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bhanu29
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Density refers to the heaviness of a certain amount of a substance: 20 Nov 2025, 06:19
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“Density” refers to the heaviness of a certain amount of a substance: A handful of a denser substance will be heavier than a handful of a less dense substance. A 50–50 alloy is an equal mix of two elements that are metals; if Element 1 is denser than Element 2, the density of a 50–50 alloy of these elements falls in between the densities of those two elements. Copper is denser than aluminum—which is denser than magnesium. X is a 50–50 alloy of two of these three elements. Does X contain magnesium?

(1) X is less dense than an alloy of copper and aluminum.

(2) X is denser than aluminum.
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Density refers to the heaviness of a certain amount of a substance: 20 Nov 2025, 06:37
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“Density” refers to the heaviness of a certain amount of a substance: A handful of a denser substance will be heavier than a handful of a less dense substance. A 50–50 alloy is an equal mix of two elements that are metals; if Element 1 is denser than Element 2, the density of a 50–50 alloy of these elements falls in between the densities of those two elements. Copper is denser than aluminum—which is denser than magnesium. X is a 50–50 alloy of two of these three elements. Does X contain magnesium?

Given: the density order is copper > aluminum > magnesium.

(1) X is less dense than an alloy of copper and aluminum.

Since the density of a copper-aluminum alloy is between aluminum and copper, X must be less dense than this alloy. This means X cannot be a copper-aluminum alloy itself. Therefore, X must be either a copper-magnesium alloy or an aluminum-magnesium alloy, both of which contain magnesium. Sufficient.

(2) X is denser than aluminum.

This means X cannot be an aluminum-magnesium alloy, as its density would be less than aluminum. Therefore, X must be either a copper-aluminum alloy or a copper-magnesium alloy. If X is copper-aluminum, it does not contain magnesium, if X is copper-magnesium, it does contain magnesium. Not sufficient.

Answer: A.
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Density refers to the heaviness of a certain amount of a substance: 20 Nov 2025, 06:42
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“Density” refers to the heaviness of a certain amount of a substance: A handful of a denser substance will be heavier than a handful of a less dense substance. A 50–50 alloy is an equal mix of two elements that are metals; if Element 1 is denser than Element 2, the density of a 50–50 alloy of these elements falls in between the densities of those two elements. Copper is denser than aluminum—which is denser than magnesium. X is a 50–50 alloy of two of these three elements. Does X contain magnesium?

Given: the density order is copper > aluminum > magnesium.

(1) X is less dense than an alloy of copper and aluminum.

Since the density of a copper-aluminum alloy is between aluminum and copper, X must be less dense than this alloy. This means X cannot be a copper-aluminum alloy itself. Therefore, X must be either a copper-magnesium alloy or an aluminum-magnesium alloy, both of which contain magnesium. Sufficient.

(2) X is denser than aluminum.

This means X cannot be an aluminum-magnesium alloy, as its density would be less than aluminum. Therefore, X must be either a copper-aluminum alloy or a copper-magnesium alloy. If X is copper-aluminum, it does not contain magnesium, if X is copper-magnesium, it does contain magnesium. Not sufficient.

Answer: A.
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Bunuel are we supposed to assume "an alloy of Cu and Al" is 50-50 Alloy?

because if we don't assume that A may not be sufficient (may be I am wrong, please correct me if I am)

let’s say"an alloy of Cu and Al" has 99% Cu and 1% Al

in this case we can have 50-50 of Cu and Al which will be less Denser... (No Mg)

Now if we have Cu 50% and Mg 50% this will be less denser (Yes Mg)

So we can’t conclusively say if Mg is present or not.

Where am I going wrong?
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Density refers to the heaviness of a certain amount of a substance: 20 Nov 2025, 06:47
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Bunuel are we supposed to assume "an alloy of Cu and Al" is 50-50 Alloy?

because if we don't assume that A may not be sufficient (may be I am wrong, please correct me if I am)

let’s say"an alloy of Cu and Al" has 99% Cu and 1% Al

in this case we can have 50-50 of Cu and Al which will be less Denser... (No Mg)

Now if we have Cu 50% and Mg 50% this will be less denser (Yes Mg)

So we can’t conclusively say if Mg is present or not.

