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

It is currently 18 Oct 2018, 00:17

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 the sum of the reciprocals of two consecutive odd integers

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

Hide Tags

Board of Directors
User avatar
P
Joined: 01 Sep 2010
Posts: 3304
If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 23 Jul 2017, 11:17
Top Contributor
6
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:31) correct 12% (02:09) wrong based on 429 sessions

HideShow timer Statistics

Intern
Intern
avatar
S
Joined: 30 May 2013
Posts: 29
GMAT 1: 600 Q50 V21
GMAT 2: 640 Q49 V29
Reviews Badge
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 23 Jul 2017, 12:19
2
1
carcass wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11


We can directly use the options as that will be the fastest method to this problem.
(1/5 + 1/7) = 12/35
Intern
Intern
User avatar
B
Joined: 06 Feb 2016
Posts: 48
Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
GPA: 3.5
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 25 Jul 2017, 03:52
2
Or algebraically: 1/x + 1/y=12/35
(x+y)/xy=12/35
You can see from the answer choices that only 7 can be the correct answer.
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4094
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 25 Jul 2017, 09:39
1
carcass wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11

\(x = 5\) & \(y = 7\)

\(\frac{1}{x} + \frac{1}{y} = \frac{1}{5} + \frac{1}{7}\) = \(\frac{12}{35}\)

Thus, the greater of the two integers is 7 answer must be (C) 7

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3863
Location: United States (CA)
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 26 Jul 2017, 16:30
4
carcass wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11


We can let the first odd integer = x and the next odd integer = x + 2; thus, the reciprocals are 1/x and 1/(x + 2). Thus:

1/x + 1/(x+2) = 12/35

Multiplying by 35x(x+2), we have:

35(x + 2) + 35x = 12x(x + 2)

35x + 70 + 35x = 12x^2 + 24x

12x^2 - 46x - 70 = 0

6x^2 - 23x - 35 = 0

(6x + 7)(x - 5) = 0

Thus, x = -7/6 or x = 5.

Since x is an integer, x must be 5 and the greater integer is x + 2 = 7.

Alternate solution:


We are given that the sum of the reciprocals of two consecutive odd integers is 12/35. We see that the denominator is 35. It’s not difficult to conjecture that the integers have to be 5 and 7 since 5 x 7 = 35. Finally, we can check the sum of 1/5 and 1/7 to see if they sum to 12/35:

1/5 + 1/7 = 7/35 + 5/35 = 12/35

Since they do add up to 12/35, the larger integer is 7.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
User avatar
B
Joined: 29 May 2012
Posts: 39
Premium Member
Re: If the sum of the reciprocals of two consecutive odd integers is 12/35  [#permalink]

Show Tags

New post 19 Oct 2017, 01:35
Assuming the two integers are x and y.

1/x + 1/y = 12/35, so

(x+y)/xy=35

xy=5 x 7 = 35

Therefore, the greater integer is 7.

Answer is C.
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3621
Premium Member Reviews Badge
Re: If the sum of the reciprocals of two consecutive odd integers is 12/35  [#permalink]

Show Tags

New post 19 Oct 2017, 01:44
1
jedit wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35, then the greater of the two integers is

A. 3
B. 5
C. 7
D. 9
E. 11

Searched this question before I posted but nothing showed up.


I always prefer to do such questions by using the options.

Three things to keep in mind:

1. We have odd integers
2. We need to find out the largest integer
3. Integers are consecutive.

Okay, let's take Option A.

If largest is 3, the smallest has to be 1. 1/1 + 1/3 is not equal to 12/35. OUT

Option B: 1/3 + 1/5 is NOT equal to 12/35. OUT

Option C: 1/5 + 1/7 = 12/35. It worked. Answer.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

New! Best Reply Functionality on GMAT Club!



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Check our new About Us Page here.

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3009
Location: Canada
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 19 Oct 2017, 07:07
1
Top Contributor
1
carcass wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11


Since the denominator of the sum is 35, and since 35 equals the product of 5 and 7 (two consecutive odd integers), let's start by testing whether 5 and 7 are the integers in question.

