Multiple choice Quants question

GRE Quant Problem Solving
1

An organization offers only three types of memberships. Basic memberships cost 50$ each, standard memberships cost 70$ each, and premium membership costs 100$ each. Last year, a total of 200 memberships were purchased at an average cost of 80$ per membership.

Which of the following statements individually provide(s) sufficient additional information to determine the number of premium memberships purchased last year?
Indicate all such statements

  • Last year, the number of basic memberships purchased was equal to the number of standard memberships
  • Last year, the number of premium memberships purchased was twice the number of basic memberships
  • Last year, the number of annual memberships purchased was 100 for one of the three types of annual memberships

My approach
From the given info we have 2 equations,

  1. (50.Nb)+(70.Ns)+(100.Np) = 80(200)
  2. Nb+Ns+Np = 200

So, options A, B are sufficient by themselves because they give us the third equation to solve the simultaneous linear equations.
What about option C? It can’t be sufficient by itself right?

2

i think so. Because option C doesn’t say clearly 100 is for which membership. The first equation has 3 different constants (50,70,100), so the value of Np would change if not given this 100 belongs to which variable.

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3

I did solve for Np = 100, Ns = 100, and Nb = 100 using an online calculator :stuck_out_tongue:
For Nb = 100, we don’t get a valid (positive and integer) solution. For the other two we get integer solutions, so yeah, it’s ambiguous and hence not the answer.

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