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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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A
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E

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  35% (medium)

Question Stats:

73% (00:35) correct 27% (00:34) wrong based on 56 sessions

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Re M07-31  [#permalink]

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New post 16 Sep 2014, 00:35
2
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
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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.
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Re: M07-31  [#permalink]

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New post 03 Dec 2017, 15:36
niks18

Quote:
\(x^2 \lt 400\);

\(|x| \lt 20\);


I understood that \(\sqrt{}x^2 = |x|\) but
\(\sqrt{400}\) can take both values as -20 and +20
Why did we consider only positive values?
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M07-31  [#permalink]

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New post 03 Dec 2017, 20:49
adkikani wrote:
niks18

Quote:
\(x^2 \lt 400\);

\(|x| \lt 20\);


I understood that \(\sqrt{}x^2 = |x|\) but
\(\sqrt{400}\) can take both values as -20 and +20
Why did we consider only positive values?


Not clear what are you implying there.

\(\sqrt{400}=20\) ONLY, not +20 and -20. In contrast x^2 = 400 has TWO solutions, x = 20 and x = -20.

In the question above we DO consider the possibility of x being negative:
\(x^2 \lt 400\);

\(|x| \lt 20\)

\(x^2 \lt 400\);

\(-20 < x <20\)
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Re: M07-31  [#permalink]

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New post 03 Dec 2017, 21:33
Bunuel

Thanks for your two cents

Quote:
Not clear what are you implying there.

\(\sqrt{400}=20\) ONLY, not +20 and -20. In contrast x^2 = 400 has TWO solutions, x = 20 and x = -20.


Is this because GMAT does not test imaginary roots ie complex number of the form \(\sqrt{-i}\)
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Re: M07-31  [#permalink]

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New post 03 Dec 2017, 21:37
adkikani wrote:
Bunuel

Thanks for your two cents

Quote:
Not clear what are you implying there.

\(\sqrt{400}=20\) ONLY, not +20 and -20. In contrast x^2 = 400 has TWO solutions, x = 20 and x = -20.


Is this because GMAT does not test imaginary roots ie complex number of the form \(\sqrt{-i}\)


GMAT deals with only Real Numbers: Integers, Fractions and Irrational Numbers.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M07-31 &nbs [#permalink] 03 Dec 2017, 21:37
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