Country C has a long-standing policy that every person who earns

Question

Country C has a long-standing policy that every person who earns an annual income above a certain specified amount in any given year must file an income tax return for that year that includes Schedule X. However, for every year, most people who file an income tax return that includes Schedule X do not earn an annual income above the specified amount.

Assume that everyone in Country C always follows the country's tax policies. Select the statement about people in Country C that must be true, given this assumption and the information provided. And select the statement about people in Country C that must be false, given this assumption and the information provided. Make only two selections, one in each column.

chetan2u · Accepted Answer

Country C has a long-standing policy that every person who earns an annual income above a certain specified amount in any given year must file an income tax return for that year that includes Schedule X. However, for every year, most people who file an income tax return that includes Schedule X do not earn an annual income above the specified amount.

We further know that everyone follows the policy.

If we look at the options every two successive options are opposite to each other: (1,2), (3,4) and (5,6), so we have three sets of (True, False) sentence. If we can say any sentence to be 'must be true', the other in the pair can be marked as False.

Let us take that amount to be K dollars and there be 1000 people earning above K dollars. So, everyone, that is all 1000 people, earning above K dollars is surely filing ITR with Sch X.

Let the actual returns filed be Y. However, most of people(of Y) filing ITR with sch X have income below K dollars.
So Y is surely more than 2*1000 people or at least 2001 people.

More people earn an income above the specified amount than file Schedule X with their income tax return.
 This has to be FALSE as we know everyone earning above specified amount files Sch X with their ITR.
1000 people earn above K, but at least 2001 file Sch X with ITR.

The other option in the pair will be TRUE, so let us see that sentence.

More people file Schedule X with their income tax return than earn an annual income above the specified amount. 
This comes directly from the para and is TRUE. - 'However, for every year, most people who file an income tax return that includes Schedule X do not earn an annual income above the specified amount.'
At least 2001 file Sch X but 1000 earn above specified amount.

sircasm · Answer

chetan2u  this question appeared in my GMAT Focus prep practice test - just in case it needs to be tagged accordingly.

Bunuel · Answer

Updated the tag. Thank you!

av722 · Answer

More people earn an income above the specified amount than file Schedule X with their income tax return. 
 False  All people that earn income  above  the specified amount file Schedule X, but  not all  people that file schedule X earn income above the specified amount. That means there's no way this choice is true.

More people file Schedule X with their income tax return than earn an annual income above the specified amount. 
 true  This is the opposite of the previous choice, which means this must be true.

More people file Schedule X than earn an income below the specified amount. 
We don't know anything about the proportion or number of people that earn an income below or above the specified amount. This may or may not be true.

More people earn an income below the specified amount than file Schedule X. 
Same as last choice.

Most people file Schedule X. 
We only know that  all  people that earn above the specified amount and  some  people that don't earn above the specified amount file schedule X. But we have no idea what the proportion of those that file schedule X are to all people in country C.

Most people do not file Schedule X. 
Same as the last choice.

Elite097 · Answer

Reason why C is not correct:

C: More people file Schedule X than earn an income below the specified amount.

What does this mean?

This implies that the total number of people filing Schedule X is greater than the total number of people earning below the threshold.
Why isn’t this necessarily true?

The observation only tells us about the proportion of people filing Schedule X who earn below the threshold. It does not give information about the total number of people in the country earning below the threshold.
It is entirely possible that the number of people earning below the threshold (who may or may not file Schedule X) is much larger than the number of people filing Schedule X.
For example:
Suppose 10,000 people file Schedule X, and 7,000 of them earn below the threshold.
If the total number of people earning below the threshold in the country is 50,000, this would mean C is false.

True Statements:
B: More people file Schedule X with their income tax return than earn an annual income above the specified amount.

Why is this true?
By the given observation, most people filing Schedule X earn below the specified threshold.
This means the total number of Schedule X filers must exceed the total number of people earning above the threshold.
For example:
If 100 people file Schedule X, and 80 of them earn below the threshold, only 20 earn above the threshold. Clearly, the total number of Schedule X filers (100) is greater than the number earning above the threshold (20).
False Statements:
A: More people earn an income above the specified amount than file Schedule X with their income tax return.

Why is this false?
By policy, everyone earning above the threshold must file Schedule X.
Therefore, the number of people earning above the threshold cannot exceed the number of people filing Schedule X—it will either be equal to or less than the number of Schedule X filers.
Since most Schedule X filers earn below the threshold, the number of Schedule X filers is greater than the number of people earning above the threshold, making this statement false.

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=83915 --- Harsha GMAT-Club-Forum-1chz0awn.png GMAT-Club-Forum-51fyfvkg.png

soumyab12 · Answer

Even thought people earning more than the threshold are supposed to file schedule X, is it necessary they actually are doing that? What if there are people who must file X but are not abiding by the law? This is why I was not able to get any solution for the FALSE statement

Bunuel · Answer

The question itself says,  “Assume that everyone in Country C always follows the country’s tax policies.”  That assumption makes your doubt irrelevant, there are no cases where someone is supposed to file Schedule X but doesn’t.

Country C has a long-standing policy that every person who earns

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True	False
		More people earn an income above the specified amount than file Schedule X with their income tax return.
		More people file Schedule X with their income tax return than earn an annual income above the specified amount.
		More people file Schedule X than earn an income below the specified amount.
		More people earn an income below the specified amount than file Schedule X.
		Most people file Schedule X.
		Most people do not file Schedule X.

GMAT Two-part Analysis (TPA) Questions

Country C has a long-standing policy that every person who earns

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