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

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

Originally posted by alltimeacheiver on 11 Feb 2011, 02:26.
Last edited by Bunuel on 05 Aug 2017, 00:16, edited 3 times in total.
Edited the question and added the OA.
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Re: Material A costs $3 per kilogram, and Material B costs $5 per kilogram  [#permalink]

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New post 11 Feb 2011, 03:50
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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


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

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

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New post 10 Mar 2011, 05:42
5
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 !!!
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Re: Material A costs $3 per kilogram, and Material B costs $5 per kilogram  [#permalink]

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New post 10 Mar 2011, 07:22
3
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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New post 13 Jun 2013, 02:15
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Re: Material A costs $3 per kilogram, and Material B costs $5 per kilogram  [#permalink]

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New post 15 Jun 2013, 14:13
2
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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New post 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.

Answer: B.


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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New post 28 Nov 2015, 07:59
2
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.

Answer: B.


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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New post 23 Dec 2015, 07:42
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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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New post 16 Mar 2016, 07:35
1
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.
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Re: Material A costs $3 per kilogram, and Material B costs $5 per kilogram  [#permalink]

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New post 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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New post 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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New post 05 Apr 2017, 11:34
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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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New post 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.
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Re: Material A costs $3 per kilogram, and Material B costs $5 per kilogram  [#permalink]

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

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New post 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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New post 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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New post 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]

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New post 23 Oct 2017, 05:19
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mixture price is less than 40/10 -- rs 4 per kg

between 3 and 5 if less than 4 then it contains more x thats all simple
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Re: Material A costs $3 per kilogram, and Material B costs $5 per kilogram   [#permalink] 23 Oct 2017, 05:19

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