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OG DS - absolute value questn

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OG DS - absolute value questn

by mavesum » Wed Mar 11, 2009 7:15 am
If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3


Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/
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Re: OG DS - absolute value questn

by marcusking » Wed Mar 11, 2009 8:08 am
mavesum wrote:If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3


Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/
1) x must be less than 4 so
x = 0 works
x = 1 works
x = 2 works
x = 3 works
but lets try - 10
x = -10 doesn't work
we have some values that work and others that dont which is ambiguous
statement 1 is not sufficient

2) x must be greater than -3
x = -2 works
x = -1 works

lets try a larger number
x = 10 doesn't work

statement 2 is not sufficient

So we are down to choices C or E

lets try both statements together
x < 4 & x > -3

x = 3 works
x = 2 works
x = 1 works
x = 0 works
x = -1 works
x = -2 works

Both statements together always satisfy the requirements with no ambiguity. This would also be sufficient if all statements did NOT work.

C.
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Re: OG DS - absolute value questn

by Ian Stewart » Wed Mar 11, 2009 1:35 pm
mavesum wrote:If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3


Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/
To answer the more difficult absolute value questions on the GMAT, it can be very useful to understand that absolute value measures distance. This approach might take some time to get used to, however. It's also a bit tricky to explain without being able to draw decent diagrams, but I'll try:

|x| = the distance, on the number line, between x and zero
|a - b| = the distance, on the number line, between a and b

Note that we need a minus sign between a and b in the above.

Back to the question:

|4 - x| is the distance between 4 and x on the number line.
|x + 3| = |x - (-3)| is the distance between x and -3 on the number line.

If we draw the number line, marking the important numbers (4 and -3), and placing x in the middle, we have:

----------(-3)------x-------------4-----------

What will |4 - x| + |x + 3| be equal to here? It's the distance from x to -3, plus the distance from x to 4. If x is in between -3 and 4, that must be equal to the total distance from -3 to 4, which is 7. On the other hand, if x is either to the left of -3, or to the right of 4, then |4 - x| + |x + 3| will be greater than 7. For example, if x is to the left of -3:

------x-------(-3)-----------------4-------------

then the distance from x to 4 is already greater than 7, so |4 - x| + |x + 3| must certainly be greater than 7. The same will happen if x is to the right of 4.
Last edited by Ian Stewart on Wed Mar 11, 2009 3:33 pm, edited 1 time in total.
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by cramya » Wed Mar 11, 2009 1:56 pm
Thanks again Ian for an excellent explanation.
On the other hand, if x is either to the right of -3, or to the left of 4, then |4 - x| + |x + 3| will be greater than 7
I am sure u meant it this way:

On the other hand, if x is either to the left of -3, or to the right of 4, then |4 - x| + |x + 3| will be greater than 7

Please correct me if I am mistaken.

Regards,
Cramya
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by Ian Stewart » Wed Mar 11, 2009 3:32 pm
cramya wrote:Thanks again Ian for an excellent explanation.
On the other hand, if x is either to the right of -3, or to the left of 4, then |4 - x| + |x + 3| will be greater than 7
I am sure u meant it this way:

On the other hand, if x is either to the left of -3, or to the right of 4, then |4 - x| + |x + 3| will be greater than 7

Please correct me if I am mistaken.

Regards,
Cramya
Thanks for catching that, Cramya! I'll edit my post to prevent any confusion.
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by mavesum » Thu Mar 12, 2009 6:40 am
Thanks Ian , that was an awesome explanation !!
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Re: OG DS - absolute value questn

by kaf » Thu Mar 19, 2009 3:09 am
Ian Stewart wrote:
mavesum wrote:If x and y are integers and y = |x+3|+|4-x| , does y equal 7 ?

1) x < 4
2) x > -3


Also , please explain a little how to solve these types of questions

I am not able to do well in absolute value questions :/
To answer the more difficult absolute value questions on the GMAT, it can be very useful to understand that absolute value measures distance. This approach might take some time to get used to, however. It's also a bit tricky to explain without being able to draw decent diagrams, but I'll try:

|x| = the distance, on the number line, between x and zero
|a - b| = the distance, on the number line, between a and b

Note that we need a minus sign between a and b in the above.

Back to the question:

|4 - x| is the distance between 4 and x on the number line.
|x + 3| = |x - (-3)| is the distance between x and -3 on the number line.

If we draw the number line, marking the important numbers (4 and -3), and placing x in the middle, we have:

----------(-3)------x-------------4-----------

What will |4 - x| + |x + 3| be equal to here? It's the distance from x to -3, plus the distance from x to 4. If x is in between -3 and 4, that must be equal to the total distance from -3 to 4, which is 7. On the other hand, if x is either to the left of -3, or to the right of 4, then |4 - x| + |x + 3| will be greater than 7. For example, if x is to the left of -3:

------x-------(-3)-----------------4-------------

then the distance from x to 4 is already greater than 7, so |4 - x| + |x + 3| must certainly be greater than 7. The same will happen if x is to the right of 4.

In you explanation are you determining the position of x from the two statements?

and secondly how can i solve this question with this explanation

If X < 0, then sqrt(-x * absolute(x) ) is:

A -x
B -1
C 1
D x
E sqrt(X)

thanks
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Re: OG DS - absolute value questn

by Ian Stewart » Thu Mar 19, 2009 3:56 am
kaf wrote: In you explanation are you determining the position of x from the two statements?
Yes, exactly - if you know, for example, that x < 4, that means "x is to the left of 4 on the number line". If x > -3, that means "x is to the right of -3 on the number line".
kaf wrote: and secondly how can i solve this question with this explanation

If X < 0, then sqrt(-x * absolute(x) ) is:

A -x
B -1
C 1
D x
E sqrt(X)

thanks
This question isn't testing anything particularly advanced about absolute value, and there'd be no advantage to applying the principles earlier in this thread - you only need to know that if x < 0, then |x| = -x. The question is a tricky example of how the GMAT can test your understanding of negative numbers, but it's the root that makes the question tricky, not the absolute value.
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by kaf » Thu Mar 19, 2009 4:08 am
Ian you are fantastic many thanks
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