So, the RECIPROCALS are 1/5 and 1/7
1/5 + 1/7 = 7/35 + 5/35
= 12/35
Voila!!

So, the odd integers are 5 and 7
The greater of the two integers is 7
Answer:

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

VP
VP
avatar
P
Joined: 07 Dec 2014
Posts: 1104
If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post Updated on: 11 Aug 2018, 12:13
carcass wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11


35=7*5
7/35+5/35=12/35
7
C

Originally posted by gracie on 19 Oct 2017, 10:08.
Last edited by gracie on 11 Aug 2018, 12:13, edited 3 times in total.
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12669
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 05 Dec 2017, 12:43
1
Hi All,

We're told that the sum of the reciprocals of two CONSECUTIVE ODD integers is 12/35. We're asked for the GREATER of the two integers. This question can be solved by TESTing THE ANSWERS.

Let's TEST Answer B: 5
IF.... the values are 3 and 5....
then the sum of the reciprocals is 1/3 + 1/5 = 5/15 + 3/15 = 8/15
This is clearly not the correct answer, but the denominator ends in a '5', so it's likely that 12/35 will ALSO include a 5...

Let's TEST Answer C: 7
IF.... the values are 5 and 7....
then the sum of the reciprocals is 1/5 + 1/7 = 7/35 + 5/35 = 12/35
This is an exact match for what we were told, so this MUST be the answer.

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

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/

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

Intern
Intern
avatar
B
Joined: 19 May 2018
Posts: 17
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 11 Aug 2018, 11:01
ScottTargetTestPrep wrote:
carcass wrote:
If the sum of the reciprocals of two consecutive odd integers is 12/35 then the greater of the two integers is

A. 3

B. 5

C. 7

D. 9

E. 11


We can let the first odd integer = x and the next odd integer = x + 2; thus, the reciprocals are 1/x and 1/(x + 2). Thus:

1/x + 1/(x+2) = 12/35

Multiplying by 35x(x+2), we have:

35(x + 2) + 35x = 12x(x + 2)

35x + 70 + 35x = 12x^2 + 24x

12x^2 - 46x - 70 = 0

6x^2 - 23x - 35 = 0

(6x + 7)(x - 5) = 0

Thus, x = -7/6 or x = 5.

Since x is an integer, x must be 5 and the greater integer is x + 2 = 7.

Alternate solution:


We are given that the sum of the reciprocals of two consecutive odd integers is 12/35. We see that the denominator is 35. It’s not difficult to conjecture that the integers have to be 5 and 7 since 5 x 7 = 35. Finally, we can check the sum of 1/5 and 1/7 to see if they sum to 12/35:

1/5 + 1/7 = 7/35 + 5/35 = 12/35

Since they do add up to 12/35, the larger integer is 7.

Answer: C


I used the alternative route for this one but I was wondering if you could elaborate on whether there are any tips/tricks to dealing with messy quadratics, those that have a constant (for my purposes, I'm referring to a constant >1) in front of the x^2 term, since it's less straight forward and more time-consuming to figure out the roots in those situations?

I get that for quadratics with no constant in front of the x^2 term, we can use the "sum" and "product" rules to quickly figure out the form of the two roots in our head but the "sum" rule doesn't hold when we have a constant in front of the x^2 term, only the "product" rule does....I know you could technically plug values into the quadratic equation to figure out the roots but that's not a viable gmat approach so just trying to figure out what I'm missing that is keeping me from quickly solving these sorts of quadratics such as 6x^2 - 23x - 35 = 0.
Manager
Manager
User avatar
G
Joined: 10 Apr 2018
Posts: 150
Re: If the sum of the reciprocals of two consecutive odd integers  [#permalink]

Show Tags

New post 18 Aug 2018, 17:39
Hi,
well this can be solved assuming integers as x and y
then 1/x+1/y= x+y/xy
x+y/xy= 12/35
5,7 are the integers
Probus
GMAT Club Bot
Re: If the sum of the reciprocals of two consecutive odd integers &nbs [#permalink] 18 Aug 2018, 17:39
Display posts from previous: Sort by

If the sum of the reciprocals of two consecutive odd integers

  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®.