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ting.cui10
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Post subject: if a, b, c, and d are positive  Posted: Mon Apr 30, 2012 7:11 pm |
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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
OA: B
how do you solve this problem?
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krishnan.anju1987
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Post subject: Re: if a, b, c, and d are positive Posted: Tue May 08, 2012 1:58 pm |
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B looks about right. This is how I tried it Given 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) a+c/b+d < a/b+ c/d we know 2 is not true so 3) is also not true as the same expression is a part of 3). Hence correct answer is B
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ting.cui10
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Post subject: Re: if a, b, c, and d are positive Posted: Wed May 16, 2012 11:20 am |
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could you explain your logic for the last part?
this part: we know 2 is not true so 3) is also not true as the same expression is a part of 3).
i dont see how you arrived at that conclusion. take for instance a hypothetical example, if (a+c) / (b+d) = 5 and a/b = 4 and c/d = 2 then (a+c) / (b+d) < a/b is false but (a+c) / (b+d) < a/b + c/d is true.
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krishnan.anju1987
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Post subject: Re: if a, b, c, and d are positive Posted: Wed May 16, 2012 12:16 pm |
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Posts: 125
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Guess I have explained better
(a+c)/(b+d) >a/b
(a+c)/(b+d) +c/d > a/b +c/d
Cross multiply and cancel and you get
Bc>ad
Which its false, hence c is wrong.
Also, the example you have taken agrees with only 2nd statement but I got your point.
Hope this
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tim
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Post subject: Re: if a, b, c, and d are positive Posted: Tue May 22, 2012 4:05 am |
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| ManhattanGMAT Staff |
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Location: Southwest Airlines, seat 21C
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looks like you've reversed the inequality, so your approach won't work on 3. the idea of cross multiplying is a good one though..
_________________
Tim Sanders
Manhattan GMAT Instructor
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krishnan.anju1987
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Post subject: Re: if a, b, c, and d are positive Posted: Tue May 22, 2012 7:24 am |
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Hi Tim,
Please help me out if I am doing something wrong.
After I cross multiplied and got the answer bc>ad, comparing it to the inequality given in the question (ad>bc) would let me know that the inference from the third statement is wrong and hence the statement is insufficient.
I went over my solution once more and came up with the same answer. Is there something wrong with this approach that I maybe missing.
Thanks for your help in advance.
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desiwolverine
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Post subject: Re: if a, b, c, and d are positive Posted: Tue May 22, 2012 9:46 pm |
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I think it should be E meaning I and III are correct.
You can cross multiply and then cancel out terms.
ad < bc is what we get from the given data.
1st case cross multiplication lines up to that.
2nd case does not.
3rd case after cross multiplication and cancelling out gives cb^2 + ad^2 > 0.
Which should be true since c,b,a and d are positive numbers.
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tim
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Post subject: Re: if a, b, c, and d are positive Posted: Mon May 28, 2012 12:37 am |
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| ManhattanGMAT Staff |
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Posts: 4404
Location: Southwest Airlines, seat 21C
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Krishnan, looks like you've done it right. Wolverine, I just ran through the calculations and got the same result as you. Unless we both made the same mistake it seems E should be the answer. Can someone post a screenshot from GMAT Prep to let us know for sure what they say the correct answer is?
_________________
Tim Sanders
Manhattan GMAT Instructor
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krishnan.anju1987
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Post subject: Re: if a, b, c, and d are positive Posted: Fri Jun 29, 2012 2:41 pm |
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Hi,
Could someone please post the answer to this question. I went over C once more and came up with another solution which makes E the answer.
We know 1) is true and hence (a+c)/(b+d)< (c/d)
now, (a+c)/(b+d) < a/b+ c/d
can be written as
(a+c)/(b+d) < a/b+ (a+c)/(b+d) + y
since c/d = (a+c)/(b+d) + y where y is some fraction or integer which when added to the fraction would give c/d
hence from above
0< a/b +y
since and b is positive and y has to be positive, this is true and hence iii) has to be true.
Does this look good?
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tim
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Post subject: Re: if a, b, c, and d are positive Posted: Sat Jun 30, 2012 8:36 pm |
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| ManhattanGMAT Staff |
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Posts: 4404
Location: Southwest Airlines, seat 21C
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still waiting for a screenshot to confirm the answer. i got E as well..
_________________
Tim Sanders
Manhattan GMAT Instructor
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Ankit Gupta
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Post subject: Re: if a, b, c, and d are positive Posted: Sun Jul 01, 2012 7:22 am |
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After solving the equation 3, I am getting the following inequality.
bc+ad >0
Please confirm.
My answer is also coming out to be E !!
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crissro
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Post subject: Re: if a, b, c, and d are positive Posted: Sun Jul 01, 2012 8:43 pm |
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(a+c)\ (b+d)=a/(b+d) + c/(b+d)< a/b + c/d when b,d#0
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jnelson0612
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Post subject: Re: if a, b, c, and d are positive Posted: Sun Jul 01, 2012 10:51 pm |
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| ManhattanGMAT Staff |
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krishnan.anju1987 wrote: Hi,
Could someone please post the answer to this question. I went over C once more and came up with another solution which makes E the answer.
We know 1) is true and hence (a+c)/(b+d)< (c/d)
now, (a+c)/(b+d) < a/b+ c/d
can be written as
(a+c)/(b+d) < a/b+ (a+c)/(b+d) + y
since c/d = (a+c)/(b+d) + y where y is some fraction or integer which when added to the fraction would give c/d
hence from above
0< a/b +y
since and b is positive and y has to be positive, this is true and hence iii) has to be true.
Does this look good? Looks good to me! That is creative.
_________________
Jamie Nelson
ManhattanGMAT Instructor
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jnelson0612
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Post subject: Re: if a, b, c, and d are positive Posted: Sun Jul 01, 2012 10:52 pm |
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Posts: 2390
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guptarulz wrote: After solving the equation 3, I am getting the following inequality.
bc+ad >0
Please confirm.
My answer is also coming out to be E !! My answer is also E. For III, I got: cb^2 + ad^2 > 0.
_________________
Jamie Nelson
ManhattanGMAT Instructor
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krishnan.anju1987
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Post subject: Re: if a, b, c, and d are positive Posted: Mon Jul 02, 2012 11:37 am |
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