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

It is currently 18 Jun 2018, 13:44

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

For positive integers a, b, and c, a < b < c < 100. Which of the follo

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

Hide Tags

Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 09 Mar 2017, 02:07
3
4
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

65% (01:27) correct 35% (01:38) wrong based on 212 sessions

HideShow timer Statistics

For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value?

A. a/100

B. (a+b)/(100+b)

C. (a+c)/(100+c)

D. (a+b+c)/(100+b+c)

E. The answer cannot be determined from the information provided.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Senior Manager
Senior Manager
avatar
B
Joined: 05 Jan 2017
Posts: 427
Location: India
Premium Member
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 09 Mar 2017, 05:03
2
1
SHORTCUT:let us assume a, b, c be 25, 50, 75 respectively
A. 25/100 =0.25
B. 75/150 = 0.5
C. 100/175 = 0.57
D. 150/225 = 0.66

Option D
Intern
Intern
avatar
B
Joined: 18 Jan 2017
Posts: 32
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 09 Mar 2017, 07:28
1
Agree... D... also it allows all the variables to feature in the option... which is necessary to ascertain the answer in this case

Sent from my GT-I9060I using GMAT Club Forum mobile app
4 KUDOS received
Intern
Intern
avatar
S
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)
GMAT ToolKit User
For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 09 Mar 2017, 11:52
4
5
For any proper fraction \(\frac{x}{y}\) (x<y and both x and y are positive)

\(\frac{x}{y}\)<\(\frac{x+1}{y+1}\)<\(\frac{x+2}{y+2}\)<...<\(\frac{x+n}{y+n}\)

where n is a positive integer. The higher the value of n, the more greater \(\frac{x+n}{y+n}\) is than the original fraction.

Example
\(\frac{x}{y}\)<\(\frac{x+5}{y+5}\)<\(\frac{x+50}{y+50}\)

Now we need to arrange

\(\frac{a}{100}\), \(\frac{a+b}{100+b}\), \(\frac{a+c}{100+c}\) and \(\frac{a+(b+c)}{100+(b+c)}\)

Since 0<b<c<b+c then the order would be

\(\frac{a}{100}\)<\(\frac{a+b}{100+b}\)<\(\frac{a+c}{100+c}\)<\(\frac{a+(b+c)}{100+(b+c)}\)

D has the greatest value. Hence Answer D
Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 192
Location: Ghana
Premium Member
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 10 Mar 2017, 11:24
Bunuel wrote:
For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value?

A. a/100

B. (a+b)/(100+b)

C. (a+c)/(100+c)

D. (a+b+c)/(100+b+c)

E. The answer cannot be determined from the information provided.



a, b, c = Pos INTs

a < b < c < 100


Let's test numbers, Let try a =1, b =2, & b =3;

so we have

A. a/100 -------------------> 1/100

B. (a+b)/(100+b) ---------> 3/102

C. (a+c)/(100+c) ---------> 4/103

D. (a+b+c)/(100+b+c) ---> 5/105

E. The answer cannot be determined from the information provided.[/quote]


Let's try another integer values: a =97, b =98, c =99

A) 97/100 B) 195/198 C) 196/199 D) 294/297

Since option D has the highest numerator and highest denominator, and the denominator of each option is greater than the numerator by the same value, option D has the greatest value.

Now, assuming at this stage you need to compare each option against the other and you have to deal with big values, here's a shortcut i just found (hope, I'm right :) ):

For instance, let's check which is bigger, A or B: A) 97/100 vs. B) 195/198 ----> A) 198*97 vs B) 195*100,

just compare the positive differences of the multiplying figures and the option with the lower difference is likely to be bigger.

That is, since 195 - 100 = 97 is less than 199 - 97 = 102, option B is bigger (check!)

For B & C: B) 195/198 vs C) 196/199 ----> B) 199*195 vs. C) 198*196 ----> 199 - 195 = 4 > 198 - 196 = 2, option C is bigger

For C & D: C) 196/199 vs. D) 294/297 ----> C) 297*196 vs. 294*199 ----> 297 - 196 = 201 > 294 - 199 = 195, option D is bigger

Answer: D
_________________

Kindly press kudos if you find my post helpful

Manager
Manager
avatar
S
Joined: 03 Jan 2017
Posts: 181
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 18 Mar 2017, 09:33
picking smart numbers here is great: try 25, 50, 75 and be careful with calculations :)
D is the answer
Intern
Intern
avatar
B
Joined: 25 Apr 2017
Posts: 15
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 21 May 2017, 14:04
Hi Bunuel,

Thanks for this question!

Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.

However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam - I can be more certain of why I am eliminating one of the options.

Thanks in advance!
Intern
Intern
avatar
B
Joined: 20 May 2017
Posts: 10
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 21 May 2017, 16:14
poojamathur21 wrote:
Hi Bunuel,

Thanks for this question!

Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.

