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1) x must be less than 4 somavesum 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: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 :/
I am sure u meant it this way: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
Thanks for catching that, Cramya! I'll edit my post to prevent any confusion.cramya wrote:Thanks again Ian for an excellent explanation.
I am sure u meant it this way: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
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
Ian Stewart wrote: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: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 :/
|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.
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: In you explanation are you determining the position of x from the two statements?
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.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
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