If a and b are positive integers

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canbtg: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Oct 11, 2013 5:42 am; Thanked: 4 times

by canbtg » Mon Jun 29, 2015 3:48 am

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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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Source: Beat The GMAT — Data Sufficiency | Mon Jun 29, 2015 3:48 am

theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » 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

answer = d

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » 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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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » 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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Mo2men: Legendary Member; Posts: 712; Joined: Fri Sep 25, 2015 4:39 amFollowed by: 5 members; Thanked: 14 times

by Mo2men » Wed May 23, 2018 1:58 pm

GMATGuruNY wrote:
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.

Dear Mitch,
Is there an easy way to convert 9/11 to 0.8181? Is just memorizing 1/11? or doing quick long division?
Thanks in advance

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed May 23, 2018 2:25 pm

Mo2men wrote:Dear Mitch,
Is there an easy way to convert 9/11 to 0.8181? Is just memorizing 1/11? or doing quick long division?
Thanks in advance

It is a good idea to know the following:
1/11 = 0.090909...
Thus:
9/11 = 9(0.090909...) = 0.818181...

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8207; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: If a and b are positive integers

by Scott@TargetTestPrep » Sat May 08, 2021 10:33 am

canbtg wrote: ↑
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

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

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