The 50 participants of a management training seminar ate dinner at a

Question

﻿The 50 participants of a management training seminar ate dinner at a certain restaurant. They had 3 choices for their meal: vegetarian lasagna for $12, blackened catfish for $15, or stuffed pork chops for $18. Each participant ordered exactly 1 meal and the total cost of the meals ordered by the participants was $810. How many participants of the management training seminar ordered blackened catfish?

(1) Six more people ordered catfish than lasagna.
(2) Twice as many pork chop meals were ordered as catfish meals.

JeffTargetTestPrep · Accepted Answer

ℓ + c + p = 50

12ℓ + 15c + 18p = 810 => 4ℓ + 5c + 6p = 270

We need to answer the question:

c = ?

Statement One Alone:

=> Six more people ordered catfish than lasagna.

c = ℓ + 6

6ℓ + 6c + 6p = 300
4ℓ + 5c + 6p = 270

2ℓ + c = 30
2(c -6) + c = 30
3c = 42
c = 14

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

Statement Two Alone:

=> Twice as many pork chop meals were ordered as catfish meals.

p = 2c

4ℓ + 5c + 6p = 270
4ℓ + 4c + 4p = 200

c + 2p = 70
c + 2(2c) = 70
5c = 70
c = 14

Statement two is sufficient.

Answer: D

KarishmaB · Answer

Say L people ate Lasagna, C people ate Catfish and P people ate pork chops. L + C + P = 50 12L + 15C + 18P = 810 (The two equations are different but there are 3 variables so we can't solve them yet) (1) Six more people ordered catfish than lasagna. C = L + 6 Another equation which is different. So now we have 3 equations with 3 variables. We can solve them to get the answer. Sufficient. (2) Twice as many pork chop meals were ordered as catfish meals. P = 2C Another equation which is different. So now we have 3 equations with 3 variables. We can solve them to get the answer. Sufficient. Answer (D) Check linear equations here: https://youtu.be/Nh77CobN9mQ

gmatophobia · Answer

Number of participants who ordered vegetarian lasagna =  x  
 Number of participants who ordered blackened catfish =  y  
 Number of participants who stuffed pork chops =  z

x + y + z = 50  ---- (1)

12*x + 15*y + 18*z = 810

4x + 5y + 6z = 270  ---- (2)

Statement 1

(1) Six more people ordered catfish than lasagna.

y = x + 6

Using Equation 1

x + x + 6 + z = 50

2x + z = 43

Using Equation 2

4x + 5(x+6) + 6z = 270

9x + 30 + 6z = 270

9x + 6z = 240

We have two equations and two variables, hence we can find a unique value of x, y, and z. The statement alone is sufficient. We can eliminate B, C, and E.

Statement 2

(2) Twice as many pork chop meals were ordered as catfish meals.

z = 2y

Using Equation 1

x + y + 2y = 50

x + 3y = 50

Using Equation 2

4x + 5y + 6(2y) = 270

4x + 17y = 270

We have two equations and two variables, hence we can find a unique value of x, y, and z. The statement alone is sufficient.

Option D

madirochelle7 · Answer

Hi! I'm not quite following how we get 6l+6c+6p=300 and 4l+4c+4p=200. How do we arrive at those values? Thanks!

Bunuel · Answer

We obtain 6l + 6c + 6p = 300 by multiplying l + c + p = 50 by 6. Likewise, 4l + 4c + 4p = 200 is obtained by multiplying l + c + p = 50 by 4.

Hope it helps.

sammmmm56 · Answer

should the answer to both the statements be same? On general is data sufficiency questions if we get a one answer of each statement and if the answer is different say as per statement one info x=2 and as per statement 2 info x=4  Bunuel

Bunuel · Answer

In the GMAT, the two data sufficiency statements always provide true information and never contradict each other or the question stem. If the statements contradict one another, the question is flawed by GMAT standards.

Not sure what you denoted by x there, but if you solve the question correctly, you’d get the same answer from each statement.

nairbb · Answer

How did you get 4 though? I understand multiplying by 6 is because statement 1 says 6 more, but wouldn't it be multiplying by 2, because statement 2 says twice as many?

Bunuel · Answer

You're mixing up the logic. Multiplying by 6 or 4 has nothing to do with the "6 more" or "twice as many" from the statements. It's done to align with the cost equation 12l + 15c + 18p = 810, which simplifies to 4l + 5c + 6p = 270.

In Statement 1, we multiply the count equation l + c + p = 50 by 6 to get 6l + 6c + 6p = 300, so we can subtract it from the cost equation. 
 In Statement 2, we multiply the same count equation by 4 to get 4l + 4c + 4p = 200, again to make subtraction easier.

It’s just a method for aligning equations, not related to the specific numbers in the statements.

bishal128 · Answer

how reasonable is it to use the following logic; 
1) there are three variables
2) if you can have three distinct equations, then equations are solvable
3) Statement 1 provides a unique solution of Cat and VL; sufficient 
4) statement 2 provides another unique solution of Pork and Cat;

Is this reasoning Okay!?

KarishmaB · Answer

Yes it is, as discussed here: https://gmatclub.com/forum/the-50-parti ... l#p3381529 The important point is not ensure that the equations are different. Also, since each statement alone gives us 3 equations with 3 variable so we know that each alone is sufficient. But keep in mind that a statement could lead to only 2 equations and may still be sufficient to answer what is asked. So we need to be careful while following the number of variables and number of equations logic.

Siddharth17 · Answer

I think the simplest thing here to consider is that we already have two equations

let x = no. of people who ordered lasagna
y = no. of people who ordered catfish
z = no. of people of ordered pork chops

Eq.1 : x + y + z = 50
Eq.2: 12x + 15y + 18z = 810

we just need one more equation that is different than above two

MarkGMATMentor · Answer

The key takeaway from this problem is the  Equation Count Pattern : As long as you have as many different linear equations as variables, you can solve for the variables. The equations must be truly different, not just variations of the same equation.

40-second summary:
 https://www.youtube.com/watch?v=yc1yKp7L9X0

Full walkthrough and discussion:
 https://www.youtube.com/watch?v=vL2HiNwdNZw

MrMaxMan · Answer

Translate the original problem into algebra,
12L+15C+18P = 810
L+C+P = 50
2 equations, 3 unknowns.

I) Relates C to L, eliminating one variable.
2 equations, 2 unknowns = solvable.
 SUFF.

II) Relates P to C, eliminating one variable.
2 equations, 2 unknowns = solvable
 SUFF.

The 50 participants of a management training seminar ate dinner at a

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