Where am I going wrong?
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Yes, it is 50–50 because the passage defines an alloy only as a 50–50 mix, so the statements use that same definition of an alloy.
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Density refers to the heaviness of a certain amount of a substance: 20 Nov 2025, 16:21
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“Density” refers to the heaviness of a certain amount of a substance: A handful of a denser substance will be heavier than a handful of a less dense substance. A 50–50 alloy is an equal mix of two elements that are metals; if Element 1 is denser than Element 2, the density of a 50–50 alloy of these elements falls in between the densities of those two elements. Copper is denser than aluminum—which is denser than magnesium. X is a 50–50 alloy of two of these three elements. Does X contain magnesium?

Key information from the passage:

Density of copper > Density of aluminum > Density of magnesium

X is a 50–50 alloy of two of these three elements.

(1) X is less dense than an alloy of copper and aluminum.

Since X is a 50–50 alloy of two of the three elements, the only way X can be less dense than an alloy of copper and aluminum is by containing magnesium, the least dense of the three elements, which would pull its density below that of an alloy of copper and aluminum.

For this statement, don't have to worry about whether X is an alloy of aluminum and magnesium or an alloy of copper and magnesium. All that matters is that this statement indicates that X must contain magnesium.

Sufficient.

(2) X is denser than aluminum.

This statement is tricky because we may get the impression that, for X to be denser than aluminum, it must be an alloy of copper and aluminum, since magnesium is less dense than aluminum.

Notice, however, that we are not given the relative densities of copper, aluminum, and magnesium. All we are given is the order of their densities.

So, for example, given what the passage says, copper could have a density of 10k, aluminum could have a density of 3k, and magnesium could have a density of 1k. In such a case, an alloy of copper and magnesium could easily have a higher density than aluminum.

Thus, we see that, given what this statement says, X could be an alloy of copper and aluminum or an alloy of copper and magnesium.

(By the way, one thing that might save us from mistakenly deciding that this statement is sufficient is noticing that statement (1) confirms that X contains magnesium. So, if this statement were to confirm that X does not contain magnesium, it would contradict statement 1, and the statements in a DS question cannot contradict each other. So, that's a sign that we likely have something wrong if we think that this statement confirms that X does not contain magnesium.)

Insufficient.

Correct answer: A
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Density refers to the heaviness of a certain amount of a substance: 21 Nov 2025, 20:04
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“Density” refers to the heaviness of a certain amount of a substance: A handful of a denser substance will be heavier than a handful of a less dense substance. A 50–50 alloy is an equal mix of two elements that are metals; if Element 1 is denser than Element 2, the density of a 50–50 alloy of these elements falls in between the densities of those two elements. Copper is denser than aluminum—which is denser than magnesium. X is a 50–50 alloy of two of these three elements. Does X contain magnesium?

(1) X is less dense than an alloy of copper and aluminum.

(2) X is denser than aluminum.
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I would say the wording of statement (1) is not very clear.

It needed to say "X is less dense than any alloy of copper and aluminum" even though it does imply the same thing, perhaps. The implication of the statement as given is somewhat confusing.
Or it needed to say "X is less dense than a 50-50 alloy of copper and aluminum."

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Density refers to the heaviness of a certain amount of a substance: 21 Nov 2025, 22:58
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I would say the wording of statement (1) is not very clear.

It needed to say "X is less dense than any alloy of copper and aluminum" even though it does imply the same thing, perhaps. The implication of the statement as given is somewhat confusing.
Or it needed to say "X is less dense than a 50-50 alloy of copper and aluminum."

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Thanks KarishmaB for the reassurance even I was confused how can "an alloy" be equivalent to "a 50-50" Alloy.
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