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

 It is currently 23 May 2019, 12:08 ### 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. ### Request Expert Reply # If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi

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

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 55266
If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

1
16 00:00

Difficulty:   55% (hard)

Question Stats: 66% (02:06) correct 34% (01:59) wrong based on 305 sessions

### HideShow timer Statistics

If $$N = \frac{5}{6} + \frac{6}{7} + \frac{7}{8} + \frac{8}{9} + \frac{9}{10} + \frac{10}{11}$$, then which of the following must be true of N?

A) 5/6 < N < 10/11

B) 21/10 < N < 9/2

C) 5 < N < 5 1/11

D) 5 < N < 5 5/11

E) 30 < N < 60

_________________
##### Most Helpful Community Reply
Manager  B
Joined: 24 Aug 2016
Posts: 68
Location: India
WE: Information Technology (Computer Software)
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

6
5
$$N = \frac{5}{6} + \frac{6}{7} + \frac{7}{8} + \frac{8}{9} + \frac{9}{10} + \frac{10}{11}$$

$$N = 1 - \frac{1}{6} + 1 - \frac{1}{7} + 1 - \frac{1}{8} + 1 - \frac{1}{9} + 1 - \frac{1}{10} + 1 - \frac{1}{11}$$

$$N = 6 - (\frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11})$$

$$\frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11}$$

Max value of above fraction will be $$\frac{6}{6}$$= 1

Minimum value = $$\frac{6}{11}$$

6-1 <= N <= 6-$$\frac{6}{11}$$

6-1 <= N <= $$\frac{60}{11}$$

6-1 <= N <= 5$$\frac{5}{11}$$

Ans. D
_________________
"If we hit that bullseye, the rest of the dominos will fall like a house of cards. Checkmate."
##### General Discussion
Current Student B
Joined: 26 Jan 2016
Posts: 103
Location: United States
GPA: 3.37
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

1
Each fraction is close to 1 so we know that the sum will be less than 6. Lets just say they're each 1 so N=6. But now we have to subtract the difference
1/6+1/7+1/8+1/9+1/10+1/11. We can estimate these each as 1/10-->5/10 which is 1/2. D is the closest representation of this.
Intern  Joined: 18 Sep 2016
Posts: 49
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

joannaecohen wrote:
Each fraction is close to 1 so we know that the sum will be less than 6. Lets just say they're each 1 so N=6. But now we have to subtract the difference
1/6+1/7+1/8+1/9+1/10+1/11. We can estimate these each as 1/10-->5/10 which is 1/2. D is the closest representation of this.

I think it isn't a matter of which is the "closest" approximation of N because the question asks which one MUST be true.

Therefore the right answer may be even a statement which is not a close approximation of N (it just has to be true), whereas a good approximation of N may be the wrong answer.

as a consequence i belive that the quickest and most certain way to answer this question in by exclusion of the impossible answers.

A) FALSE_____ N<10/11 is impossible because N=10/11+ a lot of other numbers, thus N must be >10/11

B) FALSE_____N<9/2=4.5 is impossible because each of the 6 numbers which constitute N are very close to 1( So it is between 5 and 6 and >4.5)

C)FALSE____ 51/11 <5 , whereas N is clearly >5

D) NO SENSE! because 55/11=5 therefore 5<N<5 is impossible.

E) FALSE_____ N is clearly <30 indeed it is between 5 and 6

In conclusion i think that there are not correct answers.
_________________
Please press Kudos if you like my post
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1443
Location: India
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

7
3
Here's another way to do this:

N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11

We should also know that in proper fractions (where numerator < denominator), adding same value to both numerator and denominator increases the value of fraction (eg, if we add 1 to both numerator and denominator of 5/6, we will get (5+1)/(6+1) = 6/7, which will become greater than 5/6).
Hence 5/6 < 6/7 < 7/8 < 8/9 < 9/10 < 10/11

Now if we replace all 6 terms with the smallest term 5/6, of course it will decrease the value of given number N. But still lets see what happens
5/6 + 5/6 + 5/6 + 5/6 + 5/6 + 5/6 = 5/6 * 6 = 5

