GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Apr 2019, 07:38

### 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
Your Progress

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 (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54375
If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2  [#permalink]

### Show Tags

10 Apr 2019, 23:21
00:00

Difficulty:

5% (low)

Question Stats:

94% (00:45) correct 6% (00:22) wrong based on 31 sessions

### HideShow timer Statistics

If $$\sqrt{3 - 2x} = 1$$, then what is the value of $$(3 – 2x) + (3 – 2x)^2$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

_________________
CEO
Joined: 18 Aug 2017
Posts: 3004
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2  [#permalink]

### Show Tags

11 Apr 2019, 01:01
Bunuel wrote:
If $$\sqrt{3 - 2x} = 1$$, then what is the value of $$(3 – 2x) + (3 – 2x)^2$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

$$(3 – 2x) + (3 – 2x)^2$$
3-2x= $$\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} so [m](3 – 2x) + (3 – 2x)^2$$ = $$\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} + ( [m]\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} )^2 given [m]\sqrt{3 - 2x} = 1$$
so 1+1 = 2
IMO C
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 05 Apr 2019
Posts: 7
If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2  [#permalink]

### Show Tags

11 Apr 2019, 11:20
Archit3110 wrote:
Bunuel wrote:
If $$\sqrt{3 - 2x} = 1$$, then what is the value of $$(3 – 2x) + (3 – 2x)^2$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

$$(3 – 2x) + (3 – 2x)^2$$
3-2x= $$\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} so [m](3 – 2x) + (3 – 2x)^2$$ = $$\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} + ( [m]\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} )^2 given [m]\sqrt{3 - 2x} = 1$$
so 1+1 = 2
IMO C

Why not square both sides of the first equation to eliminate the square root? and then solve.

I got 0 as my answer
CEO
Joined: 18 Aug 2017
Posts: 3004
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2  [#permalink]

### Show Tags

11 Apr 2019, 11:33
thealpine ; squaring both side will give +/- values and this question we can solve without squaring as well √x*√x=x so ; 3-2x = (√3-2x) * (√3-2x)

thealpine wrote:
Archit3110 wrote:
Bunuel wrote:
If $$\sqrt{3 - 2x} = 1$$, then what is the value of $$(3 – 2x) + (3 – 2x)^2$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

$$(3 – 2x) + (3 – 2x)^2$$
3-2x= $$\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} so [m](3 – 2x) + (3 – 2x)^2$$ = $$\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} + ( [m]\sqrt{3 - 2x} * [m]\sqrt{3 - 2x} )^2 given [m]\sqrt{3 - 2x} = 1$$
so 1+1 = 2
IMO C

Why not square both sides of the first equation to eliminate the square root? and then solve.

I got 0 as my answer

_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Joined: 05 Apr 2019
Posts: 7
Re: If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2  [#permalink]

### Show Tags

11 Apr 2019, 11:42
Archit3110 wrote:
thealpine ; squaring both side will give +/- values and this question we can solve without squaring as well √x*√x=x so ; 3-2x = (√3-2x) * (√3-2x)

I heard this on a teaching platform, that whenever the GMAT gives your the square root on the prompt, you can/it is okay to only consider positive values. However, if the square root is something you come across while solving for a problem then you have to consider both positive and negative values.

Heard this from MikeMcGarry

Thoughts on this?
Intern
Joined: 09 Apr 2019
Posts: 4
Location: Brazil
GPA: 3.45
If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2  [#permalink]

### Show Tags

16 Apr 2019, 09:54
thealpine wrote:

I heard this on a teaching platform, that whenever the GMAT gives your the square root on the prompt, you can/it is okay to only consider positive values. However, if the square root is something you come across while solving for a problem then you have to consider both positive and negative values.

Heard this from MikeMcGarry

Thoughts on this?

Indeed, it is correct to consider only positive values for the square roots on the prompt on GMAT; otherwise, you would be handling with complex roots.

It is important to bear in mind that while a "regular square root" and a "square root of some variable" may seem to be the same case, there is a difference.
Numbers have a real and an imaginary part - which is often ignored by us - but in this specific case the imaginary part plays an important role.

While the "regular square root" has an $$i^0$$ form, the variable solving find positive numbers from both $$i^0$$ and a combination of $$i^2$$ forms - which will multiply as a $$i^4$$ -, as the imaginary part follows the following power pattern:

$$i^0 = 1$$
$$i^1 = i$$
$$i^2 = – 1$$
$$i^3 = i^2 * i = (–1) * i = –i$$
$$i^4 = i^2 * i^2 = (–1) * (– 1) = 1$$
...

Having that in mind, as you may have realized, we can be sure that $$√1 = 1$$, since it is in the $$√(1*i^0)$$ form. On the hand, there is no certain when it comes to $$x^2=1$$ as it could be both:
$$(1*i^0)^2 = (1*1)^2 = 1^2 = 1$$
or
$$(1*i^2)^2 = (1*-1)^2 = (-1)^2 = 1$$

Hope it helps!

As for the problem, I would just consider that 1 to any power equals 1. Hence, the given expression would be the same of $$√1$$ and we could simply do
$$(3–2x)+(3–2x)^2 = 1 + 1^2 = 2$$
_________________
Hope some of my posts may help you. If that was the case, please hit +1 KUDOS. Thank you!

"Perfection is not attainable, but if we chase perfection we can catch excellence"
Vince Lombardi
If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2   [#permalink] 16 Apr 2019, 09:54
Display posts from previous: Sort by

# If (3 - 2x)^(1/2) = 1, then what is the value of (3 – 2x) + (3 – 2x)^2

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.