An alloy, Alloy K, is made by mixing certain quantities of iron and

Question

An alloy, Alloy K, is made by mixing certain quantities of iron and lead. The total weight of the alloy is 50 kg. What is the ratio of the weight of iron to the weight of lead in Alloy K?

(1) If 4 kg of iron were to be replaced with 4 kg of lead, the percentage of lead, by weight, in Alloy K would become 40%.

(2) The weight of iron per 100 cc is 0.7 times the weight of lead per 100 cc.

chetan2u · Accepted Answer

Iron and lead are mixed to form alloy and weight of alloy is 50 kg.

(1) If 4 kg of iron were to be replaced with 4 kg of lead, the percentage of lead, by weight, in Alloy K would become 40%. 
 40% of 50 kg is 20 kg, so after lead is increased by 4kg, the weight of lead becomes 20kg. 
Thus, Alloy K has 20-4 or 16 kgs of lead and 34 kgs of iron.
 Sufficient

(2) The weight of iron per 100 cc is 0.7 times the weight of lead per 100 cc. 
It just gives us ratio of weight per 100cc.  Nothing about the mix in Alloy K.
Insufficient

A

paradise1234   aayushkrsingh  I hope it helps

Elaborating on statement 2  
It gives you the ratio when the two metals are measured separately. This would depend on the density of material, a fact that does not matter here.

It basically means that if you take equal volume of iron and lead, iron would be 0.7 times weight of lead. If lead weighed 100 kgs, iron would weigh 70 kgs.
Now, if Alloy K has both the metal in equal volume, then you would get an answer. But you do not know in what proportion are the metals iron and lead mixed.

It could be just 10cc of iron with 1000cc of lead or 1000cc of iron with 10cc of lead, two situations which would give different answers.

Kavicogsci · Answer

For anyone who doesn't come from a science background as me I wanted to understand what's going here to understand in reality how these things work out.
In most mixture Q/s we are only concerned about weights that's why density never occurred to us. But if you stay with me till the end this will be super clear for anyone

What is Density? 
Density is a measure of how much  mass (or weight)  is packed into a given  volume .
Mathematically:
Density=Weight (Mass)/Volume 
 
 For example, if a material has a density of  5 kg per liter (5 kg/L) , this means  1 liter of the material weighs 5 kg . 
 Different materials have different densities. For instance:
 
 Iron is denser than water (more weight for the same volume). 
 Lead is denser than iron (even more weight for the same volume).  
  
I have always visualized density as a material whose atoms are packed more closely than less dense material

How Density Affects Weight 
The  weight  of a material depends on both its  density  and the  volume  present.
Weight = Density * Volume

So whenever in mixture Q/s we are talking about weights, that already accounts for the material's density and material's volume in the mixture. This is why so far we were not worried about density or volume in most of our questions.

If two materials (like iron and lead) have different densities, the same  volume  of each will have different  weights .
 
 Example:
 
 If 1 liter of iron weighs 7 kg (density = 7 kg/L) and 1 liter of lead weighs 10 kg (density = 10 kg/L):
 
 2 liters of iron weigh 14 kg. 
 2 liters of lead weigh 20 kg.

So if we are given density ratio and have to find the  weight ratio , you must know the volume ratio.

Statement 1 vs. Statement 2 
 Why Density Is Implied in Statement 1 
In  Statement 1 , we directly modify the  weight proportions  by adding or removing iron and lead. For example:
 
In Statement 1, the problem directly deals with weights. For example:  
 If 4 kg of iron is replaced with 4 kg of lead, the alloy's total weight remains the same (50 kg), but the proportion of iron and lead changes.  
Here’s why density doesn’t explicitly matter here: 
  
