If a and b are positive integers is a/b < 9/11?
A)a/b < 0.818
B)b/a > 1.223
oa
D
If a and b are positive integers
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9/11 = 0.818181...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
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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Is a/b < 9/11?canbtg wrote:If a and b are positive integers is a/b < 9/11?
A)a/b < 0.818
B)b/a > 1.223
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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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.
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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Dear Mitch,GMATGuruNY wrote:Is a/b < 9/11?canbtg wrote:If a and b are positive integers is a/b < 9/11?
A)a/b < 0.818
B)b/a > 1.223
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 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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It is a good idea to know the following: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
1/11 = 0.090909...
Thus:
9/11 = 9(0.090909...) = 0.818181...
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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
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