Telescope

[j_shreyans]

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

OAD

[GMATGuruNY]

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.

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Hi j_shreyans,

This question is perfect for TESTing THE ANSWERS (as Mitch has shown in his solution). It can also be solved with "math" by focusing on MULTIPLES of the numbers involved.

We're told that we can buy:
-Lenses in packs of 50
-Tubes in packs of 10
-Eyepieces in packs of 30

There are some additional details to consider:
-Each telescope requires 2 lens, 1 tube and 1 eyepiece
-HALF of the lenses in each pack are NOT useable (but we have to buy them anyway)
-We want to create telescopes with NO leftover parts (except for the lenses we can't use).

As mentioned at the beginning, this is an issue of MULTIPLES:

We need a number of telescopes that is a MULTIPLE of 25 (since we can only use half the lenses in each pack), 10 and 30. The least multiple is 300, BUT we need 300 lenses that we can USE, so we have to account for the extra lenses in each pack that we CAN'T use.

300 x 2 = 600

Final Answer: D

GMAT assassins aren't born, they're made,
Rich