It is currently 17 Mar 2018, 22:41

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement

Author Message
TAGS:

Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 865
If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

20 Mar 2017, 05:30
1
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

35% (01:32) correct 65% (01:47) wrong based on 79 sessions

HideShow timer Statistics

If $$2^{2x+5} - 65.2^{x+1} = - 8$$, then which of the following statement is definitely correct?

A. x can only be a positive integer
B. x can only be a negative integer
C. x can be either a positive integer or a negative integer
D. No value of x exists which satisfies the equation
E. x is not an integer

Thanks,
Saquib
Quant Expert
e-GMAT

Register for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the real-time guidance of our Experts

[Reveal] Spoiler: OA

_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Last edited by Bunuel on 20 Mar 2017, 06:06, edited 1 time in total.
Renamed the topic and edited the question.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 865
Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

20 Mar 2017, 05:31
Reserving this space to post the official solution.
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Retired Moderator
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 528
Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

21 Oct 2017, 00:09
1
KUDOS
_________________

Hasan Mahmud

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1001
Location: India
GPA: 3.82
If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

21 Oct 2017, 00:56
3
KUDOS
1
This post was
BOOKMARKED
Mahmud6 wrote:

Hi Mahmud6

$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$

$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$

Let $$2^{(x+1)}=a$$, so we have

$$8a^2-65a+8=0$$ or

$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$

so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)

or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)

Option C
Intern
Joined: 29 May 2012
Posts: 39
Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

21 Oct 2017, 01:54
niks18 wrote:
Mahmud6 wrote:

Hi Mahmud6

$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$

$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$

Let $$2^{(x+1)}=a$$, so we have

$$8a^2-65a+8=0$$ or

$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$

so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)

or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)

Option C

Hi,

Thank you.

Paul
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1001
Location: India
GPA: 3.82
Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

21 Oct 2017, 01:57
Paulli1982 wrote:
niks18 wrote:
Mahmud6 wrote:

Hi Mahmud6

$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$

$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$

Let $$2^{(x+1)}=a$$, so we have

$$8a^2-65a+8=0$$ or

$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$

so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)

or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)

Option C

Hi,

Thank you.

Paul

Hi Paulli1982

Dot in algebra mean multiplication so it is $$65*2^{x+1}$$ and not a decimal number
Senior Manager
Joined: 31 Jul 2017
Posts: 317
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

21 Oct 2017, 07:47
niks18 wrote:
Mahmud6 wrote:

Hi Mahmud6

$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$

$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$

Let $$2^{(x+1)}=a$$, so we have

$$8a^2-65a+8=0$$ or

$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$

so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)

or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)

Option C

Hi,

May I please know what is wrong with the below approach:

2^x * 32 - 65*2*2^x = -8
2^x = (2/7)^2

Please let me know where I am wrong in this.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1001
Location: India
GPA: 3.82
If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]

Show Tags

21 Oct 2017, 07:52
rahul16singh28 wrote:
niks18 wrote:
Mahmud6 wrote:

Hi Mahmud6

$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$

$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$

Let $$2^{(x+1)}=a$$, so we have

$$8a^2-65a+8=0$$ or

$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$

so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)

or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)

Option C

Hi,

May I please know what is wrong with the below approach:

2^x* 32 - 65*2*2^x = -8
2^x = (2/7)^2

Please let me know where I am wrong in this.

hi rahul16singh28

the highlighted portion is not correct. it is $$2^{2x}$$ and not $$2^x$$
If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement   [#permalink] 21 Oct 2017, 07:52
Display posts from previous: Sort by