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# What is the probability that a point satisfying the conditions |x| ≤

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VP
Joined: 19 Oct 2018
Posts: 1172
Location: India
What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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Updated on: 21 Oct 2019, 22:57
4
00:00

Difficulty:

95% (hard)

Question Stats:

22% (02:15) correct 78% (02:40) wrong based on 51 sessions

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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

Originally posted by nick1816 on 21 Oct 2019, 17:07.
Last edited by nick1816 on 21 Oct 2019, 22:57, edited 1 time in total.
VP
Joined: 19 Oct 2018
Posts: 1172
Location: India
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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21 Oct 2019, 19:13
2
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

chetan2u wrote:
nick1816 wrote:
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

Please check the question it may not be correct.
|x|≤ 2 means x can be -2,-1,0,1,2 and |y| ≤ 2 means y can be -2,-1,0,1,2
So total ways (x,y) can be chosen is 5*5=25 but none of the choices has 25 or 5 in the denominator

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Math Expert
Joined: 02 Aug 2009
Posts: 8309
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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21 Oct 2019, 19:23
nick1816 wrote:
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

chetan2u wrote:
nick1816 wrote:
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

Please check the question it may not be correct.
|x|≤ 2 means x can be -2,-1,0,1,2 and |y| ≤ 2 means y can be -2,-1,0,1,2
So total ways (x,y) can be chosen is 5*5=25 but none of the choices has 25 or 5 in the denominator

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.
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Joined: 20 Jul 2019
Posts: 55
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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21 Oct 2019, 19:24
chetan2u wrote:
nick1816 wrote:
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

Please check the question it may not be correct.
|x|≤ 2 means x can be -2,-1,0,1,2 and |y| ≤ 2 means y can be -2,-1,0,1,2
So total ways (x,y) can be chosen is 5*5=25 but none of the choices has 25 or 5 in the denominator

He didn't say x is an integer, why did you assume all integer values

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 8309
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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21 Oct 2019, 19:31
Peddi wrote:
chetan2u wrote:
nick1816 wrote:
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

Please check the question it may not be correct.
|x|≤ 2 means x can be -2,-1,0,1,2 and |y| ≤ 2 means y can be -2,-1,0,1,2
So total ways (x,y) can be chosen is 5*5=25 but none of the choices has 25 or 5 in the denominator

He didn't say x is an integer, why did you assume all integer values

Posted from my mobile device

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.
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Joined: 19 Oct 2018
Posts: 1172
Location: India
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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21 Oct 2019, 19:33
chetan2u
I will take care of that from next time. Thanks for letting me know. :
Intern
Joined: 13 Feb 2018
Posts: 10
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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25 Oct 2019, 08:49
nick1816 wrote:
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

I am unable to follow this, could please explain one more time?
Intern
Joined: 13 Feb 2018
Posts: 10
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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25 Oct 2019, 08:50
nick1816 wrote:
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

I am unable to follow this, could please explain one more time?
Intern
Joined: 27 Jul 2018
Posts: 20
Re: What is the probability that a point satisfying the conditions |x| ≤  [#permalink]

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01 Nov 2019, 01:23
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.
Re: What is the probability that a point satisfying the conditions |x| ≤   [#permalink] 01 Nov 2019, 01:23
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