But N must be more than this (the way we replaced), so N > 5

Now lets replace all 6 terms with the highest term 10/11, this will of course increase the value of N but lets see what happens
10/11 + 10/11 + 10/11 + 10/11 + 10/11 + 10/11 = 10/11 * 6 = 60/11 = 5 5/11

But N must be less than this (the way we replaced), so N < 5 5/11

Combining we get
5 < N < 5 5/11

Hence D answer
Manager  G
Joined: 23 Feb 2017
Posts: 59
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

7
1
N=$$\frac{5}{6}$$+$$\frac{6}{7}$$+$$\frac{7}{8}$$+$$\frac{8}{9}$$+$$\frac{9}{10}$$+$$\frac{10}{11}$$

Lowest term = $$\frac{5}{6}$$
What if all the terms are equal to lowest term, then sum = $$\frac{5}{6}$$ * 6 = 5

Highest term = $$\frac{10}{11}$$
What if all the terms are equal to highest term, then sum = $$\frac{10}{11}$$*6 = $$\frac{60}{11}$$

Sum of terms will lie between sum of terms if all terms are equal to lowest terms and sum terms if all terms are equal to highest terms

5 < N < 60/11

Ans. D
_________________
+1 Kudos if you find it helpful.
Senior Manager  G
Joined: 02 Apr 2014
Posts: 477
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

5/6 < 1 and 6/7 will be more closer to 1 than 5/6 is

so, min value of the addition (all elements are 5/6) will be : 6 * (5/6) = 5
so, max value of the addition (all elements are 10/11) will be : 6 * (10/11) = 60/11 = 5 5/11

so the required addition will be min < N < max => 5 < N < 5 5/11 => (D)
Intern  B
Status: preparing for GMAT
Joined: 29 Nov 2017
Posts: 22
GPA: 3.55
WE: Military Officer (Military & Defense)
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

damybox wrote:
joannaecohen wrote:
Each fraction is close to 1 so we know that the sum will be less than 6. Lets just say they're each 1 so N=6. But now we have to subtract the difference
1/6+1/7+1/8+1/9+1/10+1/11. We can estimate these each as 1/10-->5/10 which is 1/2. D is the closest representation of this.

I think it isn't a matter of which is the "closest" approximation of N because the question asks which one MUST be true.

Therefore the right answer may be even a statement which is not a close approximation of N (it just has to be true), whereas a good approximation of N may be the wrong answer.

as a consequence i belive that the quickest and most certain way to answer this question in by exclusion of the impossible answers.

A) FALSE_____ N<10/11 is impossible because N=10/11+ a lot of other numbers, thus N must be >10/11

B) FALSE_____N<9/2=4.5 is impossible because each of the 6 numbers which constitute N are very close to 1( So it is between 5 and 6 and >4.5)

C)FALSE____ 51/11 <5 , whereas N is clearly >5

D) NO SENSE! because 55/11=5 therefore 5<N<5 is impossible.

E) FALSE_____ N is clearly <30 indeed it is between 5 and 6

In conclusion i think that there are not correct answers.

lolwut the answer is that which you labelled as making no sense...
Intern  B
Joined: 01 Jan 2016
Posts: 21
Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

Joc456 wrote:
Each fraction is close to 1 so we know that the sum will be less than 6. Lets just say they're each 1 so N=6. But now we have to subtract the difference
1/6+1/7+1/8+1/9+1/10+1/11. We can estimate these each as 1/10-->5/10 which is 1/2. D is the closest representation of this.

How can you estimate each of the fractions as 1/10. Isn't that a stretch for 1/6, 1/7, 1/8?
Manager  B
Joined: 29 Jul 2018
Posts: 114
Concentration: Finance, Statistics
GMAT 1: 620 Q45 V31 Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi  [#permalink]

### Show Tags

take extreme cases
5/6 is smallest so
take all numbers be 5/6 it will give smallest value
6*5/6 = 5
largest = 6*10/11
so 5<n<60/11 Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi   [#permalink] 29 Nov 2018, 23:29
Display posts from previous: Sort by

# If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi

 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®.

#### MBA Resources  