Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 25 Jul 2012
Posts: 73
Location: United States

Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
16 Jul 2013, 10:37
1
This post received KUDOS
13
This post was BOOKMARKED
Question Stats:
37% (09:09) correct 63% (01:34) wrong based on 465 sessions
HideShow timer Statistics
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. 7,500
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^



Math Expert
Joined: 02 Sep 2009
Posts: 44351

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
16 Jul 2013, 11:11
4
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
DelSingh 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. 7,500
 If you have links to similar questions, please post! Thanks I'd use backsolving for this question. Check option C first: 300 lenses = 150 usable lenses = 75 tubes = 75 eyepieces. We cannot buy 75 tubes or 75 eyepieces, so that not to have leftovers. A and B are automatically out. Check D: 600 lenses = 300 usable lenses = 150 tubes = 150 eyepieces. We CAN buy 150 tubes and 150 eyepieces, so that not to have leftovers. Answer: D. Similar question to practise: acertainshadeofgraypaintisobtainedbymixing3parts94997.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior Manager
Joined: 06 Aug 2011
Posts: 380

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
15 Mar 2014, 00:34
DelSingh 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. 7,500
 If you have links to similar questions, please post! Thanks I was doing in totaly different way.. bt got wrong.. How i did.. L:T:E=2:1:1 T can be bought in packet of 10 and E can be bought in packet of 30.. So i thought not to waste any thing except those useless lense.. I multiplied T by 3.. so we will have 30 30 T and E respectively.. Now we want 60 lenses.. for 60 we will 25 lenses from one packet.. so we will need 3 packets to get 60.. Oh now m geting.. that if we will do like this..then we will other 15 usefull lenses left.. Oh now i got that y i was wrong with this approach.. backsolving is best choice here
_________________
Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11292
Location: United States (CA)
GRE 1: 340 Q170 V170

Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
05 Apr 2015, 15:41
Hi All, This question is perfect for TESTing THE ANSWERS (as Bunuel 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: A 50pack of lenses includes just 25 lenses that we can use, so we CAN'T have just 1 pack of 50 lenses (since a telescope requires 2 lenses, there would be a 'leftover' lens in that 1 pack). Thus, we need to buy our lenses in 'blocks' of 100  which gives us enough lenses for 25 telescopes. Considering that we need to buy our eyepieces in packs of 30, the least multiple is 150. BUT if we are making 150 telescopes, then we need 300 lenses that we can USE, AND we have to account for the extra lenses in each pack that we CAN'T use. 300 x 2 = 600 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7996
Location: Pune, India

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
05 Apr 2015, 21:39
1
This post received KUDOS
Expert's post
2
This post was BOOKMARKED
DelSingh 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. 7,500 You can use LCM to solve the question. Each pack of lenses has 25 usable lenses, tubes come in pack of 10 and eyepieces in pack of 30. You want no leftover pieces so find the LCM of 25, 10 and 30 which is 150 (assuming each telescope needs 1 lens). In this case, she would need to buy 6 packs of lenses. But she needs 2 lenses per telescope so she buys 12 packs of lenses i.e. a total of 12*50 = 600 lenses.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 29 Nov 2011
Posts: 114

Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
26 Aug 2015, 11:58
Karishma, i like the concept, but i guess LCM would be 300 rather than 150 and 300/25 = 12 and 12* 50 = 600



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7996
Location: Pune, India

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
27 Aug 2015, 01:46
sudhirmadaan wrote: Karishma, i like the concept, but i guess LCM would be 300 rather than 150 and 300/25 = 12 and 12* 50 = 600 Why would the LCM be 300? LCM of 25 (half the lenses from each pack are not usable), 10 and 30 is 150. So you need 6 packets of lenses. This assumes 1 lens so you double just the number of packs of lenses to get 12 which gives you 600 lenses.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 07 Apr 2015
Posts: 179

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
27 Aug 2015, 01:58
VeritasPrepKarishma wrote: You can use LCM to solve the question. Each pack of lenses has 25 usable lenses, tubes come in pack of 10 and eyepieces in pack of 30. You want no leftover pieces so find the LCM of 25, 10 and 30 which is 150 (assuming each telescope needs 1 lens). In this case, she would need to buy 6 packs of lenses. But she needs 2 lenses per telescope so she buys 12 packs of lenses i.e. a total of 12*50 = 600 lenses. I did it the same way, however forgot to account for double. And I am a bit confused by it, because if we take the LCM of 25 we already account only for the usable lenses, right? So the resulting LCM of 150 should already reflect that we can only take half of the amount? Thats why I multiplied 150*2 to get 300, to account for the fact that we took only the LCM of 25 and not 50. Would be great if you could clarify, if you understand what i mean



