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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] New post 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.
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Re: How to solve this [#permalink] New post 11 Feb 2011, 02:50
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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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new [#permalink] New post 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 !!!
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Re: How to solve this [#permalink] New post 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] New post 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
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Re: Material A costs $3 per kilogram, and Material B costs $5 [#permalink] New post 13 Jun 2013, 01:15
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Re: Material A costs $3 per kilogram, and Material B costs $5 [#permalink] New post 15 Jun 2013, 13:13
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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 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] New post 17 Jul 2014, 07:02
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Re: Material A costs $3 per kilogram, and Material B costs $5 [#permalink] New post 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.

Answer: B.


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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