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Re: Salary :D

by olika » Wed Jul 09, 2008 7:38 am
Is the answer "C"?

I would solve it in this way.

Lets label 'K'- Karen's salary in '95 and 'J' - Jason's salary in '95.
In 1995, the difference between Karen's salary and Jason's salary was 2,000 (K-J=2,000).
In 1998, the gap between their salaries increased by 400, which represents "p" percent. So, we have 2,000 is 100% and 400 is p%. Solving this, we get p=20%.

The answer is C. We need both statements.
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Re: Salary :D

by ksh » Thu Jul 10, 2008 3:56 am
olika wrote:Is the answer "C"?

I would solve it in this way.

Lets label 'K'- Karen's salary in '95 and 'J' - Jason's salary in '95.
In 1995, the difference between Karen's salary and Jason's salary was 2,000 (K-J=2,000).
In 1998, the gap between their salaries increased by 400, which represents "p" percent. So, we have 2,000 is 100% and 400 is p%. Solving this, we get p=20%.

The answer is C. We need both statements.
From the available data (combining 1+2), we can get value of p i.e. $440. But certaily in percentage term it can not be derived since Jason's salary is not mentioned. What is the OA codesnooker?
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Re: Salary :D

by olika » Thu Jul 10, 2008 7:15 am
ksh wrote: From the available data (combining 1+2), we can get value of p i.e. $440. But certaily in percentage term it can not be derived since Jason's salary is not mentioned. What is the OA codesnooker?
Give your solution :)
You can solve this problem in more complicated way... But still you'll get the answer C.

Lets
K - Karen's salary in '95
J - Jason's salary in '95

(100K+KP)/100 - Karen's salary in '98
(100J+JP)/100 - Jason's salary in '98

Then

K-J=2000
((100K+KP)/100) - ((100J+JP)/100)=2400
Solving these two equations, you will get p=100*400/2000, which means that C is correct answer
:D
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by lunarpower » Thu Jul 10, 2008 10:21 pm
remember that you can think of percentage increases in the same way in which you'd think of just multiplying by a constant - because that's all that percentage increases really are, after all.*

simpler analogy:
let's say you multiply a series of numbers x, y, and z by some unknown constant. now let's say i tell you that the gaps between the numbers are 3 times as big as they used to be.
what does this mean?
it means that we must have tripled the numbers, because the size of the gaps increases proportionally with the size of the numbers themselves.

this means that, if we know the number by which the gaps between the numbers have been multiplied (which is the same as knowing the % change in those gaps), we'll also know the multiplier / % change for the numbers themselves.

in this problem, if we take the 2 statements together, we know that the gap between the salaries has increased by a factor of 2440/2000 = 1.22; this means a percentage increase of 22%. (note that you don't really care about the specific percentages, since this is data sufficiency; all that matters is that you can find them.)
therefore, the salaries themselves have increased by 22 percent.
that means both statements together are sufficient.

--

note that none of the above reasoning is valid if the quantities increase by different percentages.

--

*as a side note, it's extremely useful to be able to use percentage multipliers for percent increases. some examples:
to increase a quantity by 14%, multiply by 1.14
to increase a quantity by 70%, multiply by 1.7
to decrease a quantity by 14%, multiply by 0.86
to decrease a quantity by 70%, multiply by 0.3
etc.
Ron has been teaching various standardized tests for 20 years.

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by missrochelle » Wed Sep 01, 2010 7:30 am
lunarpower wrote:remember that you can think of percentage increases in the same way in which you'd think of just multiplying by a constant - because that's all that percentage increases really are, after all.*

simpler analogy:
let's say you multiply a series of numbers x, y, and z by some unknown constant. now let's say i tell you that the gaps between the numbers are 3 times as big as they used to be.
what does this mean?
it means that we must have tripled the numbers, because the size of the gaps increases proportionally with the size of the numbers themselves.

this means that, if we know the number by which the gaps between the numbers have been multiplied (which is the same as knowing the % change in those gaps), we'll also know the multiplier / % change for the numbers themselves.

in this problem, if we take the 2 statements together, we know that the gap between the salaries has increased by a factor of 2440/2000 = 1.22; this means a percentage increase of 22%. (note that you don't really care about the specific percentages, since this is data sufficiency; all that matters is that you can find them.)
therefore, the salaries themselves have increased by 22 percent.
that means both statements together are sufficient.

