CR - Mathematical : GMAT Critical Reasoning (CR)
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# CR - Mathematical

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Senior Manager
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31 Oct 2006, 04:35
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I found correct answer by solving a mathematical inequality formed based on the statement of passage but I am interested to know how can we get a correct answer in 2 min to this without actually solving maths. Please explain!
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Recent estimates predict that between 1982 and 1995 the greatest increase in the number of people employed will be in the category of low-paying service occupations. This category, however, will not increase its share of total employment, whereas the category of high-paying service occupations will increase its share.

If the estimates above are accurate, which of the following conclusions can be drawn?
(A) In 1982 more people were working in low-paying service occupations than were working in high-paying service occupations.
(B) In 1995 more people will be working in high-paying service occupations than will be working in low-paying service occupations.
(C) Nonservice occupations will account for the same share of total employment in 1995 as in 1982.
(D) Many of the people who were working in low-paying service occupations in 1982 will be working in high-paying service occupations by 1995.
(E) The rate of growth for low-paying service occupations will be greater than the overall rate of employment growth between 1982 and 1995.
If you have any questions
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31 Oct 2006, 04:39
Looks like D to me.
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31 Oct 2006, 04:48
arjsingh1976 wrote:
I found correct answer by solving a mathematical inequality formed based on the statement of passage but I am interested to know how can we get a correct answer in 2 min to this without actually solving maths. Please explain!
------------------------------------------------------------------------------

Recent estimates predict that between 1982 and 1995 the greatest increase in the number of people employed will be in the category of low-paying service occupations. This category, however, will not increase its share of total employment, whereas the category of high-paying service occupations will increase its share.

If the estimates above are accurate, which of the following conclusions can be drawn?
(A) In 1982 more people were working in low-paying service occupations than were working in high-paying service occupations.
(B) In 1995 more people will be working in high-paying service occupations than will be working in low-paying service occupations.
(C) Nonservice occupations will account for the same share of total employment in 1995 as in 1982.
(D) Many of the people who were working in low-paying service occupations in 1982 will be working in high-paying service occupations by 1995.
(E) The rate of growth for low-paying service occupations will be greater than the overall rate of employment growth between 1982 and 1995.

I would go with A.

"low-paying service" has hightest increase in terms of absolute number, and its share in the overall employment has not increased. That means overall employment is growing atleast as fast as "low-paying service."

It is also said that "category of high-paying service occupations will increase its share". That means this category is growing faster than overall employment. Also means, the growth rate is higher than "low-paying service." Inspite of higher growth rate in high-paying service occupations, the absolute number did not increase means "in 1982 more people were working in low-paying service occupations than were working in high-paying service occupations"
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31 Oct 2006, 06:30
Let's say there were two kinds of services - LP and HP

In 1982 let's say the following was true

LP = X; HP = Y; Total = T

so X + Y = T

Share of LP = X/T
Share of HP = Y/T

Now imagine X increased by x between 1982 and 1995 and Y increased by y

So, X +x + Y + y = T + x + y

1995 share of LP = (X + x)/ (T + x + y) ----- (1)
1995 share of HP = (Y + y)/(T+x+y) ----- (2)

Now the stem says that x > y

Also (2) > (1): HP share was more than LP in 1995

This means that

X + x < Y + y where x > y

x - y < Y - X

Since x - y > 0 => Y > X; ------------ (3)

This means MORE PPL were working in the Higher Paying Service in 1982

Choice A is the OPPOSITE OF THE ABOVE SO CAN BE RULED OUT.

Also Y + y > X + x => which implies that in 1995 more ppl are working in higher paying job than in the lower paying job.

Hence after doing this calculation I believe B is correct.

What's the OA?

P.S - The calculations above seem complex because I have tried to explain every step.
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31 Oct 2006, 22:57
If I had to choose an answer within 2 mins, it wud have to be A.
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31 Oct 2006, 23:06
I'll pick A too ....
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01 Nov 2006, 04:31

do it by POE.
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01 Nov 2006, 05:41
tennis_ball wrote:

do it by POE.

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01 Nov 2006, 05:52
dwivedys wrote:
tennis_ball wrote:

do it by POE.

I mean do it by elimination. it is easier to spot the wrong ones here.
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01 Nov 2006, 05:58
tennis_ball wrote:
dwivedys wrote:
tennis_ball wrote:

do it by POE.

I mean do it by elimination. it is easier to spot the wrong ones here.

OK, Leaving the math behind for a minute - help me with this.

If more ppl were working in low paying service in 1982 and ALSO the quantum increase in low paying jobs between 1982 and 1995 was more than the increase that happened for High paying jobs, how can the total share of low paying job in 1995 be lower than that of the high paying job.

This is exactly what i got from the calculation above as well.

I am completely confused!!
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01 Nov 2006, 11:59
In 1982 more people were working in low-paying service occupations than were working in high-paying service occupations, therefore, this category had the greatest increase in the number of people employed, since its share of total employment did not increase.
If the number of people working in high-paying service occupations was more than those in low-paying service occupations in 1982, then, this category would have had the greatest increase in number of people employed, but this is not the case, therefore A is the answer
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01 Nov 2006, 21:28
arjsingh1976 wrote:
I found correct answer by solving a mathematical inequality formed based on the statement of passage but I am interested to know how can we get a correct answer in 2 min to this without actually solving maths. Please explain!
------------------------------------------------------------------------------

Recent estimates predict that between 1982 and 1995 the greatest increase in the number of people employed will be in the category of low-paying service occupations. This category, however, will not increase its share of total employment, whereas the category of high-paying service occupations will increase its share.

If the estimates above are accurate, which of the following conclusions can be drawn?
(A) In 1982 more people were working in low-paying service occupations than were working in high-paying service occupations.
(B) In 1995 more people will be working in high-paying service occupations than will be working in low-paying service occupations.
(C) Nonservice occupations will account for the same share of total employment in 1995 as in 1982.
(D) Many of the people who were working in low-paying service occupations in 1982 will be working in high-paying service occupations by 1995.
(E) The rate of growth for low-paying service occupations will be greater than the overall rate of employment growth between 1982 and 1995.

Arjsingh, can you give us your mathematical proof
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02 Nov 2006, 04:06
Hi, I have assumed that there are only two catgories of jobs: High paying and low paying. Hope this helps.

Year/Cate 1982 1995 Increase % Increase
Total Jobs 1000 1500 500 50
Low pjobs 800 1120 320 40
High pjobs 200 380 180 90
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02 Nov 2006, 09:46
Thanks buddy. If you look at my mathematical labor-lost you'll appreciate that i completely misunderstood the question.

Thanks for you explanation.
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02 Nov 2006, 10:32
OA is A...

Recent estimates predict that between 1982 and 1995 the greatest increase in the number of people employed will be in the category of low-paying service occupations. This category, however, will not increase its share of total employment, whereas the category of high-paying service occupations will increase its share.

I call low paying service occupation Category 1 and high paying occupation Category 2. In 1982, Let there be X employees in Category 1 and Y employees in Category 2. Suppose that there is increase of 'x' and 'y' in number of employees in category 1 and 2 respectively.

Now given x > y -----(1)

Important point here is to formulate second equation:

"category 2 will increase it share" means following:

Y+y/(X+Y+x+y) > Y/(X+Y) ......(2)

IF you simplify it you will get:

X> Y*(x/y)------------(3)

From 1 we know that x/y> 1

Hence X > Y....and this is first choice!
02 Nov 2006, 10:32
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