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# If x > 0, b > a, and 2x + 5 < 3x + 1, then

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CEO
Joined: 12 Sep 2015
Posts: 2593
If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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07 Jun 2018, 06:33
Top Contributor
2
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Difficulty:

55% (hard)

Question Stats:

64% (01:38) correct 36% (01:43) wrong based on 45 sessions

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If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?
i) 4.39
ii) 7.17
iii) 9.27

A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii

*kudos for all correct solutions

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Brent Hanneson – Founder of gmatprepnow.com

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Status: Asst. Manager
Joined: 01 Oct 2017
Posts: 87
Location: India
Concentration: Operations, Entrepreneurship
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WE: Supply Chain Management (Energy and Utilities)
Re: If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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07 Jun 2018, 06:47
2
GMATPrepNow wrote:

If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?
i) 4.39
ii) 7.17
iii) 9.27

A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii

*kudos for all correct solutions

Given b>a-----(1)
and (2x+5) < (3x+1)
or, c < a-------(2) (Corresponding angles)

from (1) & (2), we have

c<a<b
Or, (2x+5) < (3x+1)< (4x-8)------------(3)

Now solving the above inequality, we have

x>4-------------(4)
and x>9-------------(5)

from (4) and (5), we have

x>9-----------(6)

Hence value of x could be iii) 9.27

Ans option (D)
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Joined: 26 Feb 2016
Posts: 2846
Location: India
GPA: 3.12
If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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07 Jun 2018, 07:15
1
GMATPrepNow wrote:

If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?
i) 4.39
ii) 7.17
iii) 9.27

A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii

*kudos for all correct solutions

Since b > a, the side opposite b(4x - 8) must be greater than the side opposite to a(3x + 1)

i) $$4.39 -> 4*4.39 - 8 = 9.56 < 3*4.39 + 1 =14.17$$ -> Side opposite angle a is bigger
ii) $$7.17 -> 4*7.17 - 8 = 20.68 < 3*7.17 + 1 =22.51$$ -> Side opposite angle a is bigger
iii) $$9.27 -> 4*9.27 - 8 = 29.08 > 3*9.27 + 1 = 28.81$$ -> Side opposite angle b is bigger
(To save time, you can approximate the value of 4.39 as 4.4, 7.17 as 7.2, and 9.27 as 9.3)

Therefore, Option D(iii only) can be a value for x from the 3 options given.
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Manager
Joined: 07 Apr 2018
Posts: 106
Re: If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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08 Jun 2018, 05:01
2
Given: x>0, b>a, 2x+5 < 3x+1

Approach: As b>a, therefore 4x-8 > 3x+1
or, x>9...................................................1

we know that, 2x+5 < 3x+1
solving this, we get x>4 ............................2

From 1, we know that x>9
So, option D is correct.
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Joined: 22 May 2016
Posts: 1766
If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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08 Jun 2018, 09:53
1
GMATPrepNow wrote:

If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?
i) 4.39
ii) 7.17
iii) 9.27

A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii

*kudos for all correct solutions

I. Inequalities
Triangle Side/Angle relationship: Larger angles' opposite sides are longer than
smaller angles' opposite sides

Although we can combine inequalities, calculating them separately
is just as quick and possibly less confusing.

(1) Inequality 1, given: b > a

The side opposite b > side opposite a

$$4x-8>3x+1$$
$$x>9$$

(2) Inequality 2, given:
$$2x + 5 < 3x + 1$$
$$x>4$$

Inequality 1's lower limit in the range is 9
x MUST be greater than 9

That condition includes and satisfies Inequality 2

Any number greater than 9 is also greater than 4
By contrast, if x is between 4 and 9 (x >4 has lower limit 4),
then x is NOT greater than 9. Not valid.

x must be > 9

Only option iii) 9.27 works

II. Inequalities - Number line

Range of solutions for x > 9 [in which (9) = not including 9]

<--0----------------------------(9)-------------------->

Range of solutions for x > 4

<--0--------(4)--------------------------------------->

The lower limit, 9, from the range in Inequality 1, makes the second range true.

x > 9, by definition, means x > 4. A number greater than 9 is also greater than 4

But 4 cannot be the lower limit for the range of solutions

That is, x cannot lie between 4 and 9.

If x lies between 4 and 9, then x is not greater than 9

<--0--------(4)---------------(9)------------------>

The range of solutions for x > 9 satisfies both conditions
The range of solutions for x > 4 does not satisfy the condition that x > 9

x > 9, is the only possibility, and
only option iii) 9.27, is > 9

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CEO
Joined: 12 Sep 2015
Posts: 2593
Re: If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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09 Jun 2018, 06:21
Top Contributor
GMATPrepNow wrote:

If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?
i) 4.39
ii) 7.17
iii) 9.27

A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii

*kudos for all correct solutions

Here's a useful triangle property:

So, if b > a, then we know that 3x + 1 < 4x - 8
We're also told that 2x + 5 < 3x + 1

So, we can create the following 3-part inequality: 2x + 5 < 3x + 1 < 4x - 8
Subtract 2x from all 3 sides: 5 < x + 1 < 2x - 8
When we examine 5 < x + 1, we can conclude that 4 < x. So, x is greater than 4
When we examine x + 1 < 2x - 8, we can conclude that 9 < x. So, x is greater than 9

So, we know that x is greater than 4 AND x is greater than 9
So, it MUST be the case that x is greater than 9

Check the statements.....
Only statement iii works.

Cheers,
Brent
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Joined: 25 Nov 2015
Posts: 665
Location: India
GPA: 3.64
Re: If x > 0, b > a, and 2x + 5 < 3x + 1, then [#permalink]

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09 Jun 2018, 07:15
1
GMATPrepNow wrote:

If x > 0, b > a, and 2x + 5 < 3x + 1, then which of the following COULD be a value of x?
i) 4.39
ii) 7.17
iii) 9.27

A) i and ii only
B) ii and iii only
C) i and iii only
D) iii only
E) i, ii and iii

*kudos for all correct solutions

x>0
b > a
2x + 5 < 3x + 1 => x > 4
All three options fit.
Let us check the other given parameters
b>a means side opposite angle b > side opposite angle a
i.e. 4x-8 > 3x+1
x>9
Only iii fits 9.27
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Re: If x > 0, b > a, and 2x + 5 < 3x + 1, then   [#permalink] 09 Jun 2018, 07:15
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