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

 It is currently 20 Jun 2018, 03:59

### 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 a, b, and c are positive numbers, a+b+c=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5585
GMAT 1: 800 Q59 V59
GPA: 3.82
If a, b, and c are positive numbers, a+b+c=? [#permalink]

### Show Tags

21 Feb 2017, 01:08
00:00

Difficulty:

45% (medium)

Question Stats:

53% (00:46) correct 47% (01:11) wrong based on 55 sessions

### HideShow timer Statistics

If a, b, and c are positive numbers, a+b+c=?

$$1) a^2+b^2+c^2=56$$
$$2) ab+bc+ca=10$$

_________________

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.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 19 Apr 2016 Posts: 275 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) If a, b, and c are positive numbers, a+b+c=? [#permalink] ### Show Tags 21 Feb 2017, 01:39 5 1 MathRevolution wrote: If a, b, and c are positive numbers, a+b+c=? $$1) a^2+b^2+c^2=56$$ $$2) ab+bc+ca=10$$ $$(a+b+c)^2 = a^2+b^2+c^2 + 2*(ab+bc+ca)$$ St I a^2+b^2+c^2=56 no info about ab+bc+ca ------------Insufficient St II ab+bc+ca=10 no info about a^2+b^2+c^2 ------------Insufficient Combining St I and II, we have both the terms which are enough to find $$(a+b+c)^2$$ which in turn will give (a+b+c) $$(a+b+c)^2 = a^2+b^2+c^2 + 2*(ab+bc+ca)$$ $$(a+b+c)^2 = 56 + 20 = 76$$ $$(a+b+c) = 76^{0.5}$$ Hence Option C is correct Hit Kudos if you liked it Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5585 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: If a, b, and c are positive numbers, a+b+c=? [#permalink] ### Show Tags 23 Feb 2017, 01:06 ==> In the original condition, there are 3 variables (x, y, z) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), E is most likely to be the answer. By solving con 1) and con 2), you get $$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)=56+2(10)=76$$, which becomes $$a+b+c=\sqrt{76}$$, hence it is unique and sufficient. Therefore, the answer is C. Answer: C _________________ 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. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Joined: 06 Jan 2015
Posts: 387
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: If a, b, and c are positive numbers, a+b+c=? [#permalink]

### Show Tags

23 Feb 2017, 02:41
MathRevolution wrote:
If a, b, and c are positive numbers, a+b+c=?

$$1) a^2+b^2+c^2=56$$
$$2) ab+bc+ca=10$$

Hi,

Here there is no necessity to calculate the value if we know the formula of $$(a+b+c)^2$$ then it is more than enough

So $$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$$

$$1) a^2+b^2+c^2=56$$ We don't the value of ab+bc+ca--Not Suff

$$2) ab+bc+ca=10$$ We don't the value of $$a^2+b^2+c^2=56$$--Not Suff

By Combining 1 and 2 it is suff

Hence C
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Intern
Joined: 27 Feb 2017
Posts: 2
Location: United States
GMAT 1: 720 Q42 V47
GPA: 3.1
Re: If a, b, and c are positive numbers, a+b+c=? [#permalink]

### Show Tags

01 Mar 2017, 20:38
MathRevolution wrote:
If a, b, and c are positive numbers, a+b+c=?

$$1) a^2+b^2+c^2=56$$
$$2) ab+bc+ca=10$$

In the first condition, why can't we just take the square root of both sides and get a+b+c=sqrt(56) ?

Thanks for the help.
Senior Manager
Joined: 06 Jan 2015
Posts: 387
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: If a, b, and c are positive numbers, a+b+c=? [#permalink]

### Show Tags

01 Mar 2017, 21:06
josephlassen wrote:
MathRevolution wrote:
If a, b, and c are positive numbers, a+b+c=?

$$1) a^2+b^2+c^2=56$$
$$2) ab+bc+ca=10$$

In the first condition, why can't we just take the square root of both sides and get a+b+c=sqrt(56) ?

Thanks for the help.

Hi josephlassen,

$$\sqrt{}(a^2+b^2+c^2)=56==>a+b+c=\sqrt{}(56)$$ This is not right,However $$\sqrt{}(a+b+c)^2=a+b+c$$ is right

$$(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$$
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Re: If a, b, and c are positive numbers, a+b+c=?   [#permalink] 01 Mar 2017, 21:06
Display posts from previous: Sort by