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

 It is currently 21 Oct 2019, 05:56

### 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

# If a and b are positive integers, is a/b < 9/11 ?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58421
If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

21 Oct 2015, 21:46
12
1
46
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:46) correct 28% (02:03) wrong based on 1945 sessions

### HideShow timer Statistics

If a and b are positive integers, is a/b < 9/11 ?

(1) a/b < 0.818
(2) b/a > 1.223

Kudos for a correct solution.

_________________
Retired Moderator
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

23 Oct 2015, 00:35
35
15
Bunuel wrote:
If a and b are positive integers, is a/b < 9/11 ?

(1) a/b = 0,818
(2) b/a = 1,223

Kudos for a correct solution.

There is no need to calculate anything. We just need to know if we can ask the question: is a/b < 9/11?

1) a/b = 0,818 ->> Sufficient. You know that you COULD get the exact result and figure out if a/b is < 9/11. You do not even have to ballpark, all you need to know is, that you COULD. Sufficient.
2) b/a = 1,223 ->> Sufficient. The reciprocal would be a/b = 1/1,223, again, no need to calculate anything further, from this it is very clear that you can answer the question Y, or N.

_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.
##### General Discussion
Marshall & McDonough Moderator
Joined: 13 Apr 2015
Posts: 1684
Location: India
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

22 Oct 2015, 00:08
6
3
9/11 = (9*9)/(11*9) = 0.8181
a/b < 0.8181 ?

or

11a < 9b --> b/a > 11/9 --> b/a > 1.22222 ?

St1: Sufficient
St2: Sufficient

Current Student
Joined: 12 Aug 2015
Posts: 2564
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

19 Nov 2016, 10:16
2
This is a great question from the Official guide
Here is what i did
we need to check whether a/b<9/11
or a/b<81/99
or a/b<0.8181818181818181..

Statement 1
a/b<0.818
hmm
Since 0.818<0.8181818181..
Hence a/b<9/11
Hence Sufficient
Statement 2
Here a/b<1000/1223
Hence a/b<0.817something
Hence a/b<0.8181818
Hence Sufficient

I have a question
Can we solve it without solving the statement 2?
I mean without performing the long division
Any tricks @cheetan2u ?

Regards
Stone Cold
_________________
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4774
Location: India
GPA: 3.5
If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

20 Nov 2016, 03:25
1
1
Bunuel wrote:
If a and b are positive integers, is a/b < 9/11 ?

(1) a/b < 0.818
(2) b/a > 1.223

Kudos for a correct solution.

FROM STATEMENT - I ( SUFFICIENT )

$$\frac{a}{b} < \frac{818}{1000}$$

Or, $$\frac{a}{b} < 81.8$$ %

Now, $$\frac{9}{11} = 81.8$$ %

Thus , $$\frac{a}{b}$$ < $$\frac{9}{11}$$

FROM STATEMENT - II ( SUFFICIENT )

$$\frac{b}{a} > 1.223$$

so, $$b = 1223$$ and $$a = 1000$$

Hence, $$\frac{a}{b} = 81.77$$ %

_________________
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 )
Manager
Joined: 21 Oct 2017
Posts: 79
Location: France
Concentration: Entrepreneurship, Technology
GMAT 1: 750 Q48 V44
GPA: 4
WE: Project Management (Internet and New Media)
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

23 Nov 2017, 18:28
Same question as people above. This question is really easy with a calculator. A little less so without it, under stress and under 2 minutes.

Anyone willing to break down the mental math on this one? Because clearly approximation wither an option here.

Thanks,

Posted from my mobile device
_________________
Please Press +1 Kudos if it helps!

October 9th, 2017: Diagnostic Exam - Admit Master (GoGMAT) - 640
November 11th, 2017: CAT 1 - Admit Master (GoGMAT) - 700
November 20th, 2017: CAT 2 - GMATPrep - 700 (Q: 47, V: 40)
November 25th, 2017: CAT 3 - Admit Master (GoGMAT) - 710 (Q: 48, V: 40)
November 27th, 2017: CAT 4 - GMATPrep - 720 (Q: 49, V: 40)

December 4th, 2017: GMAT Exam - 750 (Q: 48, V: 44, IR: 8, AWA: 6)
Retired Moderator
Joined: 22 Aug 2013
Posts: 1428
Location: India
If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

23 Nov 2017, 23:35
5
Same question as people above. This question is really easy with a calculator. A little less so without it, under stress and under 2 minutes.

Anyone willing to break down the mental math on this one? Because clearly approximation wither an option here.

Thanks,

Posted from my mobile device

Hi

Knowing the fractions to decimal conversions would help here. Eg:-
1/2 = 0.5, 1/3 = 0.333.., 1/4 = 0.25, 1/5 = 0.2, 1/6 = 0.1666.., 1/7 = 0.1428.., 1/8 = 0.125, 1/9 = 0.1111.., 1/10 = 0.1, 1/11 = 0.090909.., 1/12 = 0.08333.., and so on.

Its good to practice writing these from 1/2 to 1/20 often, because this could help you in various questions. Here in this question if we remember that 1/11 = 0.090909.. we would know that 9/11 = 9*0.090909.. = 0.818181..
Intern
Joined: 05 Mar 2015
Posts: 41
Location: Azerbaijan
GMAT 1: 530 Q42 V21
GMAT 2: 600 Q42 V31
GMAT 3: 700 Q47 V38
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

26 Jul 2018, 08:22
If understand correctly,

a/b < 9/11 then b/a>9/11

I guess this rule holds only when both sides of the inequality have the same sign, am I correct?
Math Expert
Joined: 02 Sep 2009
Posts: 58421
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

26 Jul 2018, 10:39
kablayi wrote:
If understand correctly,

a/b < 9/11 then b/a>9/11

I guess this rule holds only when both sides of the inequality have the same sign, am I correct?

