A gourmet cheese shop sold several orders of English Stilton and Span

Question

﻿A gourmet cheese shop sold several orders of English Stilton and Spanish Manchego yesterday. Customer A purchased 15 pounds of English Stilton and 3.75 pounds of Spanish Manchego for a total of $438.00. If the price for each of these cheeses is proportional to its weight, what is the price of 1 pound of Spanish Manchego?

(1) Customer B purchased 5 pounds of English Stilton and 4 pounds of Spanish Manchego for a total of $214.75.
(2) Customer C purchased 6 pounds of English Stilton and 1.5 pounds of Spanish Manchego for a total of $175.20.

gmatophobia · Accepted Answer

The question premise states that the price of the cheeses is proportional to its weight.

Price = Weight * Constant

Price of 15 pounds of ES cheese =  15*x  ⇒  x  is a constant 
 Price of 3.75 pounds of SM cheese =  3.75*y  ⇒  y  is a constant

15*x + 3.75*y = 438  --- (1)

Statement 1

(1) Customer B purchased 5 pounds of English Stilton and 4 pounds of Spanish Manchego for a total of $214.75.

5*x + 4*y = 214.75

Multiplying by 3 on both sides

15*x + 12*y = (214.75*3)  --- (2)

As we have two different equations, we can find the value of  x  and  y  and use that information to find the value of 1 pound of SM cheese. We don't need to do that while solving the question, however we have the required information to do so.

Hence, equation 1 is sufficient. We can eliminate B, C, and E.

Statement 2

(2) Customer C purchased 6 pounds of English Stilton and 1.5 pounds of Spanish Manchego for a total of $175.20.

6*x + 1.5*y = 175.20

We need to check if this equation is different from the one which is given to use in the premise.

Let's multiply the equation by 2

12*x + 3*y = 350.40

Let's take the coefficient of x. The current coefficient of x is 12, however, we need a coefficient of 15. Hence, we need to add 3 to the coefficient of x.

3 = 1/4th of 12

(12+\frac{12}{4})*x + (3+\frac{3}{4})*y = (350.40+ \frac{350.40}{4})

(12+3)*x + (3+0.75)*y = (350.40+ 87.60)

15*x + 3.75*y = 438

The equation is the same as that of the premise. Hence, this statement provides us with information that we already know and hence doesn't add any additional value.

We can eliminate D.

Option A

MartyMurray · Answer

﻿A gourmet cheese shop sold several orders of English Stilton and Spanish Manchego yesterday. Customer A purchased 15 pounds of English Stilton and 3.75 pounds of Spanish Manchego for a total of $438.00. If the price for each of these cheeses is proportional to its weight, what is the price of 1 pound of Spanish Manchego?

We see that the question stem provides the information that the price of each cheese proportional to its weight. That means that the price goes up evenly as the weight goes up. For example, if the weight of cheese purchased doubles, the price doubles as well.

So, we know that, if the price of a pound of English Stilton is S and the price of a pound of Spanish Manchego is M, the cost of a purchase of English Stilton = Pounds of English Stilton * S, and the cost of a purchase of Spanish Manchego = Pounds of Spanish Manchego * M.

So, the cost of customer A's purchase is 15S + 3.75M = 438.

Statement 1:

(1) Customer B purchased 5 pounds of English Stilton and 4 pounds of Spanish Manchego for a total of $214.75.

The cost of customer B's purchase is 5S + 4M = 214.75.

It appears that we have two different equations and two variables and that, therefore, we can calculate S and M and answer the question. However, let's confirm that the equation for customer B is different from that for customer A.

We can confirm by multiplying the equation for customer B by 3 to get 15S + 12M = 644.25.

We see that we definitely have two different equations and can therefore calculate the values of S and M and answer the question.

Sufficient.

Statement 2:

(2) Customer C purchased 6 pounds of English Stilton and 1.5 pounds of Spanish Manchego for a total of $175.20.

The cost of customer C's purchase is 6S + 1.5M = 175.20.

Let's see whether we have two different equations.

Since 15/6 = 2.5, let's multiply the equation for customer C by 2.5.

We get 2.5 * 6S + 2.5 * 1.5M = 2.5 * 175.20 -> 15S + 3.75M = 438.

So, actually, in the equation for customer C, we have the same equation that we have for customer A, meaning we have only one equation and two variables. So, we don't have enough information to determine what S and M are.

Insufficient.

The correct answer is (A).

JeffTargetTestPrep · Answer

If e dollar is the price per pound of English Stilton and s dollar is the price per pound of Spanish Manchego, then we have:

15e + 3.75s = 438

We need to answer the question:

s = ?

