It is currently 21 Feb 2018, 19:01

### 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

# When a≠0, how many solutions does the equation

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

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4898
GPA: 3.82
When a≠0, how many solutions does the equation [#permalink]

### Show Tags

23 Jan 2018, 00:10
Expert's post
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:02) correct 42% (01:37) wrong based on 65 sessions

### HideShow timer Statistics

[GMAT math practice question]

When $$a≠0$$, how many solutions does the equation $$a(x+b)^2+c=0$$ have?

$$1) bc=0$$
$$2) |b|+|c|=0$$
[Reveal] Spoiler: OA

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 929
Location: India
GPA: 3.82
When a≠0, how many solutions does the equation [#permalink]

### Show Tags

23 Jan 2018, 01:41
1
KUDOS
1
This post was
BOOKMARKED
MathRevolution wrote:
[GMAT math practice question]

When $$a≠0$$, how many solutions does the equation $$a(x+b)^2+c=0$$ have?

$$1) bc=0$$
$$2) |b|+|c|=0$$

Statement 1: implies either $$b=0$$ or $$c=0$$

if $$c=0$$, then we have $$x=-b$$

but if $$b=0$$, then we have $$ax^2=-c$$, there could be multiple solutions. Insufficient

Statement 2: sum of two positive numbers is $$0$$ only when both themselves are $$0$$

$$=> b=c=0$$

hence our equation becomes $$ax^2=0$$, this is only possible when $$x=0$$ because $$a≠0$$. So we have $$1$$ solution here. Sufficient

Option B
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4898
GPA: 3.82
Re: When a≠0, how many solutions does the equation [#permalink]

### Show Tags

25 Jan 2018, 03:03
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

There are three cases to consider:
Case 1: $$a > 0, c > 0$$ or $$a < 0, c < 0$$
The equation has no roots.

Case 2: $$c = 0.$$
The equation has only one root.

Case 3: $$a > 0, c < 0$$ or $$a < 0, c > 0$$
The equation has two roots.

Condition 1):
If $$bc = 0$$, then when
$$a = 1, b = 0, c = -1$$, the equation has two roots, and when
$$a = 1, b = 0, c = 0$$, the equation has one root.
As the question does not have a unique answer, condition 1) is not sufficient.

Condition 2)
$$|b| + |c| = 0 ⇔ b = c = 0.$$
Since $$c = 0,$$ the equation has only one root.
Condition 2) is sufficient.

Therefore, the answer is B.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Re: When a≠0, how many solutions does the equation   [#permalink] 25 Jan 2018, 03:03
Display posts from previous: Sort by

# When a≠0, how many solutions does the equation

 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®.