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A is only option which can be derived from statements

B) service industry employees will rise but not sure about 3 times so out

C)no info about productive stuff

D) can't say about no of employees in both sectors

E)can't say about this

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In 2016, the service sector of the labor market had more than three times as many employees as the manufacturing sector had, yet the most prominent economists predict that by this time next year, the manufacturing segment will have just as many employees as the service sector has. They also predict that the number of employees in the service sector will be larger than what it was in 2016. There are some employees who are classified as being part of both sectors.
Assuming that the statements above are true and the predictions will turn out to be correct, which one of the following statements must also be true?

A By this time next year, the manufacturing sector will have at least three times as many employees as it had in 2016.
B By this time next year, the service industry will have at least three times as many employees as it had in 2016.
C By this time next year, the manufacturing sector will be more productive than it was in 2016.
D In comparison to 2016, by this time next year, there will be at least as many employees who are classified as being part of both sectors.
E In comparison to 2016, by this time next year there will be more employees who are classified solely as service employees.

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A) Correct
B) This is incorrect. Although, service sector is predicted to grow, but there is no mention of by how much. Moreover, using "three times" (which is mentioned in the paragraph) is an attempt in confusing the reader
C) This is incorrect. No mention of the sectors' productivity
D) This is incorrect. No mention of composition of the 'both' category
E) This is incorrect. No mention of composition of the next year's labour market
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Service: 4x(3 times more than Manufacturing)

Manufacturing:x

As per the above we can say that to be Service employees=Manufacturing employees,the manufacturing sector will have at least three times as many employees as it had in 2016.

But what about the common employees(There are some employees who are classified as being part of both sectors.).Anyone explain how to interpret this as we don't know only Service employees or Manufacturing employees.
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tejyr

Ur reasoning is absolutely correct .we don't know about common employees and only ones figures.

That's the only reason we can say that manufacturing will have as least three times employees as service sector.

Because in question stem it is given that prediction states manufacturing will have as many employees as service.
Also service sector employees will increase but we are not sure how much.it could be 4.2 times or even 4 times
But one thing we r sure that if manufacturing employees is gonna equal service employees ,it has to be at least three times.

I hope this helps.give kudos if you like explanation

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In 2016 in service 3x and in Manufacturing x. Now in next year employees in Manufacturing will be atleast equal to employees in service also employees in service will definitely larger than in 2016 i.e >3x so how employees in manufacturing in next year atleast 3x it has to be strictly greater than 3x
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Hi commoditempore,

Your chain of logic is spot on. You've correctly shown that next year's manufacturing count must be strictly greater than 3x. So far, perfect.

The one thing to fix is what the phrase "at least three times" actually claims. "At least three times" means "three times or more." It is a lower bound - it does not say "exactly three times."

So when you prove that manufacturing next year is strictly greater than 3x, you have not contradicted answer A - you've actually confirmed it. Anything that is more than 3x is automatically also at least3x. Being strictly greater than 3x is one of the cases that "at least 3x" covers.

Think of it this way:

- "More than 3x" - the value is somewhere above 3x.
- "At least 3x" - the value is 3xor anything above it.

Every value in the first list also sits in the second list. So proving the stronger "more than" guarantees the weaker "at least."

And remember the question asks which statement must be true. A safely-true, slightly weaker claim is exactly what you want - it can never fail.

Quick gut-check to lock it in:

Suppose I tell you I have more than $10 in my wallet, and it turns out I have $15.

- Is the statement "I have at least $10" false? No - it's true.
- Would "I have exactly $10" be true? No.

"At least" is satisfied by any amount from the floor upward. Same move here: manufacturing landing above 3x still makes "at least three times" true - so A holds.

Answer: A

commoditempore
In 2016 in service 3x and in Manufacturing x. Now in next year employees in Manufacturing will be atleast equal to employees in service also employees in service will definitely larger than in 2016 i.e >3x so how employees in manufacturing in next year atleast 3x it has to be strictly greater than 3x
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