Mininum number of lenses needed

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Sun Oct 13, 2013 3:14 pm

Hello,

I was just wodering if the following question can be solved algrebraically:

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?

75
150
300
600
7,500

OA: 600

Thanks a lot for your help.

Best Regards,
Sri

Source: Beat The GMAT — Problem Solving | Sun Oct 13, 2013 3:14 pm

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by [email protected] » Sun Oct 13, 2013 3:56 pm

Hi gmmattesttaker2,

This question is actually perfect for TESTING THE ANSWERS, but since you asked about a "math" approach, here it is:

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

There are some "twists" though: the ratio of items must be 2:1:1 AND half the lenses are useless.

So, we'll start with the LCM of 50, 10 and 30.....LCM = 150

However, half the lenses are useless, so we need to buy TWICE as many as needed = 150 x 2 = 300

AND the ratio is 2:1:1, so we need TWICE as many lenses as each of the other items; 300 x 2 = 600

Final Answer: D

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