GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Feb 2020, 18:28

### 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

# If a and n are positive numbers, does 2a^(2x) = n ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61396
If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

19 Jan 2020, 22:10
1
3
00:00

Difficulty:

65% (hard)

Question Stats:

41% (02:36) correct 59% (02:12) wrong based on 44 sessions

### HideShow timer Statistics

Competition Mode Question

If a and n are positive numbers, does $$2a^{2x}=n?$$

(1) $$a^x+\frac{1}{a^x}=\sqrt{n+2}$$

(2) $$x > 0$$

Are You Up For the Challenge: 700 Level Questions

_________________
VP
Joined: 20 Jul 2017
Posts: 1326
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

Updated on: 20 Jan 2020, 22:35
1
(1) $$a^x+\frac{1}{a^x} = \sqrt{n+2}$$
Squaring on both sides,
--> $$(a^x+\frac{1}{a^x})^2 = n+2$$
--> $$a^{2x} + 2*a^x*\frac{1}{a^x} + \frac{1}{a^{2x}} = n + 2$$
--> $$a^{2x} + 2 + \frac{1}{a^{2x}} = n + 2$$
--> $$a^{2x} + \frac{1}{a^{2x}} = n$$
Does $$2a^{2x} = n$$ ?
--> $$a^{2x} + \frac{1}{a^{2x}} = 2a^{2x}$$
--> $$a^{2x} = \frac{1}{a^{2x}}$$
--> $$a^{4x} = 1$$
Only Possible if $$x = 0$$
But we DO NOT know the value of x --> Insufficient

(2) $$x > 0$$
Does not talk anything about a & n --> Insufficient

Combining (1) & (2),
If $$x > 0$$, $$a^{4x}$$ is equal to 1 when a = 1
And not equal to 1 when a is not equal to 1
Insufficient

Option E

Originally posted by Dillesh4096 on 20 Jan 2020, 03:15.
Last edited by Dillesh4096 on 20 Jan 2020, 22:35, edited 1 time in total.
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5904
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 04:26
#1
a^x+1/a^x=√n+2
possible when
a=x=1 and n=2
we get yes sufficient
#2
x>0
a and n relation not know
insufficient
IMO A
VP
Joined: 24 Nov 2016
Posts: 1224
Location: United States
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 06:27
1
Quote:
If a and n are positive numbers, does $$2a^{2x}=n$$?

(1) $$a^x+1/a^x=\sqrt{n+2}$$
(2) $$x>0$$

$$a,n>0$$

(1) $$a^x+1/a^x=\sqrt{n+2}$$ insufic

$$(a^x+1/a^x)^2=(\sqrt{n+2})^2…a^{2x}+a^{-2x}+2(a^x)(a^{-x})=n+2$$
$$a^{2x}+a^{-2x}+2(a^{x+(-x)})=n+2…a^{2x}+a^{-2x}+2(a^0)=n+2$$
$$a^{2x}+a^{-2x}+2=n+2…a^{2x}+a^{-2x}=n$$

$$(rephrase): 2a^{2x}=n…2a^{2x}=a^{2x}+a^{-2x}$$
$$2a^{2x}-a^{2x}=a^{-2x}…a^{2x}=a^{-2x}$$
$$a^{2x}=1/a^{2x}…a^{2x}a^{2x}=1…a^{4x}=1$$

$$(rephrase):a^{4x}=1?…yes:a=1…or…x=0$$

(2) $$x>0$$ insufic

(1&2) insufic

$$x>0…x≠0$$ but is $$a=1$$?
$$a=1,x>0:a^{4x}=1…1^{anything}=1…answer=yes$$
$$a=2,x>0:a^{4x}=1…2^{m4}≠1…answer=no$$

Ans (E)
Director
Joined: 30 Sep 2017
Posts: 669
GMAT 1: 720 Q49 V40
GPA: 3.8
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 06:30
1
Is $$2a^{2x} = n$$?

1) Squaring both sides, one will obtain:
$$a^{2x} +a^{-2x}+2=n+2$$
$$a^{2x} +a^{-2x}=n$$

If x=0, then 1+1=2=n, then it must be true that $$2a^{2x}= 2 = n$$.

If x>0, then $$2a^{2x} =2n-2a^{-2x}$$. Thus, it is not clear that $$2a^{2x} = n$$. For clarity, consider a=1 or a=2.

NOT SUFFICIENT

2) We have no useful information on a and n.
NOT SUFFICIENT

1)+2) Since x>0, $$2a^{2x} =2n-2a^{-2x}$$. Thus, it could be true (or false) that $$2a^{2x} = n$$.
NOT SUFFICIENT

Kindly give kudos if you like the explanation
Manager
Joined: 17 Jan 2019
Posts: 155
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 07:05
If a and n are positive numbers, does 2a^2x=n?

(1) a^x+1/(a^x)=root(n+2)
a^x+a^-x=root(n+2)
(a^x+a^-x)^2=n+2
a^2x+2a^x a^-x+a-2x=n+2
a^2x+1+a^-2x=n+2
a^(2x)+a^(-2x)-1=n
they not equal
sufficient

(2) x>0
we don't have any clue about a and n
insufficient

Therefore, A
Director
Joined: 07 Mar 2019
Posts: 708
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 09:35
1
If a and n are positive numbers, does $$2a^{2x} = n$$?

(1) $$a^x+\frac{1}{a^x} = √(n+2)$$
$$a^{2x}+\frac{1}{a^{2x}} +2 = n+2$$
$$a^{2x}+\frac{1}{a^{2x}} = n$$
a, x and n can take any value so

INSUFFICIENT.

(2) x > 0
None of the values are given.

INSUFFICIENT.

Together 1 and 2
INSUFFICIENT.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager
Joined: 01 Mar 2019
Posts: 443
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 17:34
1
1) from this we won't be getting 2a^2x =n....... sufficient to say that they are not equal....but since they are positive no's...for a=1.....n becomes 2......for both of them....so insufficient

2) clearly insufficient

OA:E
Manager
Joined: 26 Dec 2017
Posts: 54
Re: If a and n are positive numbers, does 2a^(2x) = n ?  [#permalink]

### Show Tags

20 Jan 2020, 18:44
1
Ans: E

a)a^x + (1/a^x) = sqrt (n+2)
squaring both the sides
a^2x+(1/a^2x)+2=n+2
a^2x+(1/a^2x)=n
if x=0
n=2 and, 2a^(2x) = n
x=0, so, 2a^0=2...true
if x=1,a=1,n=2 and equation holds..true
if x=1,a=2,n=17/4 and equation doesn't hold..false
not sufficient

b)x>0....alone clearly not sufficient

combined..for,x=1,a=1..true
x=1,a=2..false

So, taking both not sufficient.
Re: If a and n are positive numbers, does 2a^(2x) = n ?   [#permalink] 20 Jan 2020, 18:44
Display posts from previous: Sort by