Data Sufficiency (DS) | Re: If p, q, r, s and t are positive integers such that x = 2^p3^q and y =

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
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Statistics : Posted by Kinshook • on 12 Nov 2023, 10:58 • Replies 2 • Views 152

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