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Data Sufficiency -

by narenkr » Sat Jun 19, 2010 10:07 am
Hi All,
I was trying out a Manhattan test paper and got these questions, please can any one explain how to solve such kind of questions...

What percentage of the steel workers in the country earns over $37,000 annually and has a net worth over $200,000
1) 55% of all the steel workers have an annual income over $37,000
2) 12% of all the steel workers in the country with an annual income over $37,000 also have a net worth above $200,000

**********************************************************************************************
As of 5th July, team Q had won 24% of the 50 games it played this season. What % of all its games this season did Team Q win if every game has one winner and one loser.
1) team Q won 2/3 of its remaining games this season after July 5th.
2) Team Q played 24 games after july 5th.

I'm still thinking that answer is A, but the OA was different. Taking A alone will give us the desired answer...
From the stem we know the % before July 5th and from 1) we know the % after July 5th, so wouldn't 1) suffice??
**********************************************************************************************

Is x>y ?
1) x/3y > 1/3 ==> 3x>3y ==> x>y
2) -x +p < -y +p ==>x>y

So shouldn't the answer be D ??
**********************************************************************************************
Over the past 5yrs, 95% of chemistry majors who enrolled in a specific chemistry course hav passed the final exam. During this period only 70% of the other students who enrolled in the chemistry course are able to pass the final. How many students passed the final exam in this chemistry course last semester?
1) There were 120 chemistry students enrolled in the course last semester
2) 64 chemistry majors passed the final exam last semester.

Shouldn't the answer be C, cant we not assume that 70% of (120-64) are the number of students who are not chemistry majors passed the test?

Regards,
Narendra..
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by amising6 » Sat Jun 19, 2010 10:19 am
What percentage of the steel workers in the country earns over $37,000 annually and has a net worth over $200,000
1) 55% of all the steel workers have an annual income over $37,000
2) 12% of all the steel workers in the country with an annual income over $37,000 also have a net worth above $200,000


we need to check for 2condition
1)steel workers in the country earns over $37,000 annually
2) should have net worth over $200,000

1) 55% of all the steel workers have an annual income over $37,000
it tells us 55 % earn over 37,000 annually
so it doesnt confirm net worth over $200,000

2) 12% of all the steel workers in the country with an annual income over $37,000
also have a net worth above $200,000

it says 12 % of country with an annual income over $37,000
also have a net worth above $200,000


this is also not sufficient as it says nothing about total number of steel worker

combining also wont happen as total number of steel worker not known

so statement are not sifficent to answer question
hence E
Ideation without execution is delusion
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by narenkr » Sat Jun 19, 2010 10:24 am
Hi, Doesnt the second stmt say that 12% of all the steel workers in the country has an annual income of over $37,000 and net worth above $200,000 ??
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by amising6 » Sat Jun 19, 2010 10:29 am
As of 5th July, team Q had won 24% of the 50 games it played this season. What % of all its games this season did Team Q win if every game has one winner and one loser.
1) team Q won 2/3 of its remaining games this season after July 5th.
2) Team Q played 24 games after july 5th.

universally known
as of 5th july 24 % of 50 games
% of game won this season =?
so we need to find what happened in season after 5 th july
1) team Q won 2/3 of its remaining games this season after July 5th.
this information gives us fractional value of win not number of win or number of games played after 5th july not much of a help

2) Team Q played 24 games after july 5th.
now we know number of game played after 5 th july but no idea of win or loss
so statement2 individually is insufficient

now cmbining 1 and 2
from 1 2/3 of remaining game they won
so 2/3 *24=16 games
so now you know total number of game as well as total number of games won so you can find %
hence option C
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by amising6 » Sat Jun 19, 2010 10:29 am
As of 5th July, team Q had won 24% of the 50 games it played this season. What % of all its games this season did Team Q win if every game has one winner and one loser.
1) team Q won 2/3 of its remaining games this season after July 5th.
2) Team Q played 24 games after july 5th.

universally known
as of 5th july 24 % of 50 games
% of game won this season =?
so we need to find what happened in season after 5 th july
1) team Q won 2/3 of its remaining games this season after July 5th.
this information gives us fractional value of win not number of win or number of games played after 5th july not much of a help

2) Team Q played 24 games after july 5th.
now we know number of game played after 5 th july but no idea of win or loss
so statement2 individually is insufficient

now cmbining 1 and 2
from 1 2/3 of remaining game they won
so 2/3 *24=16 games
so now you know total number of game as well as total number of games won so you can find %
hence option C
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by amising6 » Sat Jun 19, 2010 10:34 am
narenkr wrote:Hi, Doesnt the second stmt say that 12% of all the steel workers in the country has an annual income of over $37,000 and net worth above $200,000 ??
yes bus its say 12 % of steel workers earning over 37,000 but we dont know how many steel worker earn over 37,000
both the statement are talking about % .but you need some base number in order to % making sense
its like 12 % of 13% does it make sense you need some base value
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by amising6 » Sat Jun 19, 2010 10:37 am
Is x>y ?
1) x/3y > 1/3 ==> 3x>3y ==> x>y
2) -x +p < -y +p ==>x>y

So shouldn't the answer be D ??
1) x/3y > 1/3
have they given any other information about x and y because i am not sure wether x or y can take negative value or not
if not mention they can take
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by narenkr » Sat Jun 19, 2010 10:41 am
Question2
From the stem: we know that before July 5th, the win ratio is 24%
from stmt 1 - we know the win ratio post July 5th is 2/3 - 66.67% so cant we not say that the total win ratio for the whole season is (24 + 66.67)/2 ??

