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M07-31

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M07-31 [#permalink]

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New post 16 Sep 2014, 00:35
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Official Solution:

If \(x^2-100 \lt 300\) then \(x\) can take how many integer values?

A. 42
B. 39
C. 38
D. 37
E. 19


Given: \(x^2-100 \lt 300\);

\(x^2 \lt 400\);

\(|x| \lt 20\);

\(-20 \lt x \lt 20\), so \(x\) can take 39 integer values from -19 to 19, inclusive.


Answer: B
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Re: M07-31 [#permalink]

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New post 11 May 2016, 23:36
Bunuel wrote:
Official Solution:

If \(x^2-100 \lt 300\) then \(x\) can take how many integer values?

A. 42
B. 39
C. 38
D. 37
E. 19


Given: \(x^2-100 \lt 300\);

\(x^2 \lt 400\);

\(|x| \lt 20\);

\(-20 \lt x \lt 20\), so \(x\) can take 39 integer values from -19 to 19, inclusive.


Answer: B




One question here :-
can the above equation not be written as (x-20)(x+20) < 0
in that case the rang of x differs i.e x <20 or x <-20

I know i am missing some concept here (or worst some mistake) as x taking a value less than -20, just does not satisfy the give equation

Kudos [?]: 7 [0], given: 14

Expert Post
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Joined: 02 Aug 2009
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Kudos [?]: 5506 [0], given: 112

Re: M07-31 [#permalink]

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New post 12 May 2016, 00:09
grsm wrote:
Bunuel wrote:
Official Solution:

If \(x^2-100 \lt 300\) then \(x\) can take how many integer values?

A. 42
B. 39
C. 38
D. 37
E. 19


Given: \(x^2-100 \lt 300\);

\(x^2 \lt 400\);

\(|x| \lt 20\);

\(-20 \lt x \lt 20\), so \(x\) can take 39 integer values from -19 to 19, inclusive.


Answer: B




One question here :-
can the above equation not be written as (x-20)(x+20) < 0
in that case the rang of x differs i.e x <20 or x <-20

I know i am missing some concept here (or worst some mistake) as x taking a value less than -20, just does not satisfy the give equation


Hi
you are correct in equation, BUT wrong in inference from it..
(x-20)(x+20)<0...
this means that x-20 and x+20 have to be of opposite sign...
this is possible in range from -20 to +20.....
check on your range x<-20...
put x as -21..
so (-21-20)(-21+20) = -41*-1= 41 which is >0 so range does not hold
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Re M07-31 [#permalink]

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New post 25 Jul 2016, 10:38
I think this is a high-quality question and I agree with explanation.

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Re M07-31 [#permalink]

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New post 05 Sep 2017, 20:42
I think this is a high-quality question and I agree with explanation.

Kudos [?]: 38 [0], given: 29

Re M07-31   [#permalink] 05 Sep 2017, 20:42
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