Try this GRE quantitative question on word problems [Difficulty Level – Hard]

Question In the second week of February, “New Land Inc” announced a mean profit of $5304 per day. They realized this profit from the sale of x units of product Z. Of the following, Which CANNOT be the absolute difference between the cost and sale price of Product Z?

  • $3
  • $4
  • $7
  • $11
  • $51

Solution:

Let’s assume that:

R = revenue
C = cost
P = profit
q = quantity
s = sale price per unit
m = cost per unit

We know that profit is Revenue minus the Cost i.e. P = R – C

Since q items were sold hence the profit would be: P = qs – qm

Now the mean profit per day for a week is $5304, therefore we divide the profit above by 7 to get 5304.

In terms of an equation this is: (qs – qm) / 7 = 5304

Taking q as common we get: q(s – m) = 7*5304

Now the question asks us to find the value which cannot be the difference between sale and cost price i.e. s – m,

Since q is an integer, s – m must be a multiple of 7*5304.

From the given options, only 11 cannot be the factor of 7*5304.

Therefore the correct answer is D.