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For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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09 Mar 2017, 01:07
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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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09 Mar 2017, 04:03
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SHORTCUT:let us assume a, b, c be 25, 50, 75 respectively A. 25/100 =0.25 B. 75/150 = 0.5 C. 100/175 = 0.57 D. 150/225 = 0.66
Option D



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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09 Mar 2017, 06:28
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Agree... D... also it allows all the variables to feature in the option... which is necessary to ascertain the answer in this case Sent from my GTI9060I using GMAT Club Forum mobile app



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For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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09 Mar 2017, 10:52
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For any proper fraction \(\frac{x}{y}\) (x<y and both x and y are positive)
\(\frac{x}{y}\)<\(\frac{x+1}{y+1}\)<\(\frac{x+2}{y+2}\)<...<\(\frac{x+n}{y+n}\)
where n is a positive integer. The higher the value of n, the more greater \(\frac{x+n}{y+n}\) is than the original fraction.
Example \(\frac{x}{y}\)<\(\frac{x+5}{y+5}\)<\(\frac{x+50}{y+50}\)
Now we need to arrange
\(\frac{a}{100}\), \(\frac{a+b}{100+b}\), \(\frac{a+c}{100+c}\) and \(\frac{a+(b+c)}{100+(b+c)}\)
Since 0<b<c<b+c then the order would be
\(\frac{a}{100}\)<\(\frac{a+b}{100+b}\)<\(\frac{a+c}{100+c}\)<\(\frac{a+(b+c)}{100+(b+c)}\)
D has the greatest value. Hence Answer D



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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10 Mar 2017, 10:24
Bunuel wrote: For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value? A. a/100 B. (a+b)/(100+b) C. (a+c)/(100+c) D. (a+b+c)/(100+b+c) E. The answer cannot be determined from the information provided. a, b, c = Pos INTs a < b < c < 100 Let's test numbers, Let try a =1, b =2, & b =3; so we have A. a/100 > 1/100 B. (a+b)/(100+b) > 3/102 C. (a+c)/(100+c) > 4/103 D. (a+b+c)/(100+b+c) > 5/105 E. The answer cannot be determined from the information provided.[/quote] Let's try another integer values: a =97, b =98, c =99 A) 97/100 B) 195/198 C) 196/199 D) 294/297 Since option D has the highest numerator and highest denominator, and the denominator of each option is greater than the numerator by the same value, option D has the greatest value. Now, assuming at this stage you need to compare each option against the other and you have to deal with big values, here's a shortcut i just found (hope, I'm right ): For instance, let's check which is bigger, A or B: A) 97/100 vs. B) 195/198 > A) 198*97 vs B) 195*100, just compare the positive differences of the multiplying figures and the option with the lower difference is likely to be bigger. That is, since 195  100 = 97 is less than 199  97 = 102, option B is bigger (check!) For B & C: B) 195/198 vs C) 196/199 > B) 199*195 vs. C) 198*196 > 199  195 = 4 > 198  196 = 2, option C is bigger For C & D: C) 196/199 vs. D) 294/297 > C) 297*196 vs. 294*199 > 297  196 = 201 > 294  199 = 195, option D is bigger Answer: D
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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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18 Mar 2017, 08:33
picking smart numbers here is great: try 25, 50, 75 and be careful with calculations D is the answer



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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21 May 2017, 13:04
Hi Bunuel,
Thanks for this question!
Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.
However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam  I can be more certain of why I am eliminating one of the options.
Thanks in advance!



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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21 May 2017, 15:14
poojamathur21 wrote: Hi Bunuel,
Thanks for this question!
Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.
However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam  I can be more certain of why I am eliminating one of the options.
Thanks in advance! I think I know the answer. 1/n < 2/(n+1) < 3/(n+2) etc. with n >1 It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation.



