chair, CP = 60/2 = $30

Let the marked price of each chair be MP

MP = CP + Markup

Given: Markup = 40% of MP

So, MP = CP + 40% of MP

Or, 60% of MP = CP

60100MP=CPMP=10060×30=50

After 1 day, he discounted the marked price by 20%

So,new Marked Price=MP′=MP–20% of MP

=80 % of MP

MP′=40

He sold one chair at this price.

His profit on selling this chair = P1 = MP′ – CP

P1 = 40 – 30

P1 =$ 10

For the unsold chair,

He raised the marked price by 20%

New Marked Price = MP′′=MP′+20 of MP′ 

MP′′ = 120 of MP′

MP′′=$48

He sold the second chair at this price.

His profit on selling this chair

= P2 = MP′′–CP

P2 = 48 – 30

P2 = $18

Step 3: Calculating the final answer

Total profit earned on the sale of the two chairs

= P1 + P2 = $10 + $18 = $28

Looking at the answer choices, we see that Option C is correct

Steps 1 & 2: Understand Question and Draw Inferences

In this question, both CP and SP are expressed in terms of the marked price.

Let the marked price of the item be M

The cost price at which the merchant had bought the item was a % less than the marked price

=> CP = M – a % of M

=> CP = (1 - a/100) M

The selling price of the item was b % less than the marked price

=> SP = M – b % of M

=> SP = (1 - b/100) M

Discount offered to the customers = Marked Price – Selling Price

=> Discount = M - (1 - b/100) M

=> Discount = bM/100  . . . Equation 1

Thus, in order to determine the value of Discount, we need to know the values of b and M.

Step 3: Analyze Statement 1 independently

According to Statement 1,

a = 6%

However, this doesn’t give us any idea of the values of b and M.

So, Statement 1 is not sufficient.

Step 4: Analyze Statement 2 independently

As per Statement 2,

The dealer made a profit of 5%

Given: Profit = 5% of CP

But Profit = SP – CP

=> SP – CP = 5% of CP

=> SP = CP + 5% of CP

=> SP = 105% of CP

Substituting the values of SP and CP in the above expression:

However, we are not able to solve any further for the values of a and b. Moreover, we have no idea of the value of M.

Therefore, we cannot find the value of Discount using Statement 2.

Therefore, Statement 2 too is not insufficient

Step 5: Analyze Both Statements Together (if needed)

From Statement 1,

a = 6

From Statement 2,

21a – 20b = 100

Using both these Statements together, we will be able to find the value of b.

But we will still not know the value of M.

Therefore, we cannot find the value of Discount even by analysing both the statements together.

Therefore, the correct answer is E.

Note:  If the question had asked about discount percentage instead of the value of discount, we would have been able to answer the question by analysing both statements together and the answer would have been C.

This is because,

Discount percentage = b %

Step 1: Question statement and Inferences

The furniture dealer purchased 10 sofas for $500 each. An average gross profit of $90 per sofa means the average sale price is $590, and no sofa can be sold for more than $600.

Step 2: Finding required values

To find the lowest price of one sofa, assume the other 9 sofas were sold at their highest prices, which is $600 each, for an average of $590. 

Step 3: Calculating the final answer

Let the price of the lowest price sofa be $x. Then we can set up the equation like this: 

9(600)+x10=590

And solve for x:

5,400+x=5,900

x = 500

Answer: Option (D)