  Weight is a product of density and volume (Weight = Density × Volume).  
 When weight is directly given, it already incorporates the effect of density. That is, the weight reflects how much material is there, considering the material’s density. 
 By swapping equal weights (4 kg of iron with 4 kg of lead), the change is in the  weight ratio    
Thus, you can solve Statement 1 without worrying about density because the problem is framed entirely in terms of weights and we are also asked ratio of WEIGHT of IRON and lead and not volume of iron etc, density is already factored into the weights. When we talk about 4 kg of iron or lead, their different densities have already been "accounted for," so we don't need to worry about density separately.   
 Why Density Is Explicit in Statement 2 
In  Statement 2 , instead of giving direct weights, the problem introduces  densities :
  Iron’s weight per 100 cc = 0.7x 
  Lead’s weight per 100 cc = x.

Without knowing the  volumes  of iron and lead in the alloy, we cannot calculate their weights. This introduces ambiguity because:
 
 The weight depends on the  amount (volume)  of each material in the mixture. 
 The ratio of weights requires knowing how much volume of iron and lead was used, but Statement 2 does not provide this information.

If we had the  volume ratio  in which iron and lead are mixed, we could calculate the  weight ratio  as follows:

Given Volume Ratio : Suppose Iron and Lead are mixed in a volume ratio of 2:3
 
 Volume of Iron = 2 units 
 Volume of Lead = 3 units  
 Weight Calculation :
 
 Weight of Iron = Density of Iron×Volume of Iron=0.7x * 2=1.4x 
 Weight of Lead = Density of Lead×Volume of Lead=x*3=3x  
 Weight Ratio :
Weight Ratio of Iron to Lead=1.4x:3x=1.4:3

Side note: 
A)1 liter (L) and cubic centimeters (ccc) are both units of volume. Here's how they relate:
 
  Definition of a Liter: 
 
 A liter is defined as the volume of a cube that is  10 cm on each side . 
 Volume of such a cube = 10 cm×10 cm×10 cm=1000 cubic centimeters   
Thus:
1 liter=1000cc  
Mentioned this because many times densities are given as kg/l

B)Ratio of densities of two materials at a particular volume will always be fixed if external conditions such as temperature, pressure etc are controlled. That's why if I was conducting an experiment and had to mix two alloys I would refer at the densities of those two alloys lets say at 1 litre and then go about mixing right volumes to arrive at my intended weights.
The weight of alloy = Weight of iron + weight of lead
Volume of alloy = Volume of iron + Volume of lead
Density of alloy = Blended density of two materials

paradise1234 · Answer

Hi Bunuel,
The second statement states the ratio of weight of iron to that of lead. The statement doesnt specify that this ratio is a general fact or this ratio holds true for the alloy K. 
To elaborate my doubt,
"The weight of iron per cc". Is this per cc of alloy or per cc of pure iron?
Am I able to convey my doubt?

aayushkrsingh · Answer

Supose volume of alloy k is in multiple of 100cc and we have ratio of weight of iron and lead from statment b so statmwnt b is suffucient

paradise1234 · Answer

Hi  chetan2u ,

The solution does make sense but I still find the second statement ambiguous. It can be interpreted the way  aayushkrsingh  has done and also the way you have interpreted it. In both the cases, the result is exactly the opposite.  OR Is there something about the language of the question that m not focusing on that is making the statement seem ambiguous to me?

chetan2u · Answer

No, the statement is not ambigous. It gives you the ratio when the two metals are measured separately. This would depend on the density of material, a fact that does not matter here.

It basically means that if you take equal volume of iron and lead, iron would be 0.7 times weight of lead. If lead weighed 100 kgs, iron would weigh 70 kgs.
Now, if Alloy K has both the metal in equal volume, then you would get an answer. But you do not know in what proportion are the metals iron and lead mixed.

