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Powerprep Q

by smehmood » Sun Aug 17, 2008 1:11 pm
What is the process to solve these type of questions?
If I try to plug-in different numbers to see the result of the expression it takes a long time. Moreover I may miss plugging-in a number that I should have.
Are there any good plugging numbers for these kind f questions?
Thanks
M
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Source: — Data Sufficiency |
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by 4meonly » Sun Aug 17, 2008 1:25 pm
smehmood,
I hate to plug in numbers. I always try to solve questions as they are given.
Main statement:
x and y integers, y=│x+3│+│4-x│
from here we conclude that to make y=7 x should be -3, 0 and 4

My reasonong:
(1) x<4
we have 2 variants: x=-3 and x=0
INSUFFUCIENT

(2) x>-3
we have x=0 and x=4
INSUFFUCIENT

(1) AND (2)
-3<x<4
dont think that x=0. this is mistake! X=0 makes y=7, but other integers for x: -2, -1, 1, 2, 3 make y not equal to 7!
So, INSUFFUCIENT

Answer is E
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by parallel_chase » Sun Aug 17, 2008 2:04 pm
I think the answer should be C

y=lx+3l+l4-xl

Statement I

x<4

x could be anything. Insufficient.

Statement II

x> -3

x could be anything. Insufficient.


Combining I & II

-3 < x < 4

x could be -2,-1,0,1,2,3

If you insert any of these values in the above in equality,
y will always be 7.

Hence Sufficient.

Answer is C.

Get used to plugging in numbers, it not only makes the whole process easier but also saves time. Most of the algebra and inequalities can be easily solved through plugging numbers.
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by smehmood » Sun Aug 17, 2008 2:52 pm
Wow! two totally different point of views.
Correct answer is C.

I plugged in few numbers, however those numbers did not lead me to the correct answer.
So which numbers are good to plug in, in these type of inequality questions so we arrive to the answer quickly and correctly?
Thanks
M
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by Ian Stewart » Sun Aug 17, 2008 2:58 pm
Note that x could be a lot of other things- don't fall into the trap of assuming x is an integer, or you'll make a lot of mistakes on DS. Not that it matters in this question. I posted the following to another forum:

Remember that |a - b| is just the distance between a and b on the number line.

Write the question as:

y=|x-(-3)| + |4-x|

In words, this says: "y is equal to the distance from x to -3 plus the distance from x to 4. Draw a number line, draw the points -3 and 4, and put x in the middle. If you add the two distances, you clearly get 7, the distance from -3 to 4. If x is less than -3 or larger than 4, the sum of the distances will be larger than 7. Easy to see if you draw the picture. So we need both statements: C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com
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by pepeprepa » Sun Aug 17, 2008 3:06 pm
Agree with Chase, the thing with plugging in this one with 1) for example, is not to try with 3 2 or 1 and think it gives 7 anyway.
You can see the 2) which indicates you the number -3 so try around this one before and after, the question helps you to choose which number you have to check. So it is better to plugging wisely, it makes you save much more time.
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by smehmood » Sun Aug 17, 2008 3:39 pm
Thanks Destroyer and thanks Ian for the tip: draw number line in this question.

Ian, is it useful to draw a number line in most of the absolute value questions?
Are there any other useful tips in solving questions related to absolute values?

Thanks
M
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by 4meonly » Mon Aug 18, 2008 4:41 am
Ye, I've made a mistake...
Thank to everybody who corrected me!
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