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Updated on: 02 Mar 2025, 01:38
Originally posted by GMATinsight on 25 Apr 2021, 03:39.
Last edited by Bunuel on 02 Mar 2025, 01:38, edited 2 times in total.
Last edited by Bunuel on 02 Mar 2025, 01:38, edited 2 times in total.
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For integers a and b, If \(\frac{a}{b} = 12.12\) then find the value of b?
1) \(\frac{1}{b}\) is a terminating decimal
2) The odd integer b is less than \(100\)
1) \(\frac{1}{b}\) is a terminating decimal
2) The odd integer b is less than \(100\)
Source: https://www.GMATinsight.com
25 Apr 2021, 05:19
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GMATinsight
\(\frac{a}{b} = 12.12\)
\(a=12.12*b=12b+0.12b=12b+\frac{12b}{100}\)
Now \( 12b+\frac{12b}{100}=12b+\frac{3b}{25}\)
So b has to be 25 or a multiple of 25.
1) \(\frac{1}{b}\) is a terminating decimal
So b can be 2 and its powers or 5 and it’s powers or the product of their powers.
b can be 25, 50, 200 and so on.
Insufficient
2) The odd integer b is less than \(100\)
So b is odd and less than 100, so b can be 25 or 75.
Insufficient
Combined
b can not have any other factors other than 2s and 5s or their product and it is an odd integer less than 100.
Only 25 fits in.
Sufficient
C
General Discussion
25 Apr 2021, 09:25
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For integers a and b, If \(\frac{a}{b} = 12.12\) then find the value of b?
\(\frac{a}{b} = 12.12= \frac{1212}{100} = \frac{909}{75} = \frac{606}{50} = \frac{303}{25}\)
Hence b can be any multiple of 25.
1) \(\frac{1}{b}\) is a terminating decimal
Is it 25 or 50 or 100?
INSUFFICIENT.
2) The odd integer b is less than \(100\)
b = 25 or 75
INSUFFICIENT.
Together 1 and 2
b < 100 and \(\frac{1}{b}\) is terminating.
\(\implies\) b doesn't have any factor that leads to non-terminating answer e.g. 3 or 7 or 9
Since b can only be 25 and 75, where in the latter is not possible.
b = 25.
Answer C.
\(\frac{a}{b} = 12.12= \frac{1212}{100} = \frac{909}{75} = \frac{606}{50} = \frac{303}{25}\)
Hence b can be any multiple of 25.
1) \(\frac{1}{b}\) is a terminating decimal
Is it 25 or 50 or 100?
INSUFFICIENT.
2) The odd integer b is less than \(100\)
b = 25 or 75
INSUFFICIENT.
Together 1 and 2
b < 100 and \(\frac{1}{b}\) is terminating.
\(\implies\) b doesn't have any factor that leads to non-terminating answer e.g. 3 or 7 or 9
Since b can only be 25 and 75, where in the latter is not possible.
b = 25.
Answer C.
