j_shreyans wrote:A store sells a certain product at a fixed price per unit. At the product's current price, q units cost a total of exactly $300. If the price were lowered by $5 from its current value, then q + 2n units would cost exactly $300; if the price were raised by $5, then q - n units would cost exactly $300. What is the value of q?
A)10
B)15
C)20
D)25
E)30
We need 3 prices spaced $5 apart that divide evenly into 300.
Make a list of options:
5, 10, 15, 20, 25, 30...
The prices above imply that the following numbers of units can be purchased:
300/5 = 60.
300/10 = 30.
300/15 = 20.
300/20 = 15.
300/25 = 12.
300/30 = 10.
According to the problem, the numbers of units that can be purchased are -- in ascending order -- q-n, q, and q+2n.
The difference between the greatest number and the median number (2n) is TWICE the difference between the median number and the least number (n).
Only the values in red satisfy this constraint:
30-20 = 10.
20-15 = 5.
Thus, the value of q -- the median number of units that can be purchased -- is 20.
The correct answer is
C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
