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Math Expert V
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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Difficulty:   35% (medium)

Question Stats: 72% (01:46) correct 28% (02:03) wrong based on 1945 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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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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Marshall & McDonough Moderator D
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Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

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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

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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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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 ?

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

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

So, EACH statement ALONE is sufficient to answer the question asked, answer will be (D)
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Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

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

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

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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.
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GMAT 1: 500 Q39 V21 Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

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

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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.
Even if it was asked is b/a>0, your answer would be yes
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Re: If a and b are positive integers, is a/b < 9/11 ?  [#permalink]

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

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

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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

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

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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.

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

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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.
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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
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