However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam - I can be more certain of why I am eliminating one of the options.

Thanks in advance!


I think I know the answer.

1/n < 2/(n+1) < 3/(n+2) etc. with n >1

It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation.
Intern
Intern
avatar
B
Joined: 25 Apr 2017
Posts: 15
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 21 May 2017, 17:44
MaverickTone wrote:
poojamathur21 wrote:
Hi Bunuel,

Thanks for this question!

Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.

However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam - I can be more certain of why I am eliminating one of the options.

Thanks in advance!


I think I know the answer.

1/n < 2/(n+1) < 3/(n+2) etc. with n >1

It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation.


Yup, you're right. I think I got it. Bunuel, please confirm.

If we have a fraction say a / b, any number (x>0) when added to both the numerator and denominator makes the fraction bigger, and when subtracted makes the fraction smaller.

=> a-x/b-x < a/b < a+x/b+x

Posted from my mobile device
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46129
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 21 May 2017, 23:07
poojamathur21 wrote:
MaverickTone wrote:
poojamathur21 wrote:
Hi Bunuel,

Thanks for this question!

Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.

However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam - I can be more certain of why I am eliminating one of the options.

Thanks in advance!


I think I know the answer.

1/n < 2/(n+1) < 3/(n+2) etc. with n >1

It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation.


Yup, you're right. I think I got it. Bunuel, please confirm.

If we have a fraction say a / b, any number (x>0) when added to both the numerator and denominator makes the fraction bigger, and when subtracted makes the fraction smaller.

=> a-x/b-x < a/b < a+x/b+x

Posted from my mobile device


Here is a POST by Magoosh which discusses this issue in detail.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1186
Location: India
Premium Member
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 21 May 2017, 23:13
1
poojamathur21 wrote:
MaverickTone wrote:
poojamathur21 wrote:
Hi Bunuel,

Thanks for this question!

Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.

However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam - I can be more certain of why I am eliminating one of the options.

Thanks in advance!


I think I know the answer.

1/n < 2/(n+1) < 3/(n+2) etc. with n >1

It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation.


Yup, you're right. I think I got it. Bunuel, please confirm.

If we have a fraction say a / b, any number (x>0) when added to both the numerator and denominator makes the fraction bigger, and when subtracted makes the fraction smaller.

=> a-x/b-x < a/b < a+x/b+x

Posted from my mobile device


It depends on whether the fraction a/b is a proper fraction (a<b) or its an improper fraction (a>b)

If a/b is a proper fraction, then adding any positive number x (x>0) to both numerator and denominator Increases the value of the fraction
OR a/b < (a+x)/(b+x)

But if c/d is say an improper fraction (c>d), then adding any positive number x (x>0) to both numerator and denominator Decreases the value of the fraction.
OR c/d > (c+x)/(d+x)

So lets consider a proper fraction a/100 (a<100). If we add a positive number b to both numerator and denominator, its value will increase
Thus a/100 < (a+b)/(100+b)
Director
Director
User avatar
P
Joined: 13 Mar 2017
Posts: 610
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 22 May 2017, 00:52
Bunuel wrote:
For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value?

A. a/100

B. (a+b)/(100+b)

C. (a+c)/(100+c)

D. (a+b+c)/(100+b+c)

E. The answer cannot be determined from the information provided.


since b > a
so, a/100 < (a+b)/(100+b)

since c > b
so, (a+b)/(100+b) < (a+c)/(100+c)

since b+c > c
so, (a+c)/(100+c) < (a+b+c)/(100+b+c)

So , a/100 < (a+b)/(100+b) < (a+c)/(100+c) < (a+b+c)/(100+b+c)

Answer D..

_________________

CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Manager
Manager
User avatar
B
Joined: 02 Aug 2013
Posts: 64
Location: India
Concentration: Technology, Leadership
WE: Programming (Consulting)
GMAT ToolKit User
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]

Show Tags

New post 22 May 2017, 03:05
Bunuel wrote:
For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value?

A. a/100

B. (a+b)/(100+b)

C. (a+c)/(100+c)

D. (a+b+c)/(100+b+c)

E. The answer cannot be determined from the information provided.





Logical Thinking


I took 3 numbers < 100 for a,b and c such as 97,98 and 99.

I use a numerator and denominator rule (mentioned in Manhattan guide )to solve this question without calculation. To be frank I couldn't think of solid solution.

Rule : Adding the same number to both the numerator and denominator brings the fraction close to 1, regardless of the fraction value.


since, a<b<c< 100. The fraction < 1.

Now scanning through the answer options, A to D are combination of a, b and c.

Using the above rule I know that D is closed to 1. Hence D option is largest among A to D. Therefor marked D.

To understand this approach please refer to Manhattan guide

Ans: D
Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo   [#permalink] 22 May 2017, 03:05
Display posts from previous: Sort by

For positive integers a, b, and c, a < b < c < 100. Which of the follo

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


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®.