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

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

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Updated on: 28 Sep 2018, 08:50
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Difficulty:

15% (low)

Question Stats:

85% (01:07) correct 15% (01:22) wrong based on 54 sessions

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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, 08:45.
Last edited by Bunuel on 28 Sep 2018, 08:50, 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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28 Sep 2018, 09:10
2-g < 3
-g < 1
g > - 1

2-g > - 3
- g > - 5

g < 5

-1 < g < 5

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Joined: 02 Sep 2009
Posts: 49993
Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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28 Sep 2018, 09:21
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: $$5 > g > -1$$.

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

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30 Sep 2018, 06:45
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

Posted from my mobile device
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Posts: 49993
Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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30 Sep 2018, 09:01
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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Joined: 04 Jan 2015
Posts: 2066
Re: If (2-g)^2 < 9, which of the following expression of g is correct?  [#permalink]

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30 Sep 2018, 15:55

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

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

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30 Sep 2018, 15:58

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

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Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
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
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
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Re: If (2-g)^2 < 9, which of the following expression of g is correct? &nbs [#permalink] 30 Sep 2018, 15:58
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# If (2-g)^2 < 9, which of the following expression of g is correct?

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