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

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.

Answer D.

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

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)

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..

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
VeritasKarishma

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.

**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

VeritasKarishma MentorTutoring chetan2u

Can we approximate to single decimal in above question?



In above step by VeritasKarishma , I hope you used fractions and not performed weird calculation of 1/1.223.


For eg: question asks if a/b < 9/11 ?
I would simplify the above fraction and bring denominator close to 100
I know 11 * 9 = 99 so for above when I multiply above fraction by 9 in numerator and denominator , I get: Is a/b < 0.81?

St 1: a/b < 0.818
A number less than 0.818 (rounded to 0.82) is surely less than 0.81

St 2: b/a > 1.223
Here, I manipulated question stem as: Is b/a > 11/9 or b/a < 1.21 ?
A number greater than 1.223 is surely greater than 1.21

Hello, adkikani. I think I understand your question about approximating. Keep in mind, though, that you can get into trouble if you approximate too much, especially if you are working with multiple fractions that are close to one another in value. In this particular problem, a blunt approach works just fine, since you need to be able to tell only whether a fraction is less than a certain value, and you are provided enough information in either statement to make such a comparison—a relative to b in Statement (1) or b relative to a in Statement (2)—no calculation required.

- Andrew

No, the numbers are too close to approximate here.

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

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

We need to know some basic fraction decimal equivalents discussed here: https://youtu.be/HxnsYI1Rws8
You don't need much calculations if you know these well.


Question: Is a/b < 9/11? Is a/b < .818181...
or is b/a >11/9? Is b/a > 1.2222...
We should convert the fraction into decimals because we know how to convert 9/11 and 11/9 into decimals.

Now we know that each statement alone is sufficient.

How many decimals are used? I thought statement 1 was insufficient since 0.818 could be 0.8181 or 0.8184 which is slightly larger

(1) says that a/b < 0.818. While 9/11 = 0.818181... So, a/b < 0.818 < 0.818181...

Solution:

St(1):- a/b <0.818

You "know" that you can convert 9/11 into a decimal and "decide/judge" if a/b is less or more than that based on the information that a/b is less than 0.818.You do not need to calculate.) (Sufficient)
​
St(2):- b/a >1.223
=>a/b < .817
(Taking reciprocal. You "know" you can get the reciprocal and hence you have to decide that the value of 0.817 "can" be calculated and you do not need to calculate it actually).
Hence now when you know that a/b <0.817 ,you can decide and answer if it is less than 9/11. (Sufficient) option(d)

Answer: Option D

Video solution by GMATinsight



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Solution:

Question Stem Analysis:

We need to determine whether a/b < 9/11. Notice that 9/11 = 0.818181….

Statement One Alone:

Since a/b < 0.818, it’s less than 0.818181... = 9/11. Statement one alone is sufficient.

Statement Two Alone:

Since b/a > 1.223, it’s greater than 0.1.222.... = 11/9. Since b/a > 11/9, then a/b < 9/11. Statement two alone is sufficient.

Answer: D

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

If we know the fractions and corresponding percentages table, this question would be very easy.

1/2 = 50% = .5
1/4 = 25% = .25
1/8 = 12.5% = .125

1/3 = 33.33% = .33..
1/6 = 16.66 % = .1666..
1/12 = 8.33% = .0833..

1/4 = 25% = .25
1/5 = 20% = .2
1/7 = 14.28% = .1428..
1/9= 11.11% = .1111..
1/11 = 9.09% = .0909..

We know that 1/11 = 9.09 % then 9/11 = 9.09 * 9 % = 81.81% = .8181..

is a/b < 9/11 ?

So we can re frame the question stem as is a/b < .8181 ?

(1) a/b < 0.818

is a/b < .8181 ? YES

Statement 1 alone is sufficient.

(2) b/a > 1.223

Lets re-frame the question stem in terms of b/a.
a/b < 9/11 ?
11/9 < b/a ? Its given that a and b are positive integers,
is b/a > 11/9?
is b/a > 1 + 2/9?

We know from the table that 1/9 = 11.11% then 2/9 = 22.22% = .2222..
is b/a > 1 + 2/9? => is b/a > 1 +.2222?

is b/a > 1.2222?

Its clearly given in statement 2 that b/a > 1.223

Hence Statement 2 alone is sufficient.
Option D is the answer.

Hope it helps,
Clifin J Francis,
GMAT SME