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What percentage of steel workers in the country earns over $

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New post 21 Aug 2007, 20:50
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What percentage of steel workers in the country earns over $37000 annually and has a net worth over $200,000?

(1) 55% of steel workers in the country have an annual income over $37000

(2) 12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000
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Re: what percentage of steel workers in the country earns over  [#permalink]

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New post 14 Jun 2014, 01:57
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3
aashu4uiit wrote:
I am replying to old post but I also got confused in this question :


Is it " with " which makes the difference

2)12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000


The question is asking : earns over $37000 annually and has a net worth over $200,000?

B says : with an annual income over $37000 also have net worth above $200,000

So isn't B correct ?


What percentage of steel workers in the country earns over $37000 annually and has a net worth over $200,000?

(1) 55% of steel workers in the country have an annual income over $37000. We don't know what percentage of those 55% has a net worth over $200,000. Not sufficient.

(2) 12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000. 12% of those who have an annual income over $37000 also have net worth above $200,000. We don't know what percentage have an annual income over $37000. Not sufficient.

(1)+(2) 55% have an annual income over $37000 and 12% of those 55%, so 6.6%, earns over $37000 annually and has a net worth over $200,000. Sufficient.

Answer: C.

Hope it's clear.
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What percentage of steel workers in the country earns over $  [#permalink]

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New post 20 Dec 2017, 21:42
One great way to look at this problem is to visualize it as a Venn Diagram. We have two overlapping groups: those steel workers who make over $37,000 annually (I will call them group “\(A\)”), and those who have a net worth above $200,000 (I will call them group “\(B\)”). There is an overlap between the groups, containing people who meet both criteria. I will call them group “\(M\)”. There is technically also a “neither” group (“\(N\)”): steel workers who do not meet either of the criteria. The total number of steel workers \((T) = A + B + N – M\). (Remember, when you add overlapping groups, you double count the mixed group, \(M\).)

The target for this problem is the percentage of steel workers who meet both criteria. (Notice the critical leverage word “also.”) This percentage is calculated by knowing the mixed group, \(M\), and dividing it by \(T\). Thus, we need to find a numerical value for \(\frac{M}{T}\).

Statement #1 tells us that 55% of all the steel workers in the country (\(T\)) fit into group \(A\). Mathematically, this means that \(A = (.55)T\). However, we cannot manipulate this equation to solve for \(\frac{M}{T}\), since it gives us no information on the mixed group, \(M\). Statement #1 is insufficient.

Statement #2 tells us that 12% of the steel workers with an annual income over $37,000 also have a net worth above $200,000. (Once again, notice the critical leverage word “also.”) Mathematically, this means that \((.12)A=M\). Again, this equation alone does not allow us to calculate \(\frac{M}{T}\), since it gives us no information on the total group, \(T\). Statement #2 is insufficient by itself.

However, when we substitute the first equation into the second equation, we get the equation \((.12)*(.55)*T = M\). There is no reason to do any more math, because it is easy to see that we can solve this combined equation for the term \(\frac{M}{T}\). The two statements together are sufficient, and the answer is C.

It might be worth noting here that we never actually able to solve for the individual values for \(M\) and \(T\). We don’t have to. We can solve for a chunk of an equation without needing to know the individual components. This is a concept I call “Chunky-quations” in my classes. The GMAT often gets you to assume that you need to know each piece, instead of just looking for a combined value. This is a classic GMAT trap.
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New post 22 Aug 2007, 01:31
ughm

it asks you for % of workers >37k & networth >200k

B gives you that.

of steel workers, 12% who have income >37k also have networth over 200k

oh OOPS

you need both, you dont know what % the people who earn >37k are of the population

hence C)

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Re: what percentage of steel workers in the country earns over  [#permalink]

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New post 13 Jun 2014, 18:33
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I am replying to old post but I also got confused in this question :


Is it " with " which makes the difference

2)12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000


The question is asking : earns over $37000 annually and has a net worth over $200,000?

B says : with an annual income over $37000 also have net worth above $200,000

So isn't B correct ?
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New post 14 Jun 2014, 08:31
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:) Great Thanks

Now I got the logic
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Re: what percentage of steel workers in the country earns over  [#permalink]

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New post 15 Jun 2014, 08:20
Bunuel wrote:
aashu4uiit wrote:
I am replying to old post but I also got confused in this question :


Is it " with " which makes the difference

2)12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000


The question is asking : earns over $37000 annually and has a net worth over $200,000?

B says : with an annual income over $37000 also have net worth above $200,000

So isn't B correct ?


What percentage of steel workers in the country earns over $37000 annually and has a net worth over $200,000?

(1) 55% of steel workers in the country have an annual income over $37000. We don't know what percentage of those 55% has a net worth over $200,000. Not sufficient.

(2) 12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000. 12% of those who have an annual income over $37000 also have net worth above $200,000. We don't know what percentage have an annual income over $37000. Not sufficient.

(1)+(2) 55% have an annual income over $37000 and 12% of those 55%, so 6.6%, earns over $37000 annually and has a net worth over $200,000. Sufficient.

Answer: C.

Hope it's clear.


Curious wording, Bunnel!
The rest of the 45% workers with annual income under 37K could still have a net worth of over 200K
I mean there never was an established connection between Annual income and Net worth
I maybe thinking too much, but it's a tempting perspective under test pressure
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Re: What percentage of steel workers in the country earns over $  [#permalink]

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New post 30 Oct 2014, 20:37
Curious wording, Bunnel!
The rest of the 45% workers with annual income under 37K could still have a net worth of over 200K
I mean there never was an established connection between Annual income and Net worth
I maybe thinking too much, but it's a tempting perspective under test pressure

Why would we consider the remaining 45 % ? we are to find those who earn 37000 and has networth above 200k
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Re: What percentage of steel workers in the country earns over $  [#permalink]

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New post 31 Oct 2014, 05:22
Kconfused wrote:
Bunuel wrote:
aashu4uiit wrote:
I am replying to old post but I also got confused in this question :


Is it " with " which makes the difference

2)12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000


The question is asking : earns over $37000 annually and has a net worth over $200,000?

B says : with an annual income over $37000 also have net worth above $200,000

So isn't B correct ?


What percentage of steel workers in the country earns over $37000 annually and has a net worth over $200,000?

(1) 55% of steel workers in the country have an annual income over $37000. We don't know what percentage of those 55% has a net worth over $200,000. Not sufficient.

(2) 12% of steel workers in the country with an annual income over $37000 also have net worth above $200,000. 12% of those who have an annual income over $37000 also have net worth above $200,000. We don't know what percentage have an annual income over $37000. Not sufficient.

(1)+(2) 55% have an annual income over $37000 and 12% of those 55%, so 6.6%, earns over $37000 annually and has a net worth over $200,000. Sufficient.

Answer: C.

Hope it's clear.


Curious wording, Bunnel!
The rest of the 45% workers with annual income under 37K could still have a net worth of over 200K
I mean there never was an established connection between Annual income and Net worth
I maybe thinking too much, but it's a tempting perspective under test pressure


The question asks about the percentage of workers who earns over $37000 annually AND, at the same time, has a net worth over $200,000.

We know that 55% earn over 37K, and that 12% of them have a net worth over 200K. Therefore 0.55*0.12 = 6.6% both earn over 37K AND have a net worth over 200K.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: What percentage of steel workers in the country earns over $ &nbs [#permalink] 31 Oct 2014, 05:22
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