--

note that none of the above reasoning is valid if the quantities increase by different percentages.

--

*as a side note, it's extremely useful to be able to use percentage multipliers for percent increases. some examples:
to increase a quantity by 14%, multiply by 1.14
to increase a quantity by 70%, multiply by 1.7
to decrease a quantity by 14%, multiply by 0.86
to decrease a quantity by 70%, multiply by 0.3
etc.
i was struggling with this problem and this explanation was amazing..... definietly makes sense and now i have a "go-to" example whenever i encounter percent change problems on d.s.

thanks!
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by missrochelle » Wed Sep 01, 2010 9:34 am
lunarpower wrote:remember that you can think of percentage increases in the same way in which you'd think of just multiplying by a constant - because that's all that percentage increases really are, after all.*

simpler analogy:
let's say you multiply a series of numbers x, y, and z by some unknown constant. now let's say i tell you that the gaps between the numbers are 3 times as big as they used to be.
what does this mean?
it means that we must have tripled the numbers, because the size of the gaps increases proportionally with the size of the numbers themselves.

this means that, if we know the number by which the gaps between the numbers have been multiplied (which is the same as knowing the % change in those gaps), we'll also know the multiplier / % change for the numbers themselves.

in this problem, if we take the 2 statements together, we know that the gap between the salaries has increased by a factor of 2440/2000 = 1.22; this means a percentage increase of 22%. (note that you don't really care about the specific percentages, since this is data sufficiency; all that matters is that you can find them.)
therefore, the salaries themselves have increased by 22 percent.
that means both statements together are sufficient.

etc.
Ron - Im curious to know if you can think of a simpler non-algebraic way to do this type of problem?

What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1970

The answer is c, but I'm trying to look at in a similar way -- in terms of the relationship between the two and if that tells you sufficiency or not.... does ur method work here?
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by lunarpower » Fri Sep 10, 2010 4:39 am
missrochelle wrote: i was struggling with this problem and this explanation was amazing..... definietly makes sense and now i have a "go-to" example whenever i encounter percent change problems on d.s.

thanks!
thanks for the kind words.
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by lunarpower » Fri Sep 10, 2010 5:00 am
missrochelle wrote: Ron - Im curious to know if you can think of a simpler non-algebraic way to do this type of problem?

What is the % increase in population of City K from 1980 to 1990?
a. In 1970 population of K was 160,000
b. In 1980 population of K was 20% greater than 1970 and in 1990 population is 30% greater than in 1970

The answer is c, but I'm trying to look at in a similar way -- in terms of the relationship between the two and if that tells you sufficiency or not.... does ur method work here?
whoa, no, the answer to that one shouldn't be (c). it should be (b).

two things:
1) the actual reason why:
let the 1970 population be 'x'.
then the 1980 population was 1.2x, and the 1990 population was 1.3x.
you can definitely find the % increase from 1.2x to 1.3x as a hard number. (it's (1.3x - 1.2x)/(1.2x), an expression in which the x's cancel and you're left with 0.1/1.2.) so, that's sufficient by itself.

2) this is a problem on which the two statements together (i.e., (c)) is a "sucker answer".
if you have the two statements together, then you have ALL HARD NUMBERS for ALL the population figures in the problem -- and, moreover, those numbers are basically just handed to you on a plate.
this is almost never how real gmat problems work, because this is just too "obvious". on DS, if you see a very obvious-looking answer that requires nothing more than 1-2 steps of elementary arithmetic and/or just plugging numbers into expressions, then that answer is probably wrong.
this mostly applies to choice (c), as in problems like the above.
Ron has been teaching various standardized tests for 20 years.

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