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If (2-g)^2 < 9, which of the following expression of g is correct?

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If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post Updated on: 28 Sep 2018, 07:50
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If \((2-g)^2 < 9\), which of the following expression of \(g\) is correct?


A) \(g < -1\)

B) \(-3/\sqrt{2}< g <3/\sqrt{2}\)

C) \(-9/2 < g < 9/2\)

D) \(g > 5\)

E) \(-1 < g < 5\)

Originally posted by reynaldreni on 28 Sep 2018, 07:45.
Last edited by Bunuel on 28 Sep 2018, 07:50, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 28 Sep 2018, 08:10
2-g < 3
-g < 1
g > - 1

2-g > - 3
- g > - 5

g < 5

-1 < g < 5

Answer choice E

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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 28 Sep 2018, 08:21
reynaldreni wrote:
If \((2-g)^2 < 9\), which of the following expression of \(g\) is correct?


A) \(g < -1\)

B) \(-3/\sqrt{2}< g <3/\sqrt{2}\)

C) \(-9/2 < g < 9/2\)

D) \(g > 5\)

E) \(-1 < g < 5\)


Take the square root from both ides of \((2-g)^2 < 9\) (note that we can safely do that sine both sides are non-negative):

\(|2 - g| < 3\);

Get rid of the modulus: \(-3 < 2 - g < 3\);

Subtract 2: \(-5 < -g < 1\);

Multiply by -1 and flip the signs: \(5 > g > -1\).

Answer: E.
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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 30 Sep 2018, 05:45
Dear Bunuel,

Please review my approach is it okay ?

(2-g)^2 < 9
(g-2)^2 < 9
(g-2)^2 -9 <0
(g-2)^2 - 3^2 < 0
Now applying (a^2 - b^2) = (a+b)(a-b)

(g-2+3)(g-2-3)<0
(g+1)(g-5)<0

Now putting on number line , we will get
-1<g<5

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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 30 Sep 2018, 08:01
vipulshahi wrote:
Dear Bunuel,

Please review my approach is it okay ?

(2-g)^2 < 9
(g-2)^2 < 9
(g-2)^2 -9 <0
(g-2)^2 - 3^2 < 0
Now applying (a^2 - b^2) = (a+b)(a-b)

(g-2+3)(g-2-3)<0
(g+1)(g-5)<0

Now putting on number line , we will get
-1<g<5

Posted from my mobile device

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The above is correct.
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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: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 30 Sep 2018, 14:55
Answer: B

Solution



Given:

• \((2−g)^2<9\)

To find:
• The correct expression of g

Approach and Working out:

Method-1)

• \((2−g)^2-9 <0\)
• \((2-g)^2 – 3^2 <0\)
• (2-g-3) (2-g+3)<0
• (-1-g)(5-g) <0
• (g+1)(g-5)<0
• -1 < g < 5

Answer: E
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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 30 Sep 2018, 14:58

Solution



Given:

• \((2−g)^2<9\)

To find:
• The correct expression of g

Approach and Working out:

Method-2)

• |(2−g)|< 3
• -3 < (2-g) < 3
• -5 < -g < 1
• 5> g > -1

Answer: E
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Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
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Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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New post 16 Dec 2018, 04:22
Bunuel wrote:
reynaldreni wrote:
If \((2-g)^2 < 9\), which of the following expression of \(g\) is correct?


A) \(g < -1\)

B) \(-3/\sqrt{2}< g <3/\sqrt{2}\)

C) \(-9/2 < g < 9/2\)

D) \(g > 5\)

E) \(-1 < g < 5\)


Take the square root from both ides of \((2-g)^2 < 9\) (note that we can safely do that sine both sides are non-negative):

\(|2 - g| < 3\);

Get rid of the modulus: \(-3 < 2 - g < 3\);

Subtract 2: \(-5 < -g < 1\);

Multiply by -1 and flip the signs: \(5 > g > -1\).

Answer: E.


Dear Bunuel,

I have issues with this "since both sides are non-negative". I came across this assumption for several times now. Most often in the module regarding absolute values. However, I already didn't get to the real bottom of the issue. May you elaborate your thought behind "since both sides are non-negative"?

I would like to add the following: I understand that distances in general can't be negative and that absolute values can be interpreted as distances! However, even after understanding that fact, I still don't understand, situations like the following:

|x-y|

In my understanding, this would simply be some distance from point x to y on a number line. But we can't say foe sure that this is expression will yield some positive value, because we don't know either value of x or y. Why is that?

Best, gota900
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Re: If (2-g)^2 < 9, which of the following expression of g is correct? &nbs [#permalink] 16 Dec 2018, 04:22
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If (2-g)^2 < 9, which of the following expression of g is correct?

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