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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
30% (02:47) correct
70%
(02:34)
wrong
based on 261
sessions
History
Date
Time
Result
Not Attempted Yet
What is the probability that a point satisfying the conditions |x| ≤ 2 and |y| ≤ 2 also satisfies |x + y| ≤ 1?
A. 1/16
B. 1/4
C. 7/16
D. 9/16
E. 3/4
Source: Career Launcher
A. 1/16
B. 1/4
C. 7/16
D. 9/16
E. 3/4
Source: Career Launcher
x and y can be any real number in the range.
|x| ≤ 2 and |y| ≤ 2
Area bounded by these 2 curves= 4*4=16
Area bounded by |x| ≤ 2, |y| ≤ 2 and |x+y| ≤ 1
16-(1/2*3*3)-(1/2*3*3)=7
Probability= 7/16
Source: Career Launcher
|x| ≤ 2 and |y| ≤ 2
Area bounded by these 2 curves= 4*4=16
Area bounded by |x| ≤ 2, |y| ≤ 2 and |x+y| ≤ 1
16-(1/2*3*3)-(1/2*3*3)=7
Probability= 7/16
Source: Career Launcher
chetan2u
Attachments
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General Discussion
nick1816
Yes, I missed out that you have not mentioned that x and y are integers, but a GMAT question would be in a format which will either tell you that x,y are integers or it will mention area bounded by |x|<2 and |y|<2. This is more of a language of a CAT question and Career launcher also has more to do with CAT preparation.
Please mention source along with the question.
_________________
chetan2u
He didn't say x is an integer, why did you assume all integer values
Posted from my mobile device
Peddi
Yes you are correct and that is what I mentioned above. Although I realised that even while I wrote the post but felt that the post actually meant them as integers since most of the GMAT question would be in that language.
I would delete my post as it would unnecessarily create confusion.
_________________
Posts: 9
nick1816
I am unable to follow this, could please explain one more time?
Posts: 9
nick1816
I am unable to follow this, could please explain one more time?
chetan2u I got 7/25 (I assumed that it mentions integer) Without the assumption the answer would be Infinity/Infinity. 
. However I clicked on C because that was the only option with 7 in the numerator. 
Good question, poorly written.
. However I clicked on C because that was the only option with 7 in the numerator. Good question, poorly written.
Hi Rajshek,
the total area filled by the conditions for x,y is 2*2 per quadrant. We have 4 quandrants, so its 4^2=16.
Now, how much of that area is occupied with Ix+yI<=1?
For that, check the picture that nick posted.
Now, if you draw the square (4x4 square) into the coordinate system, and also draw the stuff that nick posted, you can see that two equal triangles are created. Each has two sides of length 3 (a,b, hypotenuse c leave open, u dont need it now).
So in total, the two triangles take 3*3=9 of the area.
This means that 9/16 is free -> 7/16 is occupied.
the total area filled by the conditions for x,y is 2*2 per quadrant. We have 4 quandrants, so its 4^2=16.
Now, how much of that area is occupied with Ix+yI<=1?
For that, check the picture that nick posted.
Now, if you draw the square (4x4 square) into the coordinate system, and also draw the stuff that nick posted, you can see that two equal triangles are created. Each has two sides of length 3 (a,b, hypotenuse c leave open, u dont need it now).
So in total, the two triangles take 3*3=9 of the area.
This means that 9/16 is free -> 7/16 is occupied.
@Experts
Can someone please explain me this question?
Can someone please explain me this question?
chetan2u
[/quote]
Yes, I missed out that you have not mentioned that x and y are integers, but a GMAT question would be in a format which will either tell you that x,y are integers or it will mention area bounded by |x|<2 and |y|<2. This is more of a language of a CAT question and Career launcher also has more to do with CAT preparation.
Please mention source along with the question.[/quote]
Chetan2u may you kindly solve the question?
iam unable to understand why 0 is excluded?
hadimadi
i didn't get how do u take 2*2 per quadrant?please explain ...I'm unable to understand it
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