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fireagablast
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The percentage of local businesses with more than ten employees is hig 31 Dec 2020, 20:26
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I don't see how D could be a MUST be true answer (I went with E).
It COULD be true, but I don't see anything in the question that would prohibit it from the following:

Lakeview:
1-9 employees: 20%
10-14 employees: 0%
15+ employees: 80%

As for E, if Lakeview has a higher percentage of 15+ employee buisnesses, then wouldn't it also have a higher employee to buisness ratio over grandview?
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The percentage of local businesses with more than ten employees is hig 01 Jan 2021, 00:41
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fireagablast
D is definitely the right answer. This is a pretty direct copy of an official question: https://gmatclub.com/forum/the-percenta ... l#p2565089

The trick you're missing is that if Lakeshore has the most businesses with 15 or more, but Grandview has the most with 10 or more (which of course includes 15+), then Grandview must have some with 10 but not 15. If all of Grandview's 10+ businesses were also 15+, then Grandview would be the one with the most 15+ businesses, which we're told it's not. Using your numbers for Grandview, there's no way for Lakeshore to have more than 80% at the 15+ level without thereby having more than 80% at the 10+ level, since this is inclusive of the higher category.

As for E, we have no idea about employee to business ratios, since we don't know the average size of the businesses, just the relative amounts in two categories.
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The percentage of local businesses with more than ten employees is hig 02 Jan 2021, 19:18
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DmitryFarber
Looking back, i read the answer as "some businesses in LAKEVIEW city have between 10-15", not some businesses in Grandview.
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The percentage of local businesses with more than ten employees is hig 05 Feb 2021, 02:15
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hi expert still confuse why C is wrong ?
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The percentage of local businesses with more than ten employees is hig 17 Feb 2021, 01:53
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Anshuman0902
hi expert still confuse why C is wrong ?
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Hi Anshuman

Let me try to address your query.

We are told the following:

1) The percentage of local businesses with more than ten employees is higher in Grandview City than in any another city in the state.
2) The percentage of local businesses with 15 employees or more is higher in Lakeshore City, which is in the same state, than in any other city in the state.

Option (C) states:

The number of local business with 15 or more employees is greater in Lakeshore city than in Grandview city.

We do not know anything about the number of businesses in these categories in these cities. This is a must be true question, which means it has to be true for all possible numbers of businesses in these two cities. Now consider the following situation:

Lakeshore city has only 2 local businesses, one with 20 employees (proportion of businesses having >15 employees is 50%, let all other cities having a lower proportion) and another with 5 employees (which means proportion of businesses with >10 employees is also 50%)

Grandview city has 10 local businesses, 3 of whom have 12 employees, 3 others have 17 employees and other four have 5 employees.

Proportion of businesses with >10 employees = 60% (highest in the state, also higher than Lakeview city)
Proportion of businesses with >15 employees = 30% (< Lakeshore city)
Number of businesses with >15 employees = 3 (> Lakeshore city)

This breaks option (C) and we cannot say that it must be true. Hope this clarifies.
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The percentage of local businesses with more than ten employees is hig 11 Jul 2026, 15:07
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Answer: D.
This is an inference / "must be true" question, and the whole thing turns on one structural insight: businesses with 15+ employees are a subset of businesses with more than 10 employees. (If you have 15+, you automatically have >10.) Once you see the nesting, D is forced.
Set up the two facts as percentages:
  • Grandview has the highest % of businesses with >10 employees (so >10 means 11 or more).
  • Lakeshore has the highest % of businesses with ≥15 employees.
Both are strict ("higher than any other city"), so comparing the two cities directly:

Code:
%(>10) in Grandview  >  %(>10) in Lakeshore     ← Grandview leads on >10
%(≥15) in Lakeshore  >  %(≥15) in Grandview     ← Lakeshore leads on ≥15

Chain them using the subset fact. In any city, %(≥15) ≤ %(>10) (subset can't exceed the whole). So for Lakeshore, %(>10) ≥ %(≥15). Putting it together:

Code:
%(>10)_Grandview  >  %(>10)_Lakeshore  ≥  %(≥15)_Lakeshore  >  %(≥15)_Grandview

Read the two ends: %(>10)_Grandview > %(≥15)_Grandview.
That gap — businesses that have more than 10 but fewer than 15 employees (i.e., 11–14, "between 10 and 15") — is strictly positive in Grandview. A positive percentage means such businesses exist. D must be true. ✅
Why the others fail:
  • A — >18 is a further subdivision of ≥15; nothing forces Lakeshore to lead there. Not supported.
  • B — other states: completely out of scope. The stimulus is one state only.
  • C — the trap. It swaps percentage for number (count). Lakeshore has a higher percentage of ≥15 businesses, but if Grandview has far more total businesses, Grandview could still have a larger count. Percentages don't pin down absolute numbers.
  • E — average employees per business depends on the whole distribution (including businesses with ≤10), which you know nothing about.

nickb99
The percentage of local businesses with more than ten employees is higher in Grandview City than in any another city in the state. However, the percentage of local businesses with 15 employees or more is higher in Lakeshore City, which is in the same state, than in any other city in the state. If the statements above are true, then which of the following must also be true?


A. The percentage of local business with more than 18 employees is higher in Lakeshore city than in any other city in the state.

B. The state has more local business with more than ten employees than any other state in the country

C. The number of local business with 15 or more employees is greater in Lakeshore city than in Grandview city.

D. Some local businesses in Grandview City have between 10 and 15 employees

E. The average number of employees per business is higher in Lakeshore city than in Grandview City.[/i]


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My issue is that the question says "which of the following must also be true? ". I can see that the answer can be/is likely to be true, but must? Trying to get my head around how I should best come to this answer. Any help appreciated. Best, Nick
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