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# Material A costs $3 per kilogram, and Material B costs$5

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Material A costs $3 per kilogram, and Material B costs$5 [#permalink]  11 Feb 2011, 01:26
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Material A costs $3 per kilogram, and Material B costs$5 per kilogram. If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B, is x > y ?

(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40. [Reveal] Spoiler: OA Last edited by Bunuel on 07 Dec 2012, 09:35, edited 2 times in total. Edited the question and added the OA. Math Expert Joined: 02 Sep 2009 Posts: 27215 Followers: 4228 Kudos [?]: 41011 [3] , given: 5654 Re: How to solve this [#permalink] 11 Feb 2011, 02:50 3 This post received KUDOS Expert's post 1 This post was BOOKMARKED alltimeacheiver wrote: Material A costs$3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x >y? (1) y > 4 (2) The cost of the 10 kilograms of material K is less than$40

Material A costs $3 per kilogram, and material B costs$5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x >y?

Given: x+y=10. Question: is x>y?

(1) y > 4. Clearly insufficient: if y=4.5<x=5.5 the answer will be YES but if y=6>x=4 the answer will be NO.

(2) The cost of the 10 kilograms of material K is less than $40 ---> 3x+5y<40, as y=10-x then: 3x+5(10-x)<40 --> 2x>10 --> x>5, so x>y. Sufficient. Answer: B. _________________ Intern Joined: 21 Feb 2011 Posts: 1 Followers: 0 Kudos [?]: 0 [0], given: 0 new [#permalink] 10 Mar 2011, 04:42 Material A cost 3$/kg and B cost 5$/kg. If 10 kg of material K consist of x kg of A and y kg of B, is x>y? 1- y>4 2- the cost of 10kg of K is less than$40.

Solution: -

1) Insufficient
Material A cost 3$/kg and B cost 5$/kg
x+y=10 and y>4 is all we have from statement 1. Since the total price is not fixed, (x,y) can be anything satisfying x+y=10 ....even (5,5) can't be wrong in this case

2) Sufficient
Material A cost 3$/kg and B cost 5$/kg
x+y=10 and the cost of 10kg of K is less than $40. Therefore, 3x+5y<40 => 3x+(10-x)5<40 => 10<2x => 5<x So, x>5 and x+y=10 means x>y Hope it helps !!! _________________ Set out each day believing in your dreams. Know without a doubt that you were made for amazing things. Director Status: Matriculating Affiliations: Chicago Booth Class of 2015 Joined: 03 Feb 2011 Posts: 926 Followers: 13 Kudos [?]: 219 [0], given: 123 Re: How to solve this [#permalink] 10 Mar 2011, 06:22 x = 10 - y Rephrasing the question - Is x > y? or Is 10 - y > y Is y < 5 ? 1. Insufficient 2. Sufficient 3x + 5y < 40 3(10 - y) + 4y < 40 2y < 10 Hence y < 5 Hence B. alltimeacheiver wrote: Material A costs$3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x > y? (1) y > 4 (2) The cost of the 10 kilograms of material K is less than$40
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material [#permalink]  16 Feb 2012, 07:47
The answer has to be B.

Let's setup the weighted average equation for this question:

$$x$$ kilograms at 3$per Kilogram $$y$$ kilograms at 5$ per Kilogram
Yields $$10$$ kilograms at z$per Kilogram We also know that $$x+y=10$$ So Equation would be : $$3(x)+5(y)=10(z)$$ Now let's look at the statements: Statement 1: $$y>4$$ Remember: $$x+y=10$$ So: $$x$$ could range between 0 and 6. Insufficient Statement 2: Cost is $$<40$$ So $$3(x)+5(y)<40$$ But $$x+y=10$$ so $$x=10-y$$ So $$3(10-y)+5(y)<40$$ So $$30-2y+5y<40$$ So $$2y<10$$ So $$y<5$$ If $$y<5$$ then $$x>5$$ so $$x>y$$ Sufficient Hence B _________________ "Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde Math Expert Joined: 02 Sep 2009 Posts: 27215 Followers: 4228 Kudos [?]: 41011 [1] , given: 5654 Re: Material A costs$3 per kilogram, and Material B costs $5 [#permalink] 13 Jun 2013, 01:15 1 This post received KUDOS Expert's post Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE All DS Mixture Problems to practice: search.php?search_id=tag&tag_id=43 All PS Mixture Problems to practice: search.php?search_id=tag&tag_id=114 _________________ Moderator Joined: 25 Apr 2012 Posts: 734 Location: India GPA: 3.21 WE: Business Development (Other) Followers: 26 Kudos [?]: 419 [2] , given: 723 Re: Material A costs$3 per kilogram, and Material B costs $5 [#permalink] 15 Jun 2013, 13:13 2 This post received KUDOS alltimeacheiver wrote: Material A costs$3 per kilogram, and Material B costs $5 per kilogram. If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B, is x > y ? (1) y > 4 (2) The cost of the 10 kilograms of Material K is less than$40.

Material K cost "C" can be found out by calculating

C= (3*x+5*y)/10

Now the cost C will be close to Material A cost if x is more than y and vice versa

from St 1 we have y>4
For eg y=5, x=5 Cost of Material K will be $4/kg (in between price of Material A and Material B) now if x=4,y=6 ,Cost of material K will be be$ 4.2/kg
if x=1,y=9 then Cost of material will be 4.8$per kg but if we take y=4 and x=6 we get cost of material K as$ 3.8 per kg less than $4 which would have been the price had both material A and B were added equally. Therefore if x>y we should have price of Material K <$ 4kg

Hence St1 alone not sufficient as we can have x=y or x<y

St 2, The cost of the 10 kilograms of Material K is less than $40.[/quote] Cost of Material per kg <$4 which meets our above requirement which means x>y

Therefore ans st B
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]  17 Jul 2014, 07:02
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]  27 Oct 2014, 01:21
Bunuel wrote:
alltimeacheiver wrote:
Material A costs $3 per kilogram, and material B costs$5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x >y?

(1) y > 4
(2) The cost of the 10 kilograms of material K is less than $40 Material A costs$3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x >y? Given: x+y=10. Question: is x>y? (1) y > 4. Clearly insufficient: if y=4.5<x=5.5 the answer will be YES but if y=6>x=4 the answer will be NO. (2) The cost of the 10 kilograms of material K is less than$40 ---> 3x+5y<40, as y=10-x then: 3x+5(10-x)<40 --> 2x>10 --> x>5, so x>y. Sufficient.

Bunuel,
Can you, please, advise, if the problem stated that x and y can only be integers, would statement 1 be sufficient? I guess YES.
Re: Material A costs $3 per kilogram, and Material B costs$5   [#permalink] 27 Oct 2014, 01:21
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