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## If a and b are positive integers

This topic has 2 expert replies and 1 member reply
canbtg Senior | Next Rank: 100 Posts
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#### If a and b are positive integers

Mon Jun 29, 2015 3:48 am
If a and b are positive integers is a/b < 9/11?

A)a/b < 0.818

B)b/a > 1.223

oa

D

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Matt@VeritasPrep GMAT Instructor
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Mon Jun 29, 2015 4:12 pm
If we remember some of our common fractional to decimal conversions, we can use the fact that

1/11 = .09090909...

to determine that

9/11 = 9 * (1/11) = .81818181...

Since a/b < .818 < .81818181 = 9/11, we have a/b < 9/11, and S1 is sufficient.

We can use similar conversions for the second step. a/b < 9/11 if b/a > 11/9.

1/9 = .1111...., so 11/9 = 11 * (.1111...) = 1.222...

b/a > 1/223 > 1/222... = 11/9, so again this is sufficient.

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GMATGuruNY GMAT Instructor
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Mon Jun 29, 2015 4:15 am
canbtg wrote:
If a and b are positive integers is a/b < 9/11?

A)a/b < 0.818

B)b/a > 1.223
Is a/b < 9/11?

9/11 = 0.8181...

Questions stem rephrased:
Is a/b < 0.8181?

Statement 1: a/b < 0.818
Since 0.818 < 0.8181, we get:
a/b < 0.818 < 0.8181
a/b < 0.8181.
SUFFICIENT.

Is a/b < 9/11?

Cross-multiplying, we get:
11a < 9b
11/9 < b/a
b/a > 11/9.

11/9 = 1.2222...

Question stem, rephrased:
Is b/a > 1.2222?

Statement 2: b/a > 1.223
Since 1.223 > 1.2222, we get:
b/a > 1.223 > 1.2222
b/a > 1.2222.
SUFFICIENT.

The correct answer is D.

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theCEO Master | Next Rank: 500 Posts
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Mon Jun 29, 2015 4:03 am
canbtg wrote:
If a and b are positive integers is a/b < 9/11?

A)a/b < 0.818

B)b/a > 1.223

oa

D
9/11 = 0.818181...

1)
if a/b < 0.818, a/b will always be less tan 0.818181... Statement is sufficent

2)
b/a > 1.223
a/b < 1/1.223 = 0.8177
If a/b < 0.8177,a/b will always be less tan 0.818... statement is sufficent

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