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

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

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21 Oct 2015, 21:46
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35% (medium)

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72% (01:20) correct 28% (01:38) wrong based on 1159 sessions

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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.

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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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23 Oct 2015, 00:35
19
4
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.

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##### General Discussion
SC Moderator
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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22 Oct 2015, 00:08
5
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

Manager
Joined: 02 Jul 2015
Posts: 106
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GMAT 1: 680 Q49 V33
Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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22 Oct 2015, 04:30

1. states that a/b=0.818 while stem states 0.818181...

2. 1/1223 is definitely smaller then 9/11
Manager
Joined: 02 Jul 2015
Posts: 106
Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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23 Oct 2015, 00:50
1
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.

reto

In retrospect I agree that DS merely asks if the information is enough or not. So no need to calculate.
Manager
Joined: 20 Mar 2015
Posts: 62
If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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03 Jul 2016, 10:29
St.1 $$\frac{a}{b}$$ $$<$$ $$\frac{9}{11}$$ Sufficient.

St.2 $$\frac{b}{a}$$ $$>$$ $$\frac{1223}{1000}$$ Sufficient.

Do we really need to calculate in this question? The answer will be either yes or no, but not both. The answer to any fraction, be it$$\frac{1000}{1224}$$, $$\frac{1000}{1225}$$ or any other will be different than $$\frac{9}{11}$$.

Abhishek009
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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28 Jul 2016, 01:37
yes here it should be calculated
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Joined: 12 Aug 2015
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GRE 1: Q169 V154
Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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19 Nov 2016, 10:16
1
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
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If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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20 Nov 2016, 03:25
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, $$\frac{a}{b} = 81.77$$ %

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Abhishek....

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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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27 Dec 2016, 12:23
Guys could you post a compilation of these exotic rules for fractions? like that the number of 9's in the denominator defines the number of repeating decimals, etc?? Thank you!
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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16 Mar 2017, 13:01
Bunuel wrote:
GinGMAT wrote:
The statements here are posted incorrectly (this question is in GMAC OG 2016). Statement 1 is a/b < 0.818 and statement 2 is b/a > 1.223. So you do need to do calculations since it is not an equal sign.

You are right. Edited. Thank you.

Even with the inequalities, do we need to calculate here?
Senior Manager
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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01 Jul 2017, 05:29
And how is it possible to answer "without calculation"??? We are given a range so it can be yes or no, you have to be sure!
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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

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23 Nov 2017, 23:35
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..
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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24 Nov 2017, 09:20
amanvermagmat wrote:
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 = 0.90909.., 1/12 = 0.8333.., 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 = 0.90909.. we would know that 9/11 = 9*0.90909.. = 0.818181..

I actually tried that. I have a formula sheet with fractions/decimals/percents up to 12.
So 1/9 = 0.111
and 1/11 = 0.0909

But again, going from 1/11 = 0.0909 to 9/11 = 0.8181 isn't exactly natural for me, unfortunately. I need to write down the multiplication/division, and that usually leads me to exceed the 2-minute mark.
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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27 Feb 2018, 11:33
b/a = 1.2222222222 this rounded makes 1.223, I don't think D is the right answer
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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27 Feb 2018, 22:31
AjayRawtani wrote:
b/a = 1.2222222222 this rounded makes 1.223, I don't think D is the right answer

Hi

First of all 1.2222222.. if rounded to thousandth decimal place, does NOT become 1.223, rather it becomes 1.222 (because the digit after that is '2' which is less than 5)

And secondly, we simply dont need to do rounding off here. The second statement tells us that:
b/a > 1.223

So anything which is greater than 1.223 will obviously also be greater than 1.2222222 (because 1.223 itself is greater than 1.2222222...). Thus we are getting the answer
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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27 Feb 2018, 23:04
amanvermagmat wrote:
AjayRawtani wrote:
b/a = 1.2222222222 this rounded makes 1.223, I don't think D is the right answer

Hi

First of all 1.2222222.. if rounded to thousandth decimal place, does NOT become 1.223, rather it becomes 1.222 (because the digit after that is '2' which is less than 5)

And secondly, we simply dont need to do rounding off here. The second statement tells us that:
b/a > 1.223

So anything which is greater than 1.223 will obviously also be greater than 1.2222222 (because 1.223 itself is greater than 1.2222222...). Thus we are getting the answer

I really need to work on cutting down silly mistakes.

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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Re: If a and b are positive integers, is a/b < 9/11 ? [#permalink]

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01 Jul 2018, 22:30
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.

Hello, many thanks for this answer. What would be the right and the fastest way to get to the right answer if we did not use the equal signs but "<" and ">" signs as in the original question?
Would we still do NOT have to calculate?
" If a and b are positive integers, is a/b < 9/11 ?

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

Thank you!
Have a nice day
Aleks
Re: If a and b are positive integers, is a/b < 9/11 ?   [#permalink] 01 Jul 2018, 22:30
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