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12 Nov 2023, 11:58
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
60% (01:38) correct
40%
(01:59)
wrong
based on 50
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If p, q, r, s and t are positive integers such that \(x = 2^p3^q\) and \(y = 2^r3^s5^t\), can the fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits ?
(1) \(\frac{x}{y} >1\)
(2) \(\frac{q}{s} > 1\)
(1) \(\frac{x}{y} >1\)
(2) \(\frac{q}{s} > 1\)
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ankitmba95
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Schools: Columbia CBS'26 Booth '26 Kellogg '26 Stern '26 (S)
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12 Nov 2023, 17:00
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Finite decimal is possible if the denominator is 2 (1/2=0.5) or 5 (1/5=0.2).
However, with denominator as 3, finite decimal may not be possible (1/3 = 0.333333333....).
Thus answer is B as if q>s, then 3 would not be in denominator.
However, with denominator as 3, finite decimal may not be possible (1/3 = 0.333333333....).
Thus answer is B as if q>s, then 3 would not be in denominator.
13 Nov 2023, 01:49
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Asked: If p, q, r, s and t are positive integers such that \(x = 2^p3^q\) and \(y = 2^r3^s5^t\), can the fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits ?
\(\frac{x}{y} = \frac{2^p3^q}{2^r3^s5^t} = 2^{p-r}3^{q-s}5^{-t}\)
(1) \(\frac{x}{y} >1\)
\(\frac{x}{y} = \frac{2^p3^q}{2^r3^s5^t} = 2^{p-r}3^{q-s}5^{-t} > 1\)
If q >= s ; the fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits
But if q<s ; the fraction \(\frac{x}{y}\) can not be expressed as decimal with only finite number of non zero digits
NOT SUFFICIENT
(2) \(\frac{q}{s} > 1\)[/quote]
\(\frac{x}{y} = \frac{2^p3^q}{2^r3^s5^t} = 2^{p-r}3^{q-s}5^{-t} > 1\)
If q >= s ; the fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits
But if q<s ; the fraction \(\frac{x}{y}\) can not be expressed as decimal with only finite number of non zero digits
q/s > 1 => q > s
The fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits
SUFFICIENT
IMO B
\(\frac{x}{y} = \frac{2^p3^q}{2^r3^s5^t} = 2^{p-r}3^{q-s}5^{-t}\)
(1) \(\frac{x}{y} >1\)
\(\frac{x}{y} = \frac{2^p3^q}{2^r3^s5^t} = 2^{p-r}3^{q-s}5^{-t} > 1\)
If q >= s ; the fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits
But if q<s ; the fraction \(\frac{x}{y}\) can not be expressed as decimal with only finite number of non zero digits
NOT SUFFICIENT
(2) \(\frac{q}{s} > 1\)[/quote]
\(\frac{x}{y} = \frac{2^p3^q}{2^r3^s5^t} = 2^{p-r}3^{q-s}5^{-t} > 1\)
If q >= s ; the fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits
But if q<s ; the fraction \(\frac{x}{y}\) can not be expressed as decimal with only finite number of non zero digits
q/s > 1 => q > s
The fraction \(\frac{x}{y}\) be expressed as decimal with only finite number of non zero digits
SUFFICIENT
IMO B