It could be just 10cc of iron with 1000cc of lead or 1000cc of iron with 10cc of lead, two situations which would give different answers.

playthegame · Answer

This question is gentle reminder that when dealing with ratios the unit of measure should be the same. Meaning, that when the unit of measure is cc. we would need to know about the alloy in the same unit of measure ie cc rather than kilograms. Interesting question somehow I assumed that cc. would not matter and chose D which is the wrong answer.

hughng92 · Answer

Correct me if I am wrong, but if they introduce a concept that is not defined in the question (such as "1000cc", which I had no clue what it was when I worked on this problem), is it safe to assume that I need to consider this CONCEPT as "basic" / "fundamental"? I got the right answer because I thought Statement (ii) was gibberish given I had no idea what it was. But to universally think about this question, I had the same logic: I had no clue what their weight mixture was within the Alloy.

Bunuel · Answer

Statement (2) gives a ratio of the weight per the same volume, which should be clear from the statement itself. The fact that "cc" stands for cubic centimeters is irrelevant to solving the problem. The key task is understanding two things:

1. Statement (2) is talking about the ratio of the weight per same volume of iron and lead.
2. Knowing the weight ratio per volume is not enough to determine the ratio of iron to lead in the total 50 kg of the alloy, since it doesn’t tell us how much of each material was used in terms of volume.

This makes statement (2) insufficient.

Diwen2000 · Answer

Why is  cc is known by anybody  assumed?
 cm3  is the standard expression of  cubic centimeters . What is the necessity of using  cc ? Just to confuse some of the exam takers?

Bunuel · Answer

Please read here: https://gmatclub.com/forum/an-alloy-all ... l#p3451928

KarishmaB · Answer

Total weight = 50 kg
We need the weight of either iron or lead in the alloy to get the ratio of weight of iron : weight of lead

(1) If 4 kg of iron were to be replaced with 4 kg of lead, the percentage of lead, by weight, in Alloy K would become 40%.

The percentage of lead would become 40% of 50 kg i.e. weight of lead would become 20 kg if 4 kg lead were added. This means currently, we have 16 kg lead which means we have 34 kg iron. 
So ratio of weight of iron : weight of lead = 34 : 16
Sufficient Alone

(2) The weight of iron per 100 cc is 0.7 times the weight of lead per 100 cc.

This option gives us the relative densities of the two substances. There is no mention of their their weights in alloy K or volumes in alloy K (using which we could calculate their weights in allow K). This is extraneous information irrelevant to our question. Our question deals with the weights of the substances.

Answer (A)

Ratios are discussed here:

https://youtu.be/5ODENGG5dvc

https://anaprep.com/arithmetic-ratios-the-one-where-it-all-starts/

elslyknight · Answer

This is a good example of a Q/math question where reading every detail is a key reminder.
I swiftly implied statement 2 as suggesting the weight of Lead/iron  per volume of the alloy.  Which is incorrect.

Usernamevisible · Answer

Let:
Iron = I kg
Lead = L kg

Given:
I + L = 50

Need:
I : L

---

Statement (1)

After replacing 4 kg iron with 4 kg lead:

Iron = I - 4
Lead = L + 4

Total weight remains 50 kg.

Lead becomes 40% of alloy:

(L + 4)/50 = 0.4

L + 4 = 20

L = 16

I = 34

Ratio:

I : L = 34 : 16 = 17 : 8

Unique ratio obtained.

Statement (1) is sufficient.

---

Statement (2)

Weight of iron per 100 cc = 0.7 × weight of lead per 100 cc.

This gives only density information:

Density of iron = 0.7 × density of lead

Need weight ratio, not density ratio.

No information about volumes used.

Example 1:
Iron = 10 kg
Lead = 40 kg
Ratio = 1 : 4

Example 2:
Iron = 20 kg
Lead = 30 kg
Ratio = 2 : 3

Both satisfy the density relationship.

Ratio cannot be uniquely determined.

Statement (2) is not sufficient.

---

Answer

A

Statement (1) alone is sufficient.
Statement (2) alone is not sufficient.

An alloy, Alloy K, is made by mixing certain quantities of iron and

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An alloy, Alloy K, is made by mixing certain quantities of iron and

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