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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]

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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, 10:35, edited 2 times in total. Edited the question and added the OA. Math Expert Joined: 02 Sep 2009 Posts: 38908 Followers: 7741 Kudos [?]: 106273 [9] , given: 11618 Re: How to solve this [#permalink] Show Tags 11 Feb 2011, 03:50 9 This post received KUDOS Expert's post 14 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 $40 ---> 3x+5y<40, as y=10-x then: 3x+5(10-x)<40 --> 2x>10 --> x>5, so x>y. Sufficient. Answer: B. _________________ Intern Joined: 21 Feb 2011 Posts: 1 Followers: 0 Kudos [?]: 3 [3] , given: 0 new [#permalink] Show Tags 10 Mar 2011, 05:42 3 This post received KUDOS Material A cost 3$/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: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing. Affiliations: University of Chicago Booth School of Business Joined: 03 Feb 2011 Posts: 906 Followers: 14 Kudos [?]: 359 [2] , given: 123 Re: How to solve this [#permalink] Show Tags 10 Mar 2011, 07:22 2 This post received KUDOS 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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16 Feb 2012, 08:47
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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: 38908 Followers: 7741 Kudos [?]: 106273 [2] , given: 11618 Re: Material A costs$3 per kilogram, and Material B costs $5 [#permalink] Show Tags 13 Jun 2013, 02:15 2 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 _________________ Director Joined: 25 Apr 2012 Posts: 727 Location: India GPA: 3.21 WE: Business Development (Other) Followers: 44 Kudos [?]: 748 [2] , given: 723 Re: Material A costs$3 per kilogram, and Material B costs $5 [#permalink] Show Tags 15 Jun 2013, 14:13 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]

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17 Jul 2014, 08:02
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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27 Oct 2014, 02:21
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.
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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28 Oct 2015, 05:48
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I thought that in DS, (1) and (2) could not contradict eachother. However, it seems that they do in this question since

(1) says y> 4 which is the same as y ≥ 5 while

(2) gives us y < 5 which is the same as y ≤ 4

Could someone help me with that ?
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Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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28 Nov 2015, 04:50
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.

Hi...If in the question it is mentioned that x and y are integers, then will the answer be D? because it will lead to contradiction that 'x is not greater than y' or will still answer be b because (there is no clarity whether x may be equal to y or may be less than y'?
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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28 Nov 2015, 07:59
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Alok322 wrote:
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.

Hi...If in the question it is mentioned that x and y are integers, then will the answer be D? because it will lead to contradiction that 'x is not greater than y' or will still answer be b because (there is no clarity whether x may be equal to y or may be less than y'?

If we were told that x and y are integers then y > 4 (5, 6, 7, ...) together with x + y = 10, would be sufficient to say that x is NOT greater than y. But in this case the question would be flawed because the statements would contradict each other which never happens in proper GMAT DS questions.

Hope it's clear.
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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23 Dec 2015, 07:42
Thank you Buennel!

Very important point since i came here with the same problem and i pulled my hair over this for a solid 20 minutes.

If you simplify (2) it results in y < 5. While (1) says that y > 4.

Contradicting? No. We might think its contradictory if we assume that the qty involved are integers (common mistake, since qty usually are).

Do note that the question does not say that x or y are integers. And it is for this reason, otherwise, the question would logically be incorrect.

My takeaway:
1) Always remember that GMAT statements are never contradictory
2) If at some point, it seems like they are contradicting, it could mean
a) i've done it incorrectly
b) they aren't contradicting in the first place! :p
3) In such WP questions, ask yourself, are the quantities divisible into decimals?
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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16 Mar 2016, 07:35
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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. Responding to a pm: Quote: In solving the B part of this question (like in many situation i have faced) 3[5]+5[5]=15+25="40<40" This is my question: [Q-1] Can we ever take 40<40 ie x<x when x is same number. Similarly x>x and so on in GMAT? To be honest, I am not sure what your question means. 40 < 40 is not correct and neither is x < x since both are equal. And no, x > x doesn't work either. If they are the same number, one cannot be greater than the other. You might want to show me the steps of where you come across this problem. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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17 Dec 2016, 11:31
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.

Hi Bunuel,

Can this be solve via weighted average?
By the formulae n1/n2= (m2-m)/(m-m1)
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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08 Jan 2017, 18:51
I thought about this conceptually. Since A costs $3 per kg and B costs$5 per kg, I used that in conjunction with statement 2 to prove sufficiency. In statement 2, 10kg of K is less than $40. Dividing both sides by 10, 1 kg of K is less than$4. Knowing the costs of X and Y, that to me would mean that there would have to be more of A than B to be less than $4 (equal amounts would have it equal$4).

It's not perfect as we could be dealing with integers and you can't assume one of A or B isn't 0....but it's how I went about it.
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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05 Apr 2017, 10:35
I have a question,

the question provide 10=x+y, it's about the weight

but it doesn't mean 3x+5y<40 (money), cuz 40=10k, we don't know the unit price of k, so i don't think it's right.

Is there anything wrong of me? I was confused a litte...hehe
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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05 Apr 2017, 11:34
dxhzhu wrote:
I have a question,

the question provide 10=x+y, it's about the weight

but it doesn't mean 3x+5y<40 (money), cuz 40=10k, we don't know the unit price of k, so i don't think it's right.

Is there anything wrong of me? I was confused a litte...hehe

x + y = 10 ---equation (1)

from stmt-2 we can say 3x + 5y < 40

multiply equation (1) by 3 and you get 3x + 3y = 30

3x + 5y < 40 (to subtract the below equation, consider < as = sign)
3x + 3y = 30

2y < 10 (isnt it? because if you subtract 30 from somthing less than 40 then you get something less than 10)

hence y < 5, it means x > y because x + y = 10

so B is correct. Hope your doubt is clear.
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Re: Material A costs $3 per kilogram, and Material B costs$5 [#permalink]

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30 Apr 2017, 19:45
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