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If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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18 Dec 2015, 07:33
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If a, b, c, and d are positive numbers and a/b < c/d , which of the following must be true? I. (a+c) / (b+d) < c/ d II. (a+c) / (b+d) < a/b III. (a+c) / (b+d) = a/b + c/d a) none b) I only c) II only d) I and II e) I and III Pls press kudos if you like the question and would like me to discuss more such questions
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If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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18 Dec 2015, 07:36
a/b<c/d implies ad<bc Consider 1) a+c/b+d < c/d is true then, cross multiplying ad+dc<bc+cd thus, ad<bc which is true and hence 1) is true. Consider 2) a+c/b+d < a/b implies ab+bc<ba+ad bc<ad which we know to be false 3) We can't prove equality from inequality. Hence can't be 'must be true'. Bunuel, is my logic correct in here? Hence correct answer is B
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If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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18 Dec 2015, 07:54
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NoHalfMeasures wrote: If a, b, c, and d are positive numbers and a/b < c/d , which of the following must be true?
I. (a+c) / (b+d) < c/ d
II. (a+c) / (b+d) < a/b
III. (a+c) / (b+d) = a/b + c/d
a) none b) I only c) II only d) I and II e) I and III
Pls press kudos if you like the question and would like me to discuss more such questions Your method is correct as well as all the 4 numbers are positive. This question can be tackled easily by the method below: You are given a/b < c/d > as all the numbers are positive you can cross multiply to get , a/c < b/d > (a/c) + 1 < (b/d) + 1 > (a+c)/c < (b+d)/d > (a+c) / (b+d) < c/ d which is statement I and is hence true. Now, again consider a/b < c/d > d/b < c/a > (d/b) + 1 < (c/a) + 1 > (d+b)/b < (c+a)/a > a/b < (c+a)/(b+d) but this is not what statement II mentions, making statement II false. Finally, for (a+c) / (b+d) = a/b + c/d , you can clearly prove this wrong by taking a,b,c,d as 1,2,3,4. So this is also not true. For a MUST BE TRUE question, you need to get a yes ALWAYS. Thus, only statement I is true , making B the correct answer. Hope this helps.



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If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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18 Dec 2015, 08:04
Thanks for your reply. But can you also comment on the following St3) We can't prove equality from inequality. Hence st3 can't be 'must be true'. Is my logic correct specifically for st3?
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Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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18 Dec 2015, 08:16
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NoHalfMeasures wrote: Thanks for your reply.
But can you also comment on the following St3) We can't prove equality from inequality. Hence can't be 'must be true'. Is my logic correct specifically for st3? No this is a very broad statement that you are mentioning. Take a simpler example: If I say x<3 and then ask whether x =2 is true ? You will say "yes" but here you used the inequality to arrive at your answer for an equality. I have shown 1 way of using particular values to see that III is NOT must be true. The other way is to assume that (a+c) / (b+d) = a/b + c/d is indeed true. Then you end up getting \(b^2*c+a*d^2=0\) > \((a/c)= b^2/d^2\) but this can not possible as a and c are given to be of the same sign (both are positive) and as such this will make (a/c) a negative quantity. Additionally, you also know that \(b^2/d^2\) can never be <0 . Thus you have this contradiction, making this statement not a must be true. Hope this helps.



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Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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23 Mar 2017, 10:10
bumpbot wrote: Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. Bunuel I am very confused why 3rd statement is not correct. Here is my take on it  (a+c) / (b+d) = a/b + c/d Taking LCM  so, (a+c)/(b+d)= (ad+cb)/(bd) cross multiplying  abd + bcd =abd +bcd, which is true. So the answer should be E. Can you please let me know why this approach is wrong. Thanks for all your help !



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Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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27 Mar 2017, 22:14
I used real values and came to the answer. Used 1/2 and 3/4.



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If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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06 Nov 2017, 08:17
vtomar20 wrote: bumpbot wrote: Hello from the GMAT Club BumpBot!
I am very confused why 3rd statement is not correct. Here is my take on it  (a+c) / (b+d) = a/b + c/d Taking LCM  so, (a+c)/(b+d)= (ad+cb)/(bd) cross multiplying  abd + bcd =abd +bcd, which is true. So the answer should be E. Can you please let me know why this approach is wrong. Thanks for all your help ! Hi vtomar20 I see a problem in your algebra. Even i did the same mistake and eventually found what i was doing wrong. When you simplify the expression: (a+c) / (b+d) = a/b + c/d you will get abd + bcd =abd +bcd + ad^2 + cb^2 and this however is not true, since in the above expression we have an extra ad^2 + cb^2 on the right side which will make the right side bigger (and we know this because all the a, b, c, and d, are positive numbers ). so E is out and B is the answer. I hope its clear Thankyou Arunabh saxena



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Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo [#permalink]
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11 Jan 2018, 20:55
a/b<c/d we multiple two side by bd. remember all number are positive. ac<cb.
this simple multiply make the fraction from into factors form. this is key to do inequality problem.




Re: If a, b, c, and d are positive numbers and a/b < c/d , which of the fo
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11 Jan 2018, 20:55






