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Critical reasoning question

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Critical reasoning question

by paosilvestre » Fri Feb 04, 2011 8:31 am
Hi!!! I´m struggling with this question.....the answer is D, but I´m not sure I understand why.....tks!!!

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
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by mundasingh123 » Fri Feb 04, 2011 8:36 am
Can U Pls reveal the Source ?
I Seek Explanations Not Answers
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by fitzgerald23 » Fri Feb 04, 2011 12:29 pm
What this question wants is for you to be able to explain how two statements that seem to contradict one another can both be true.

1. Grandview city has the highest percentage of businesses with 10 or more
2. Lakeshore has the highest percentage with 15 or more.

So think of this like a math question and come up with a condition for how both can work.

Assume Grandview has 100 businesses of which 50 have more than 10. 50% of their businesses are greater than 10%. However assume that only 35 of the 50 are larger than 15. Thus 35% of businesses have 15 or more.

Now look at Lakeshore and their 100 businesses. If they have 40 businesses of 10 or more and all 40 of them are greater than 15 it gives you the answer. 40% have 10+ and 40% have 15+.

Now combine the two and you get that Grandview has the greater amount of 10+ and Lakeshore the greater amount of 15+

D is the only answer choice to give you that scenario. For the statements to both be true Grandview must have businesses between 10 and 14 people.
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by GMATMadeEasy » Fri Feb 04, 2011 12:30 pm
i should be D
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by paosilvestre » Fri Feb 04, 2011 12:35 pm
Thank you!!!!
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by cyrwr1 » Fri Feb 04, 2011 1:34 pm
G has the highest % >10 empl.
L has the highest % >15 empl.

A) tells nothing of those two, out
B) we don't care about other states with this this state, out
C) don't confuse # with %, out
D) yes can be true if there are business with 10-14 empl. keep
E)average---> number of empl, out

D is the only one left.

In the future, please do not list the answer in your opening line. It was distracting haha.
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by nickb » Fri Mar 02, 2012 4:45 pm
Hi everyone. First post here and first maths study for 25+ years so please go easy on me :)
I am also struggling to understand how to arrive at the correct answer given the use of the word 'must' in the question. Would welcome some guidance.

The question says "If the statements above are true, then which of the following must also be true?"

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

Frankly I don't understand how this must be true? Is there something in the math I don't understand that confirms it? Its obvious its possible it CAN be true, but must?

I understand also the logic of striking out obviously wrong answers in order to get to the right one. The other answers in this question cannot be stated as true as there is not enough related information in the statement. But for me the D answer is the same. I can see that its possible, but not that it must be true.

So where am I going wrong? Thanks in advance for your help.
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