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

It is currently 24 May 2019, 10:08

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If m and n are integers, what is the value of m + n ?

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55271
If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 26 Apr 2019, 02:20
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

77% (01:11) correct 23% (01:31) wrong based on 111 sessions

HideShow timer Statistics

Director
Director
User avatar
D
Joined: 18 Jul 2018
Posts: 906
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 26 Apr 2019, 04:18
1
From S1:

\((x + m)(x + n) = x^2 + 5x + mn\)

\(x^2+x(m+n)+mn = x^2+5x+mn\)

5x = x(m+n)

x(5-(m+n)) = 0

As x ≠ 0, m+n = 5

Sufficient.

From S2:

Clearly Insufficient.

A is the answer.
_________________
Press +1 Kudo If my post helps!
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7686
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 26 Apr 2019, 04:51
1
If m and n are integers, what is the value of m + n ?

(1) (x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
(x + m)(x + n) is a quadratic equation that has m and n as roots..
\((x + m)(x + n)=x^2+(m+n)x+mn\)..
Therefore, \(x^2+(m+n)x+mn=x^2 + 5x + mn\)
Thus m+n is the sum of roots and is equal to 5

(2) mn = 4
Mainly for C trap.
Insuff

A
_________________
Intern
Intern
User avatar
S
Joined: 14 Apr 2017
Posts: 44
Location: Hungary
GMAT 1: 690 Q50 V34
GMAT 2: 760 Q50 V42
GMAT 3: 700 Q50 V33
WE: Education (Education)
CAT Tests
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 27 Apr 2019, 05:34
Bunuel wrote:
If m and n are integers, what is the value of m + n ?

(1) (x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
(2) mn = 4


DS53602.01
OG2020 NEW QUESTION


We know that \(m\) and \(n\) are integers. The original question: \(m+n=?\)

1) We know that \((x+m)(x+n)=x^2+5x+mn\) and \(x\neq 0\).

\(x^2+mx+nx+mn=x^2+5x+mn\)

\(x(m+n)=5x\)

Since \(x\neq 0\), we can divide both sides of the above equation by \(x\).

\(m+n=5\). Thus, the answer to the original question is a unique value. \(\implies\) Sufficient

2) We know that \(mn=4\) and can test possible cases. If \(m=2\) and \(n=2\), then \(m+n=4\). However, if \(m=4\) and \(n=1\), then \(m+n=5\). Thus, we can't get a unique value to answer the original question. \(\implies\) Insufficient

Answer: A
_________________
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3529
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 27 Apr 2019, 06:53
Bunuel wrote:
If m and n are integers, what is the value of m + n ?

(1) (x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
(2) mn = 4


DS53602.01
OG2020 NEW QUESTION



#1
solve for
(x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
we get m+n= 5
sufficeint
#2
mn=4
not sufficeint
IMO A
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3727
Location: Canada
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 29 Apr 2019, 09:33
Top Contributor
Bunuel wrote:
If m and n are integers, what is the value of m + n ?

(1) (x + m)(x + n) = x² + 5x + mn and x ≠ 0.
(2) mn = 4

Given: m and n are integers

Target question: What is the value of m + n ?

Statement 1: (x + m)(x + n) = x² + 5x + mn and x ≠ 0.
Use FOIL to expand the left side: x² + nx + mx + mn = x² + 5x + mn
Factor the two middle terms: x² + x(n + m) + mn = x² + 5x + mn
At this point, we should see that m+n = 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

If you're not convinced, we can take a few more steps.
Take: x² + x(n + m) + mn = x² + 5x + mn
Subtract x² from both sides: x(n + m) + mn = 5x + mn
Subtract mn from both sides: x(n + m) = 5x
Divide both sides by x to get: n + m = 5
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: mn = 4
There are many values of m and n that satisfy statement 2. Here are two:
Case a: m = 4 and n = 1. In this case, the answer to the target question is m + n = 4 + 1 = 5
Case b: m = 2 and n = 2. In this case, the answer to the target question is m + n = 2 + 2 = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6231
Location: United States (CA)
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 06 May 2019, 20:20
Bunuel wrote:
If m and n are integers, what is the value of m + n ?

(1) (x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.
(2) mn = 4


DS53602.01
OG2020 NEW QUESTION


Statement One Alone:

(x + m)(x + n) = x^2 + 5x + mn and x ≠ 0.

Foiling we have:

x^2 + mx + nx + mn = x^2 + 5x + mn

mx + nx = 5x

x(m + n) = 5x

m + n = 5

Statement one alone is sufficient to answer the question.

Statement Two Alone:

mn = 4

Only knowing the product and m and n does not give us enough information to determine the sum of n and m. For example, if m = 1 and n = 4, then m + n = 5. However, if m = n = 2, then m + n = 4. Statement two alone is not sufficient to answer the question.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If m and n are integers, what is the value of m + n ?  [#permalink]

Show Tags

New post 20 May 2019, 13:28
Hi All,

We're told that M and N are INTEGERS. We're asked for the value of M+N. This question can be solved with a mix of Algebra and TESTing VALUES.

(1) (X + M)(X + N) = X^2 + 5X + (M)(N) and X ≠ 0.

The equation in Fact 1 should get us thinking about a Quadratic and how we can F.O.I.L. the parentheses and get the given result. Notice that the 'middle' term is "+5X"; this provides a huge clue about how M and N relate to one another. Since the SUM of M and N must be +5, you can stop right here (since the question asks for that exact value). If you didn't immediately recognize that though, you can run a few TESTs and see what happens...

IF....
M=1 and N=4, then (X+1)(X+4) = X^2 +5X + 4 and the answer to the question is 5.
M=2 and N=3, then (X+2)(X+3) = X^2 +5X + 6 and the answer to the question is 5.
M=6 and N= -1, then (X+6)(X-1) = X^2 +5X - 6 and the answer to the question is 5.
Etc.
The answer to the question is ALWAYS 5.
Fact 1 is SUFFICIENT

(2) (M)(N) = 4

With the equation in Fact 2, we can come up with a couple of simple examples...
IF....
M=1 and N=4, then the answer to the question is 5.
M=2 and N=2, then the answer to the question is 4.
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
GMAT Club Bot
Re: If m and n are integers, what is the value of m + n ?   [#permalink] 20 May 2019, 13:28
Display posts from previous: Sort by

If m and n are integers, what is the value of m + n ?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.