When a and b have the same sign.
_________________
Manager
Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

09 Jun 2019, 01:20
in statement 2 we get B/A>1.222, While statement 2 states B/A>1.223. What if B/A is 1.223 then it is B/A>1.222 but B/A=1.223

chetan2u
Bunuel
Math Expert
Joined: 02 Aug 2009
Posts: 8005
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

09 Jun 2019, 01:38
Manat wrote:
in statement 2 we get B/A>1.222, While statement 2 states B/A>1.223. What if B/A is 1.223 then it is B/A>1.222 but B/A=1.223

chetan2u
Bunuel

Hi,

You have used statement ii on both instances.
I am sure you meant the question is a/b<9/11 means is b/a>1.2222
Now the statement II says that b/a>1.223.. that is b/a>1.223>1.222.. yes

If b/a >1.223, then surely it is greater than 1.222 hence your answer will be yes and sufficient.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

09 Jun 2019, 21:35
1
Manat wrote:
in statement 2 we get B/A>1.222, While statement 2 states B/A>1.223. What if B/A is 1.223 then it is B/A>1.222 but B/A=1.223

chetan2u
Bunuel

Stmnt 2: b/a > 1.223
which means we are given that a/b < .817 (taking reciprocal of both sides of the inequality)

So a/b could be .1 or .345 or .81 or .812 etc. Whatever it will be, it will be less than .817.

Question: Is a/b < 9/11?
Is a/b < .818?

Considering that a/b is less than .817, it MUST be less than .818 too.

Note that if I know that x is less than 4, can I say it must be less than 5? Of course! If x is less than 4, it is always going to be less than 5 no matter what value it takes. This is the same case.

Check this post for more: https://www.veritasprep.com/blog/2017/0 ... -question/
_________________
Karishma
Veritas Prep GMAT Instructor

Director
Joined: 19 Oct 2013
Posts: 516
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

09 Jun 2019, 22:06
Bunuel wrote:
If a and b are positive integers, is a/b < 9/11 ?

(1) a/b < 0.818
(2) b/a > 1.223

Kudos for a correct solution.

1/10 = 0.10
1/11 = 0.0909090 and so it goes.

so 9/11 = 0.818181 etc.. now the question asks whether a/b is < 0.818181...

From statement 1) we could tell that a/b < 0.818 so a/b would then be less than 9/11. We have a clear definitive answer.

For statement 2)

b/a > 1.223

1/9 = 0.1111

so having 10/9 = 1.11111 and 11/9 would be 1.22222

Now since b/a > 1.2223 then we know that b/a is larger than 11/9. Then we could tell that a/b is < 9/11

Hence sufficient.

Both statements are sufficient, thus, the answer is D.
Director
Joined: 20 Jul 2017
Posts: 930
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

09 Jun 2019, 22:38
1
Bunuel wrote:
If a and b are positive integers, is a/b < 9/11 ?

(1) a/b < 0.818
(2) b/a > 1.223

Kudos for a correct solution.

**Edited

1/11 = 0.090909.....
So, 9/11 = 9*1/11 = 0.8181818181.....

Is a/b < 9/11
—> Is a/b < 0.818181818181.....

(1) a/b < 0.818
—> a/b will definitely be less than 0.818181..... as it is less than a lower value 0.818

Sufficient.

1/9 = 0.11111111......
So, 2/9 would be 2*1/9 = 0.222222....
11/9 = 1 + 2/9 = 1.222222......

(2) b/a > 1.223
And 1.223 is greater than 1.222222.... (11/9)
—> b/a > 11/9
—> 9b > 11a
—> 11a < 9b
—> a/b < 9/11

Sufficient

IMO Option D.

Pls Hit kudos if you like the solution

Posted from my mobile device
Intern
Joined: 10 Jun 2017
Posts: 12
Location: India
Schools: Sloan '22
GMAT 1: 690 Q49 V40
GPA: 3.82
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

02 Aug 2019, 21:11
I don't think the solution is correct, question has < & > sign rather than = sign. hence statement 2 has to be calculated. However, smarter way would be to calculate b/a using 9/11 & compare it with 1.223.

Thanks
reto wrote:
Bunuel wrote:
If a and b are positive integers, is a/b < 9/11 ?

(1) a/b = 0,818
(2) b/a = 1,223

Kudos for a correct solution.

There is no need to calculate anything. We just need to know if we can ask the question: is a/b < 9/11?

1) a/b = 0,818 ->> Sufficient. You know that you COULD get the exact result and figure out if a/b is < 9/11. You do not even have to ballpark, all you need to know is, that you COULD. Sufficient.
2) b/a = 1,223 ->> Sufficient. The reciprocal would be a/b = 1/1,223, again, no need to calculate anything further, from this it is very clear that you can answer the question Y, or N.

Senior Manager
Joined: 10 Aug 2018
Posts: 336
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

### Show Tags

07 Aug 2019, 00:00
For this question, we don't need to solve actually.
We know that with both statements we will get to know that a/b will either be greater or less. We will have a fixed answer.
Both are sufficient without solving.
_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL"

GMAT:[640 Q44, V34, IR4, AWA5]
Re: If a and b are positive integers, is a/b < 9/11 ?   [#permalink] 07 Aug 2019, 00:00
Display posts from previous: Sort by