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

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

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11 Feb 2011, 02:26
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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 05 Aug 2017, 00:16, edited 3 times in total. Edited the question and added the OA. Math Expert Joined: 02 Sep 2009 Posts: 44290 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 11 Feb 2011, 03:50 12 This post received KUDOS Expert's post 24 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 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 10 Mar 2011, 05:42 4 This post received KUDOS Material A cost 3$/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: 834 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 10 Mar 2011, 07:22 3 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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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram [#permalink]

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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: 44290 Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#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: 720 Location: India GPA: 3.21 WE: Business Development (Other) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#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 per kilogram [#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 per kilogram [#permalink]

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28 Nov 2015, 07:59
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Expert's post
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 per kilogram [#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 per kilogram [#permalink]

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16 Mar 2016, 07:35
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Expert's post
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 per kilogram [#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 per kilogram [#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 per kilogram [#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 per kilogram [#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 per kilogram [#permalink]

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05 Aug 2017, 00:13
We can work this out using weighted average method as well.

Statement A: y>4 - clearly insufficient.

Statement B: Cost of 10kg of Material K is less than $40. Cost of A is$3/kg and of B is $5/kg. Average cost of 10 kgs of combined material is <$4 ($40/10kgs). Using weighted average method: 3------------------------5 l------------4 Weighted average is less than 4, which means ratio of quantity of A:B i.e. x:y is skewed towards A. Thus, x>y. Director Joined: 29 Jun 2017 Posts: 518 GMAT 1: 570 Q49 V19 GPA: 4 WE: Engineering (Transportation) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 17 Aug 2017, 03:23 1) A 3$.
B 5$. x+y =10 x. 5 4 3 y. 5 6 7 x=y and x<y. Insufficient A,D gone 2) A 3$ and B 5 $suppose all material is A then cost will be 30$ when x=10
suppose all material is B then cost will be 50 $when y = 10 and when x=y=5 equal the cost is 40$

now since it is given that cost < 40$means proportion of A is more than B x>y clearly B is sufficient B is answer _________________ Give Kudos for correct answer and/or if you like the solution. Manager Joined: 13 Mar 2013 Posts: 176 Location: United States Concentration: Leadership, Technology GPA: 3.5 WE: Engineering (Telecommunications) Re: Material A costs$3 per kilogram, and Material B costs $5 per kilogram [#permalink] ### Show Tags 17 Aug 2017, 09:44 1) Insufficient Material A cost 3$/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
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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram [#permalink]

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19 Aug 2017, 01:03
Very nice Question ... I got it wrong because I didn't calculated statement 2 fully.
I have come down to below points:
3x+7Y<40, 4x+6Y<40 and so on but I didn't solve without knowing that all will give the solution x>5.
and as x+y is 10, x must be 6 and here we get the answer.

Kudos to the question.
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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram [#permalink]

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29 Aug 2017, 12:13
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. The question can solved using weighted average concept easily without pen and paper calculation i.e can be solved within 30 seconds. 10kg of mixture uses x kg of Material A and y kg of Material B. If both X and Y are equal, the cost of the 10kg of material K will be right in the middle of$30 and $50 i.e. at$40.

But using stmt B, 10kg of K costs less than $40 dollars i.e. the cost shift towards$30. Hence clearly the quantity of X is more and Y. Hence B is sufficient.

I hope that helps.
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Re: Material A costs $3 per kilogram, and Material B costs$5 per kilogram   [#permalink] 29 Aug 2017, 12:13

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