j_shreyans wrote:Mira is making telescopes, each consisting of 2 lenses, 1 tube, and 1 eyepiece. Lenses can be purchased only in packs of 50, tubes only in packs of 10, and eyepieces only in packs of 30. However, half of the lenses in each pack are not usable for telescopes. If all parts are used only for the telescopes, what is the minimum number of lenses Mira must purchase to make a set of telescopes with no leftover components other than the unusable lenses?

A)75
B)150
C)300
D)600
E)7500

We can PLUG IN THE ANSWERS, which represent the minimum number of lenses Mira must purchase if there are to be no leftover components.
Since the question stem asks for the MINIMUM number of lenses that must be purchased, start with the smallest answer choice.

A: 75
Since lenses come in packs of 50, the minimum number of lenses must be a MULTIPLE OF 50.
Eliminate A.

B: 150
Since only 1/2 the lenses are usable, the number of usable lenses = (1/2)(150) = 75.
Not viable:
Since each telescope requires 2 lenses, the total number of usable lenses must be EVEN.
Eliminate B.

C: 300
Since only 1/2 the lenses are usable, the number of usable lenses = (1/2)(300) = 150.
Since each telescope requires 2 lenses, 150 usable lenses are sufficient to make 75 telescopes.
Not viable.
Since tubes come in packs of 10, the number of telescopes must be a MULTIPLE OF 10.

D: 600
Since only 1/2 the lenses are usable, the number of usable lenses = (1/2)(600) = 300.
Since each telescope requires 2 lenses, 300 usable lenses are sufficient to make 150 telescopes.
This works.
To build 150 telescopes, Mira must purchase 15 packs of tubes (since each pack contains 10 tubes) and 5 packs of eyepieces (since each pack contains 30 eyepieces).

The correct answer is D.