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As x increases from 209 to 210, which of the following must
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Updated on: 04 Mar 2012, 13:25
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As x increases from 209 to 210, which of the following must increase? I. \(3x  4\) II. \(\frac{x  1}{x}\) III. \(x  x^2\) (A) I only (B) III only (C) I and II (D) I and III (E) II and III How come the answer is C guys?
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Originally posted by enigma123 on 04 Mar 2012, 09:33.
Last edited by enigma123 on 04 Mar 2012, 13:25, edited 1 time in total.




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Re: As x increases from 209 to 210, which of the following must
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18 Aug 2016, 02:05
ameyaprabhu wrote: What's the best way to compare such large fractions? Bunuel wrote: enigma123 wrote: As x increases from 209 to 210, which of the following must increase?
II. \(\frac{x  1}{x}\) > \(\frac{2091}{209}=\frac{208}{209}\) which is less than \(\frac{2101}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.
Answer: C. Hey ameyaprabhu, To understand the nature of a fraction, you should first simplify the fraction as far as possible. So, in this case you can rewrite \(\frac{(x1)}{x} = \frac{x}{x} – \frac{1}{x} = 1 – \frac{1}{x}.\) Now, from this simplified version, you can see that x is in the denominator. So, as x increases, the value of \(\frac{1}{x}\) would decrease. Since \(\frac{1}{x}\) is being subtracted from 1, the decrease in the value of \(\frac{1}{x}\) would result in increase in value of the overall fraction. For example: consider x = 2. So, we have \(1  \frac{1}{x} = 1  \frac{1}{2} = \frac{1}{2}\). Now, when x = 3, we have \(1  \frac{1}{x} = 1  \frac{1}{3} = \frac{2}{3}\). So, as x increases from 2 to 3, the value of the fraction \(1  \frac{1}{x}\) also increases from \(\frac{1}{2}\) to \(\frac{2}{3}\). So, you can now confidently say that as x increases from 209 to 210, the value of \(\frac{(x1)}{x}\) would increase as well. Hope this helps. Regards, Harsh
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Re: Must increase
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04 Mar 2012, 15:30



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Re: As x increases from 209 to 210, which of the following must
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25 Jul 2016, 21:18
When x increases from 209 to 210.
I. 3x4 will also increase as x is increasing. II.((x1)/x) can be written as 11/x. As x increases, 1/x will decrease. That means, lesser value will be subtracted from 1 now. Hence, Increases. III. As x increases, x^2 increase faster than x. Hence, xx^2 will decrease.
So, Answer should be C.



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Re: As x increases from 209 to 210, which of the following must
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18 Aug 2016, 01:39
What's the best way to compare such large fractions? Bunuel wrote: enigma123 wrote: As x increases from 209 to 210, which of the following must increase?
II. \(\frac{x  1}{x}\) > \(\frac{2091}{209}=\frac{208}{209}\) which is less than \(\frac{2101}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.
Answer: C.



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Re: As x increases from 209 to 210, which of the following must
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18 Aug 2016, 05:44
I. The answer clearly will increase as a negative constant stays the same (4) whereas the variable with a positive constant(3x) increases. II. Any proper and improper fraction that gets a number added to both the numerator and the denominator gets closer to 1. 100/101 is closer to 1 than 99/100. 100/99 is further away from 1 than 101/100. As the fraction (x1)/x is less than 1 it will increase. (note how the question would change if II. stated (x+1)/x In that case the fraction would decrease(towards 1). III. The positive part (x) gets +1 whereas the negative part (x^2) receives an exponential increase larger than 1. I and II must increase. Answer choice: C.
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Re: As x increases from 209 to 210, which of the following must
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11 Oct 2017, 22:06
ameyaprabhu wrote: What's the best way to compare such large fractions? Bunuel wrote: enigma123 wrote: As x increases from 209 to 210, which of the following must increase?
II. \(\frac{x  1}{x}\) > \(\frac{2091}{209}=\frac{208}{209}\) which is less than \(\frac{2101}{210}=\frac{209}{210}\), (the same way as 1/2 is less than 2/3). Correct.
Answer: C. One way could be we replace the large number with a smaller one say X will increase from 3 to 4. let us first check the extremes. 1 3x4=94=5 and 124=8 8>5Increase 2. x1/x=(31)/3=2/3=2/3 and (41)/4=3/4 2/3>3/4 or 0.6>0.7 3. x\(x^2\)=39=(6) and 416=(12) (6)>(12)decrease hence C



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Re: As x increases from 209 to 210, which of the following must
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16 Oct 2017, 15:54
enigma123 wrote: As x increases from 209 to 210, which of the following must increase?
I. \(3x  4\) II. \(\frac{x  1}{x}\) III. \(x  x^2\)
(A) I only (B) III only (C) I and II (D) I and III (E) II and III We are being tested on the result when an integer is increased. So, rather than using 209 to 210, let’s use 2 to 3 (since the relationship won’t change). I. 3(2)  4 = 2 3(3)  4 = 5 We see that an increase occurs. II. (2  1)/2 = 1/2 (3  1)/3 = 2/3 We see that an increase occurs. III. 2  2^2 = 2 3  3^2 = 6 We see that an increase DOES NOT occur. Answer: C
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Re: As x increases from 209 to 210, which of the following must &nbs
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