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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21 May 2017, 16:44
MaverickTone wrote: poojamathur21 wrote: Hi Bunuel,
Thanks for this question!
Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.
However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam  I can be more certain of why I am eliminating one of the options.
Thanks in advance! I think I know the answer. 1/n < 2/(n+1) < 3/(n+2) etc. with n >1 It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation. Yup, you're right. I think I got it. Bunuel, please confirm. If we have a fraction say a / b, any number (x>0) when added to both the numerator and denominator makes the fraction bigger, and when subtracted makes the fraction smaller. => ax/bx < a/b < a+x/b+x Posted from my mobile device



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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21 May 2017, 22:07
poojamathur21 wrote: MaverickTone wrote: poojamathur21 wrote: Hi Bunuel,
Thanks for this question!
Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.
However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam  I can be more certain of why I am eliminating one of the options.
Thanks in advance! I think I know the answer. 1/n < 2/(n+1) < 3/(n+2) etc. with n >1 It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation. Yup, you're right. I think I got it. Bunuel, please confirm. If we have a fraction say a / b, any number (x>0) when added to both the numerator and denominator makes the fraction bigger, and when subtracted makes the fraction smaller. => ax/bx < a/b < a+x/b+x Posted from my mobile deviceHere is a POST by Magoosh which discusses this issue in detail. Hope it helps.
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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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21 May 2017, 22:13
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poojamathur21 wrote: MaverickTone wrote: poojamathur21 wrote: Hi Bunuel,
Thanks for this question!
Although I did get the correct answer ( I used two examples of a, b and c to verify: 1,2,3 and 25,50, 75). And since option D was higher in both the cases, I assumed D would be correct.
However, how can we be so sure that E isn't the correct option? I wanted to understand the question better so that if a similar question comes up during the exam  I can be more certain of why I am eliminating one of the options.
Thanks in advance! I think I know the answer. 1/n < 2/(n+1) < 3/(n+2) etc. with n >1 It could be said in a logic form but I don't know how to put it. Still waiting for Bunuel's explanation. Yup, you're right. I think I got it. Bunuel, please confirm. If we have a fraction say a / b, any number (x>0) when added to both the numerator and denominator makes the fraction bigger, and when subtracted makes the fraction smaller. => ax/bx < a/b < a+x/b+x Posted from my mobile deviceIt depends on whether the fraction a/b is a proper fraction (a<b) or its an improper fraction (a>b) If a/b is a proper fraction, then adding any positive number x (x>0) to both numerator and denominator Increases the value of the fraction OR a/b < (a+x)/(b+x) But if c/d is say an improper fraction (c>d), then adding any positive number x (x>0) to both numerator and denominator Decreases the value of the fraction. OR c/d > (c+x)/(d+x) So lets consider a proper fraction a/100 (a<100). If we add a positive number b to both numerator and denominator, its value will increase Thus a/100 < (a+b)/(100+b)



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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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21 May 2017, 23:52
Bunuel wrote: For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value? A. a/100 B. (a+b)/(100+b) C. (a+c)/(100+c) D. (a+b+c)/(100+b+c) E. The answer cannot be determined from the information provided. since b > a so, a/100 < (a+b)/(100+b) since c > b so, (a+b)/(100+b) < (a+c)/(100+c) since b+c > c so, (a+c)/(100+c) < (a+b+c)/(100+b+c) So , a/100 < (a+b)/(100+b) < (a+c)/(100+c) < (a+b+c)/(100+b+c)
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Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo [#permalink]
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22 May 2017, 02:05
Bunuel wrote: For positive integers a, b, and c, a < b < c < 100. Which of the following has the greatest value? A. a/100 B. (a+b)/(100+b) C. (a+c)/(100+c) D. (a+b+c)/(100+b+c) E. The answer cannot be determined from the information provided. Logical Thinking I took 3 numbers < 100 for a,b and c such as 97,98 and 99. I use a numerator and denominator rule (mentioned in Manhattan guide )to solve this question without calculation. To be frank I couldn't think of solid solution.Rule : Adding the same number to both the numerator and denominator brings the fraction close to 1, regardless of the fraction value.
since, a<b<c< 100. The fraction < 1. Now scanning through the answer options, A to D are combination of a, b and c. Using the above rule I know that D is closed to 1. Hence D option is largest among A to D. Therefor marked D. To understand this approach please refer to Manhattan guide Ans: D




Re: For positive integers a, b, and c, a < b < c < 100. Which of the follo
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