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7996
Location: Pune, India

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
27 Aug 2015, 04:26
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
noTh1ng wrote: VeritasPrepKarishma wrote: You can use LCM to solve the question. Each pack of lenses has 25 usable lenses, tubes come in pack of 10 and eyepieces in pack of 30. You want no leftover pieces so find the LCM of 25, 10 and 30 which is 150 (assuming each telescope needs 1 lens). In this case, she would need to buy 6 packs of lenses. But she needs 2 lenses per telescope so she buys 12 packs of lenses i.e. a total of 12*50 = 600 lenses. I did it the same way, however forgot to account for double. And I am a bit confused by it, because if we take the LCM of 25 we already account only for the usable lenses, right? So the resulting LCM of 150 should already reflect that we can only take half of the amount? Thats why I multiplied 150*2 to get 300, to account for the fact that we took only the LCM of 25 and not 50. Would be great if you could clarify, if you understand what i mean LCM of 3 numbers is that number which is a multiple of all of them. You get lenses in multiples of 25 (one packet has 25 usable lenses), tubes in multiples of 10 and eye pieces in multiples of 30. You need to use all these. So how can you ensure that there is no wastage? 25, 10 and 30 must be divisible by the number of telescopes. Take LCM 150 to get the minimum number of telescopes and you get 150 telescopes. So buy 6 packs of lenses, 15 packs of tubes and 5 packs of eye pieces for making the minimum number of telescopes which is 150. But you need 2 lenses per telescope so buy another 6 packs of lenses. Total you bought 12 pack of lenses which means you bought 12*50 = 600 lenses (usable and non usable) Hope this helps.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11292
Location: United States (CA)
GRE 1: 340 Q170 V170

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
27 Aug 2015, 13:42
Hi noTh1ng, It might help if you visualize what it takes to make a group of telescopes. If you buy a 'block' of 100 lenses, then you have 50 useful lens and 50 lens that you CAN'T use. Since it takes 2 lenses to make a telescope, those 50 useful lens will give you 25 telescopes.... The eyepieces come in packs of 30. Since we're not supposed to have any 'leftover' parts, we need the LCM of 25 and 30.....150 TELESCOPES Those 150 telescopes would require 5 packs of eyepieces and 6 BLOCKS of lenses (remember that, in this case, a 'block' is 100 lenses).... 6(100) = 600 lenses. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 29 Jul 2015
Posts: 159

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
27 Aug 2015, 18:26
Things needed for making a telescope along with their respective number of packs are shown below
Things needed  2 lenses 1 tube 1 eyepiece Packs 1 1 1 No. of things 50 10 30
This combination of pack is not possible because half of the lenses are unusable which means 25 lenses are left for use. But the number of usable lenses should be multiple of 2. Next possible combination
Things needed 2 lenses 1 tube 1 eyepiece Packs 2 2 2 No. of things 100 20 60
In this case the number of usable lenses (50) is a multiple of 2. But there will be wastage of eyepieces and lenses as there are just 20 tubes. So,to prevent any wastage, lcm of 100,20 and 60 must be taken. The lcm will be 600. And the combination without any wastage will look like this
Things needed 2 lenses 1 tube 1 eyepiece Packs 12 30 10 No. of things 600 300 300
Answer D



Manager
Joined: 23 Dec 2013
Posts: 228
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
21 May 2017, 16:49
DelSingh 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. 7,500 Backsolving makes the most sense here. If we start with (C), then she buys 300 lenses, of which 150 are usable, that make 75 telescopes. But she cannot buy tubes in factors of 75. So (C) is eliminated. Next, for (D), she buys 600 lenses, of which 300 are usable, that make 150 telescopes. 150 is a multiple of both 10 and 30, so (D) is the correct answer.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2319
Location: United States (CA)

Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu [#permalink]
Show Tags
21 Jan 2018, 20:06
DelSingh 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. 7,500 Let’s assume that Mira is making n telescopes, thus she need 2n lenses, n tubes and n eyepieces. Let’s also assume that she bought a packs of lenses, b packs of tubes and c packs of eyepieces, thus she bought 50a lenses, 10b tubes and 30c eyepieces. Since she can only use half of the lenses, she used 25a lenses. So we have: 2n = 25a, n = 10b and n = 30c Since n, a, b, and c have to be integers, we see that the smallest value of a is 2. If that is the case, then n will be 25, but then b will be 2.5, which is not an integer. So a can’t be 2. The next smallest value of a is 4. If that is the case, then n will be 50 and b will be 5, but then c will be 5/3, which is not an integer. So a can’t be 4. Notice that a has to be even in order for n to be an integer and we can keep trying values for a (and make sure that b and c will be integers also): If a = 6, then n = 75 and b = 7.5. If a = 8, then n = 100 and c = 10/3. If a = 10, then n = 125 and b = 12.5. If a = 12, then n = 150 and b = 15 and c = 5. We’ve founded the value of a (a = 12) so that n, b and c are all integers. Thus the minimum number of lenses she’s used is 25 x 12 = 300. However, she needed to buy twice as many lenses, or 600 lenses, since half of them are unusable. Alternate Solution: Let’s test each answer choice, starting from the smallest: Answer Choice A: 75 lenses cannot be purchased since lenses come in packs of 50 Answer Choice B: If 150 lenses are purchased, only 75 of them can be used for making a telescope and since each telescope uses two lenses, one usable lens will be leftover. Answer Choice C: If 300 lenses are purchased, only 150 of them can be used for making a telescope and since each telescope uses two lenses, a total of 75 telescopes can be made. But to make 75 telescopes, Mira will have to buy at least 8 packs of tubes for a total of 8 x 10 = 80 tubes; 5 of which will be leftover. Answer Choice D: If 600 lenses are purchased, only 300 of them can be used for making a telescope and since each telescope uses two lenses, a total of 150 telescopes can be made. To make 150 telescopes, Mira can purchase 15 packs of tubes and 5 packs of eyepieces with no leftover parts besides unusable eyepieces. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Mira is making telescopes, each consisting of 2 lenses, 1 tu
[#permalink]
21 Jan 2018, 20:06