Statement One Alone:

=> Customer B purchased 5 pounds of English Stilton and 4 pounds of Spanish Manchego for a total of $214.75.

5e + 4s = 214.75

Since the question stem and the statement equations are not equivalent  , this system of equations would give us a unique value for s.

Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> Customer C purchased 6 pounds of English Stilton and 1.5 pounds of Spanish Manchego for a total of $175.20.

6e + 1.5s = 175.2
(6e + 1.5s = 175.2) × 2.5
15e + 3.75s = 438

Since the question stem and the statement equations are equivalent  , this system of equations would give us multiple possible values for s.

Statement two is not sufficient.

Answer: A

GMATGuruNY · Answer

15x + 3.75y = 438
Since 3.75 = 15/4, multiply by 4 so that the coefficients on the left are both integers.
Resulting equation:
60x + 15y = 1752

Statement 1: 5x + 4y = 214.75
Here, the expression on the left is clearly DIFFERENT from 60x + 15y, since multiplying 5x + 4y by 12 yields 60x + 48y.
Implication:
Statement 1 and the prompt imply two different equations.
the sum for 60x + 15y and the sum for 60x + 48y
Since we have two variables and two distinct linear equations, we can solve.
SUFFICIENT.

Statement 2: 6x + 1.5y = 175.20
Here, multiplying 6x + 1.5y by 10 yields 60x + 15y --> the same expression as that yielded by the prompt.
Implication:
Statement 2 and the prompt both imply the same equation:
the sum for 60x + 15y
Since we have two variables but only ONE linear equation -- and the two variables can be noninteger values -- we cannot solve.
INSUFFICIENT.

A

KarishmaB · Answer

Say price of English Stilton is E and that of Spanish Manchego is S. Given: Customer A 15*E + 3.75S = 438 We need the value of S. (1) Customer B purchased 5 pounds of English Stilton and 4 pounds of Spanish Manchego for a total of $214.75. 5E + 4S = 214.75 I can see that this equation is distinct from the previous given equation. The ratio of 15/5 is not the same as 3.75/4. So the two lines will intersect at one point and give unique values for E and S. Sufficient alone. (2) Customer C purchased 6 pounds of English Stilton and 1.5 pounds of Spanish Manchego for a total of $175.20. 6E + 1.5S = 175.2 This equation also looks different from the given equation 15*E + 3.75S = 438 but I must check the ratios. I know that this is trap - simultaneous equations that look different but are the same. 15/6 = 5/2 To find whether 3.75/1.5 is also 5/2, I will check if 0.75 * 5 is 3.75. It is! Ideally, I must check the ratio of constants also since we could have no solution here but this is a real life case. We have customers A and C who did make these purchases. Hence I know for sure that there must be a solution. So then these two equations MUST BE the same and hence we cannot solve them to get the values of E and S Not Sufficient. Answer (A) Discussion on linear equations: https://youtu.be/Nh77CobN9mQ

AnkurGMAT20 · Answer

MartyMurray   KarishmaB  how and why you divided 15/6? How did you figure that out and also how we can figure this out in span of 2-3 minutes?

KarishmaB · Answer

I have discussed this in my post above and the relevant theory in the link I have given above.

Oppenheimer1945 · Answer

Look at the coefficients of simultaneous linear eq, (Cramer's Rule)

ax+by=c

we need 2 eq for 2 variables to solve.

A trap is another equuation which is a multiple of eq given in ques stem, here we have 1:4 (given) and S2 is also the same eq..

Hence A)

siddharth_ · Answer

KarishmaB   Bunuel  can you kindly share your thoughts on this -

'If the price for each of these cheeses is proportional to its weight' 
What's the purpose of this statement? Isn't this something that's always true and rarely mentioned (at least practically and in most GMAT questions)?

Although I right away noticed the 4:1 ratio of QS and 2nd statement while reattempting this post the test, but the statement above confused me immensely while answering this question in the test setting. I understood this as the 'rate' is varying, ie, price per pound varies with weight, in which case the price for 15 pound would be 225p.

KarishmaB · Answer

Yes, it is obvious and yes, rarely mentioned but GMAT does clarify such things sometimes. So don't let it confuse you. 
Even if I were to think that there must be a specific reason here for this statement, what can it be? Can the shop charge differently for each pound of a cheese based on how many pounds you are buying? If that were true, would this statement in the question make any sense: what is the price of 1 pound of Spanish Manchego?
Then the price per pound would vary for each customer and this question would make no sense. So that should make you realize that the question is just over clarifying, nothing else.

A gourmet cheese shop sold several orders of English Stilton and Span

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