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If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one
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13 Aug 2018, 04:08
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Re: If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one
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13 Aug 2018, 04:37
\(\frac{3^x5^2}{3^55^3}\) = \(\frac{3^x}{3^55}\). Since \(\frac{1}{5}\) =0.2. Inorder for a fraction to have a terminating decimal, the denominator should only consist of either 2s or 5s. Hence \(x\geq{5}\). D is the answer.
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If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one
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13 Aug 2018, 11:10
Bunuel wrote: If \(3^x(5^2)\) is divided by \(3^5(5^3)\), the quotient terminates with one decimal digit. If x > 0, which of the following statements must be true?
(A) x is even (B) x is odd (C) x < 5 (D) x ≥ 5 (E) x = 5 Note: The quotient terminates with one decimal digit. Fraction * fraction yields more decimal points. 0.2 * 0.2 = 0.04 and 2 * 0.2 = 0.4. we have 0.4 type result. thus one must be integer and the other is fraction. Given, \(\frac{3^x 5^2}{3^55^3}\) = \(3^{(x5)} 5^{(23)}\) = \(3^{(x5)} 5^{(1)}\) =\(3^{(x5)}* \frac{1}{5}\) \(\frac{1}{5} = 0.2\) Thus , \(3^{(x5)}\) has to an integer. \(x\geq5\) is a must to have integer in this case. Thus the best answer is D.



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Re: If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one
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13 Aug 2018, 12:09
selim wrote: Bunuel wrote: If \(3^x(5^2)\) is divided by \(3^5(5^3)\), the quotient terminates with one decimal digit. If x > 0, which of the following statements must be true?
(A) x is even (B) x is odd (C) x < 5 (D) x ≥ 5 (E) x = 5 Note: The quotient terminates with one decimal digit. Fraction * fraction yields more decimal points. 0.2 * 0.2 = 0.04 and 2 * 0.2 = 0.4. we have 0.4 type result. thus one must be integer and the other is fraction. Given, \(\frac{3^x 5^2}{3^55^3}\) = \(3^{(x5)} 5^{(23)}\) = \(3^{(x5)} 5^{(1)}\) =\(3^{(x5)}* \frac{1}{5}\) \(\frac{1}{5} = 0.2\) Thus , \(3^{(x5)}\) has to an integer. \(x\geq5\) is a must to have integer in this case. Thus the best answer is D. Thanks Selim for the explanation. I also solved the problem but by substituting different values of x (x>0). It took a bit longer time as I couldn't think of the logic of 3 ^(x5) to be an integer. How to develop such logics ? Pls suggest.
BTW, my answer fraction will be reduced to \(3^{(x5)}* \frac{1}{5}\) If x=1, \(1/(3)^{4}* 1/5\), since 1/3 itself is non terminating so the whole fraction is nonterminating If x=2, x=3, x=4, same issue as in x=1 If x=5, fraction =1/5 =0.2; so x can be 5 If x=6, fraction = 3/5 = 3 x 0.2 = 0.6, so x can be 6 If x=7, fraction = 9/5 = 9 x 0.2 = 1.8; so x can be 7 So on so forth, we can conclude from the above results that x>=5. Hence, answer is D



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If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one
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13 Aug 2018, 23:10
Bunuel wrote: If \(3^x(5^2)\) is divided by \(3^5(5^3)\), the quotient terminates with one decimal digit. If x > 0, which of the following statements must be true?
(A) x is even (B) x is odd (C) x < 5 (D) x ≥ 5 (E) x = 5 \(\frac{3^x(5^2)}{3^5(5^3)}\), this quotient terminates , implies that x is an integer. You know 2 or 5 or both 2 and 5, in the denominator always terminates. When a multiple of 3 is divided by 3, then the quotient is never terminated. So, as long as \(3^5\) is active in the denominator, the quotient won't terminate. We need to cancel out \(3^5\) in the denominator in order to get a terminating decimal of the quotient. So, x=5 satisfies the condition. however, we need to find out the MUST BE TRUE condition, which is true at all points of the condition rather than at a single point. So, \(x\geq5\) Ans. (D)
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If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one
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14 Aug 2018, 00:54
tatz wrote: selim wrote: Bunuel wrote: If \(3^x(5^2)\) is divided by \(3^5(5^3)\), the quotient terminates with one decimal digit. If x > 0, which of the following statements must be true?
(A) x is even (B) x is odd (C) x < 5 (D) x ≥ 5 (E) x = 5 Note: The quotient terminates with one decimal digit. Fraction * fraction yields more decimal points. 0.2 * 0.2 = 0.04 and 2 * 0.2 = 0.4. we have 0.4 type result. thus one must be integer and the other is fraction. Given, \(\frac{3^x 5^2}{3^55^3}\) = \(3^{(x5)} 5^{(23)}\) = \(3^{(x5)} 5^{(1)}\) =\(3^{(x5)}* \frac{1}{5}\) \(\frac{1}{5} = 0.2\) Thus , \(3^{(x5)}\) has to an integer. \(x\geq5\) is a must to have integer in this case. Thus the best answer is D. Thanks Selim for the explanation. I also solved the problem but by substituting different values of x (x>0). It took a bit longer time as I couldn't think of the logic of 3 ^(x5) to be an integer. How to develop such logics ? Pls suggest.
BTW, my answer fraction will be reduced to \(3^{(x5)}* \frac{1}{5}\)
[color=#ff0000]If x=1, \(1/(3)^{4}* 1/5\), since 1/3 itself is non terminating so the whole fraction is nonterminatingIf x=2, x=3, x=4, same issue as in x=1If x=5, fraction =1/5 =0.2; so x can be 5 If x=6, fraction = 3/5 = 3 x 0.2 = 0.6, so x can be 6 If x=7, fraction = 9/5 = 9 x 0.2 = 1.8; so x can be 7 So on so forth, we can conclude from the above results that x>=5. Hence, answer is D[/color] Bro , i applied the same concept as u described above. I did it directly. If u put any value for x less than 5 it gives us non terminating decimal but we need one terminating decimal. Thus i said that 3^{(x5)} has to be an integer. Any value of x less than 5 will give us negative exponent but if \(x \geq5\) we can't avoid the problem. Thanks.




If 3^x(5^2) is divided by 3^5(5^3), the quotient terminates with one &nbs
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