And for Question 1, since it asks only the % of steel workers who earn more than $37,000 annually and has net worth over $200,000, stmt 2 directly says that it is 12% .... This is what puzzles me... directly from the stmt... I might be wrong... but can you please explain...

Regards,
Narendra.
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by amising6 » Sat Jun 19, 2010 10:52 am
narenkr wrote:Question2
From the stem: we know that before July 5th, the win ratio is 24%
from stmt 1 - we know the win ratio post July 5th is 2/3 - 66.67% so cant we not say that the total win ratio for the whole season is (24 + 66.67)/2 ??

it not the same thing you cant add percentage these are on two different thing
let us say 20 % of 50 i.e 10
and 2/3 of 100 i.e 67
now based on you observation this should be equal to 20+67= 87 /2=43%
but if you find percentage i.e 10+67/150*100 you will get 51 %

And for Question 1, since it asks only the % of steel workers who earn more than $37,000 annually and has net worth over $200,000, stmt 2 directly says that it is 12% .... This is what puzzles me... directly from the stmt... I might be wrong... but can you please explain...


statement 2) 12% of all the steel workers in the country with an annual income over $37,000 also have a net worth above $200,000
from staement 1 you get 55 % of steel worker earn more than 37,000 and second stamenet says 12% of this 55% steeel workers
but since we just cand find percentage of percentageRegards,
Narendra.
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by a380006 » Sun Jun 20, 2010 11:14 am
If toal worker are 100 , 55 workers are earning more than $37K.

Now 12% of 55 will be answer


amising6 wrote:
narenkr wrote:Hi, Doesnt the second stmt say that 12% of all the steel workers in the country has an annual income of over $37,000 and net worth above $200,000 ??
yes bus its say 12 % of steel workers earning over 37,000 but we dont know how many steel worker earn over 37,000
both the statement are talking about % .but you need some base number in order to % making sense
its like 12 % of 13% does it make sense you need some base value
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by rash.patil » Mon Jun 28, 2010 3:53 am
**********************************************************************************************
As of 5th July, team Q had won 24% of the 50 games it played this season. What % of all its games this season did Team Q win if every game has one winner and one loser.
1) team Q won 2/3 of its remaining games this season after July 5th.
2) Team Q played 24 games after july 5th.

I'm still thinking that answer is A, but the OA was different. Taking A alone will give us the desired answer...
From the stem we know the % before July 5th and from 1) we know the % after July 5th, so wouldn't 1) suffice??
**********************************************************************************************

Ans: C.
Statement 1:
We can not add (24 + 66.67)/2 as the total win ratio.
Suppose gmaes played after 5th july are 30... winning ration =2/3 * 30 = 20.
So the total number of games won = 24% of 50 + 20 = 12+20 = 34.
So winning ratio = 34/80 = 42.5 %

Now suppose games played after 5th huly are 60, then winning ratio = 2/3 * 60 = 40
Total games won = 12 + 40 = 52.
winning ration = 52/90 = 57.77 %.
So A is not sufficient.

statement 2:
gives only total number of games played after 5th july... insufficient

Together:
total games won = 12 + 2/3 * 24 = 28.
So % games won = 28 / 74 = 37.8 %.


**********************************************************************************************
Over the past 5yrs, 95% of chemistry majors who enrolled in a specific chemistry course hav passed the final exam. During this period only 70% of the other students who enrolled in the chemistry course are able to pass the final. How many students passed the final exam in this chemistry course last semester?
1) There were 120 chemistry students enrolled in the course last semester
2) 64 chemistry majors passed the final exam last semester.

Shouldn't the answer be C, cant we not assume that 70% of (120-64) are the number of students who are not chemistry majors passed the test?
**********************************************************************************************
Given:
95% of chemistry majors enrolled for the course have passed
70% of other students enrolled have passed.

Ans: E
Statement 1:
total no. of students : 120.
We dont know how many of these are chemistry majors or the other students.
Insufficient

Statement 2:
64 chemistry majors passed the final exam last semester.
From this we can get the number of chemistry majors but not the total number of other students who passed the last sem.
Insufficient.

Together:
Sufficient.
I think Ans: C

Can you pls post the OAs for all the questions.
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by narenkr » Mon Jun 28, 2010 4:34 am
The original answers are below:
1) % of steel Workers: C
2) % of games won by Team Q: C
3) x>y : B (From Stmt 1, x & y could be both positive or negative)
4) Chemistry Majors: E (Explanation given: We have no way to know how last semester compared to a semester in the last 5years. Its pass to fail ratio could have been higher or lower than average. Therefore E)

I'm quite convinced about the explanations for 2 & 4. 1 & 3 are still baffling me...

Regards,
Narendra.
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by sumanr84 » Mon Jun 28, 2010 9:04 am
Please post one question per thread..Its like a mess here.
I am on a break !!
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by Rahul@gurome » Mon Jun 28, 2010 7:06 pm
Is x>y ?
1) x/3y > 1/3 ==> 3x>3y ==> x>y
2) -x +p < -y +p ==>x>y

So shouldn't the answer be D ?


Solution to this question:

(1) says x/3y > 1/3
Or x/3y - 1/3 > 0
Or (x-y)/(3y) > 0
This means that either (a) (x-y) >0 and 3y > 0
Or (b) (x-y) < 0 and 3y < 0

Which is (a) x > y and y > 0
Or (b) x < y and y < 0

We can hence conclude that if y >0, x > y and if y < 0, x < y.
Since nothing definite can be said (1) alone is not sufficient.

Statement (2) says that -x+p < -y+p
Or -x < -y.
Or x > y (multiplying both sides by -1 results in inequality sign being changed)

So statement (2) alone is sufficient to answer the question.

The correct answer is (B).
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