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Material

by saurabhmahajan » Tue May 04, 2010 7:25 pm
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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
ALONE is sufficient, but statement (1) alone is not sufficient.
B. Statement (2)
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My answer was E as we cant find out the total number of kgs for any type of material.
But answer is B
Plz explain.

thanks and regards,
saurabh.
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Source: — Data Sufficiency |
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by sk818020 » Tue May 04, 2010 7:41 pm
From the passage:

x+y=10
3x+5y=?

(1) y>4. This is insufficient because it tells us the following will apply;

From the passage x + y = 10, thus;

5 + 5 =10
or 5.1+4.9=10
or 4.9+5.1=10

It tells us that x=y, x<y, or y<x, because it does not say x or y have to be integers. So, (1) not sufficient.

(2) Cost of 10 kilograms is less than $40

From the passage this tells us;

3x + 5y < 40, also because x+y=10,

x=10-y, thus;

3(10-y) + 5y < 40

30 - 3y +5y < 40

2y < 10

y < 5


Thus, if x+y =10 and y<5 then x>y. (2) sufficient. So the answer is B.
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by kstv » Wed May 05, 2010 12:01 am
3x+5y < 40 -------1
x+y = 10 -----2
or 3x+3y = 30
3x+3y+2y < 40
30+2y< 40
2y < 10 or y < 5
if y < 5 , x > 5
IMO B
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by gmatmachoman » Wed May 05, 2010 5:12 am
Rule of alligation/Mixtures :

Quantity of cheaper/Quantity of Dearer = (Cost of Dearer -Cost of mixture)/(Cost of Mixture- Cost of cheaper)

I am taking Cost of Mixture as 3.9$ ( as it has to be less than 4$)

X/Y =(5- 3.9)/(3.9-3)
(1.1)/(0.9)

=1.22

so X =1.22Y

Implies that X >Y

You can try cost of mixture to be bare minimum as 3.1$ .Still X>Y

Pick [spoiler]B
[/spoiler]
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by [email protected] » Tue Mar 13, 2012 6:16 am
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.


Try however, the answer is B

Statement 1 does not have the total cost or the weighted average cost. How can you calculate anything...
Take number of total costs and you find that the answer for x will be variable.
Hence A is simply not sufficient...
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by GMATGuruNY » Tue Mar 13, 2012 7:11 am
saurabhmahajan 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.
Since statement 1 is in terms of y, we should rephrase the question stem in terms of y.

x = the number of kilograms of A.
y = the number of kilograms of B.
Since a total of 10 kilograms are purchased:
x + y = 10.
x = 10-y.

Substituting x=10-y into the question stem (Is x>y?), we get:
10-y > y?
10 > 2y?
5 > y?

Question rephrased: Is y < 5?

Statement 1: y>4.
Since it's possible that y=4.5 or that y=6, no way to determine whether y<5.
INSUFFICIENT.

Statement 2: The cost of the 10 kilograms of material K is less than $40.
Since the cost of each of the x kilograms is $3 and the cost of each of the y kilograms is $5, we get:
3x + 5y < 40.

Substituting x=10-y into 3x+5y<40, we get:
3(10-y) + 5y < 40
30 - 3y + 5y < 40
2y < 10
y < 5.
SUFFICIENT.

The correct answer is B.
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by Brent@GMATPrepNow » Thu Nov 14, 2019 7:09 am
saurabhmahajan 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.
Given: Material A costs $3 per kilogram, and Material B costs $5 per kilogram. 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B
We can write: x + y = 10
We can also say the COST of 10 kg of Material K = 3x + 5y

Target question: Is x > y?

Statement 1: y > 4
How does this information work with the fact that x + y = 10?
We'll, there are several possible cases that satisfy statement 1 (and satisfy the equation x + y = 10). Here are two:
Case a: y = 4.5 and x = 5.5. In this case, the answer to the target question is YES, x IS greater than y
Case b: y = 6 and x = 4. In this case, the answer to the target question is NO, x in NOT greater than y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The cost of the 10 kilograms of Material K is LESS THAN $40.
We already know that the COST of 10 kg of Material K = 3x + 5y
So, we can now write: 3x + 5y < 40
Let's reduce this inequality to ONE variable by taking x + y = 10 and rewriting it to get: x = 10 - y
Now replace the x in the inequality with 10-y to get: 3(10-y) + 5y < 40
Expand: 30 - 3y+ 5y < 40
Simplify: 30 + 2y < 40
Subtract 30 from both sides: 2y < 10
Divide both sides by 2 to get: y < 5
Since y is LESS THAN 5, and since x and y add to 10, we know that x is GREATER THAN 5
In other words: y < 5 < x
We can clearly see that the answer to the target question is YES, x IS greater than y
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Brent
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