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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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01 Oct 2017, 05:19
Picking nos is the best approach. m,p,s & v are +ve. m/p<s/v. Let m/p=1/2=0.5 ie m=1, p=2 and s/v=4/5=0.8 ie s=4 and v=5 0.5<0.8 Plugin the values in the answer choices. I. (m+s)/(p+v)=(1+4)/(2+5)=5/7=0.71 this is between 0.5 and 0.8 II. ms/pv=4/10=0.4 not between 0.5 and 0.8 III. s/v−m/p=4/51/2=0.3 again not between 0.5 and 0.8.



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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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08 Dec 2017, 11:28
imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\) II. \(\frac{ms}{pv}\) III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both Let’s analyze each statement using specific values for the variables. We can let m = 2, s = 3, p = 4, and v = 5. Thus: m/p = 2/4 = 0.5 and s/v = 3/5 = 0.6. Notice that m/p = 0.5 is less than s/v = 0.6. Now let’s analyze each statement. I. (m+s)/(p+v) (2 + 3)/(4 + 5) = 5/9 = 0.555… is between m/p = 0.5 and s/v = 0.6. II. (ms)/(pv) (2 x 3)/(4 x 5) = 6/20 = 0.3 is NOT between 0.5 and 0.6. III. s/v  m/p 3/5  2/4 = 0.6  0.5 = 0.1 is NOT between 0.5 and 0.6. From the above, we see that only statement I is true. However, this was illustrated by using one set of numbers (m = 2, s = 3, p = 4, and v = 5). It’s possible that it could be false when we use another set of values for m, s, p, and m. However, we can prove that (m+s)/(p+v) is between m/p and s/v; that is, we can prove that m/p < (m+s)/(p+v) < s/v regardless of the values we use for m, s, p, and m, as long as the values are positive. Notice that m/p < (m+s)/(p+v) < s/v means m/p < (m+s)/(p+v) and (m+s)/(p+v) < s/v. Also, keep in mind that we are given that m/p < s/v, which is equivalent to mv < ps. Let’s prove that m/p < (m+s)/(p+v): m/p < (m+s)/(p+v) ? m(p+v) < p(m + s) ? mp + mv < mp + ps? mv < ps ? (YES) Since mv < ps is true, m/p < (m+s)/(p+v) is true. Finally, let’s prove that (m+s)/(p+v) < s/v: (m+s)/(p+v) < s/v ? v(m+s) < s(p+v)? mv + sv < sp + sv ? mv < ps ? (YES) Again, since mv < ps is true, (m+s)/(p+v) < s/v is true. Thus we have shown that m/p < (m+s)/(p+v) < s/v is always true. Answer: B
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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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22 Dec 2017, 09:29
imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\)
II. \(\frac{ms}{pv}\)
III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both THIS IS HARD the point tested here is that we need to change from ratio from to factor form m/p<s/v multiple two sides with s.v mv<sp from this point you can solve the problem.



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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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07 Jan 2018, 06:02
One very easy way to make I correct is as below Any number can be expressed in form of A/1 (lets say 3/2 it can be written as 1.5/1) so basically if you see option 1 is asking us A/1 < (A+B)/(2) < B/1
The average is always in btw A & B
II & III can simply be rejected by taking values 1,2,3,4.



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If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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19 Apr 2018, 00:36
imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\)
II. \(\frac{ms}{pv}\)
III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both I. if \(\frac{m+s}{p+v}\) is to be more than \(\frac{m}{p}\), ==> \(\frac{m}{p}\)<\(\frac{m+s}{p+v}\) ==> pm+mv<pm+ps and since all numbers are positive, ==> \(\frac{m}{p}\)<\(\frac{s}{v}\) which is true as per question stem. if \(\frac{m+s}{p+v}\) is to be less than \(\frac{s}{v}\), ==> \(\frac{s}{v}\)>\(\frac{m+s}{p+v}\) ==> sp+sv>mv+sv ==> \(\frac{m}{p}\)<\(\frac{s}{v}\) which is true as per question stem. II. if \(\frac{ms}{pv}\) is to be more than \(\frac{m}{p}\), ==> \(\frac{s}{v}\) must be greater than 1, which is not conclusive as per stem of question. III. if \(\frac{s}{v}  \frac{m}{p}\) is to be more than \(\frac{m}{p}\), ==> \(\frac{s}{v} must be greater than 2 X [m]\frac{m}{p}\), which is not conclusive as per stem of question. So only (I) can be derived with 100% confidence. Hence Answer must be B.



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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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11 May 2018, 12:36
Bunuel wrote: siriusblack1106 wrote: which of the following 'must be' between m/p and s/v?
I didn't understand the question. What does the question mean here by 'must be'? "Must be" means for any (possible) values of m, p, s and v. So, \(\frac{m}{p}< (option) <\frac{s}{v}\), must hold true fo any positive values of m, p, s and v. Must or Could be True Questions to practice: http://gmatclub.com/forum/search.php?se ... tag_id=193Hope it helps. Do you have a more elegant solution to this problem Bunuel? Most of the answers here are either choosing numbers or doing complicated calculations that I would find difficult to try during the test.



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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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13 May 2018, 16:44
DarkBlizzard wrote: imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\) II. \(\frac{ms}{pv}\) III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both This question is quite easy: III. is clearly out, because this will be smaller than m/p. II. is clearly out. Test this with m/p=0 or s/v=1 I. Struggled a minute here, but then I got this idea: If we pick a number for m/p and a number for s/v: For example: m/p = 1/3 and s/v = 3/4 Now, I we try to get these numbers to the same denominator we get: 4/12 < 9/12 If these numbers are added ab (4+9)/(12+12), we always get a number that is higher than m/p but lower than s/v. This is how I solved this This works for every number pair. We add the same denominator, but an enumerator which is bigger than the original one. Therefore this has to be bigger than m/p but smaller than s/v! :wink: is III clearly out? 1 < 100, but 1001 is in between the 2. am i misreading something? I picked 1/8 < 2/3 to plug in, and III does work here. with 1/2 < 3/4 however it does not.



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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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14 May 2018, 05:57
imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\)
II. \(\frac{ms}{pv}\)
III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both As the question asks for Must, we can take test with only one set of value  s = 5, m = 4, p,v = 1 Only Statement II Satisfies. Hence, Option B.
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If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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14 May 2018, 07:16
rahul16singh28 wrote: imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\)
II. \(\frac{ms}{pv}\)
III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both As the question asks for Must, we can take test with only one set of value  s = 5, m = 4, p,v = 1 Only Statement II Satisfies. Hence, Option B. Yeah I understand. I guess what I'm saying is that picking the right numbers is essential on this one, as if the wrong numbers are picked, III works too. Just realized that there isn't a I and III option though, so it were down to I and III one could pick new numbers



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Re: If m, p, s and v are positive, and m/p < s/v, which of the following [#permalink]
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15 May 2018, 12:17
bp2013 wrote: rahul16singh28 wrote: imhimanshu wrote: If m, p, s and v are positive, and \(\frac{m}{p} <\frac{s}{v}\), which of the following must be between \(\frac{m}{p}\) and \(\frac{s}{v}\)
I. \(\frac{m+s}{p+v}\)
II. \(\frac{ms}{pv}\)
III. \(\frac{s}{v}  \frac{m}{p}\)
A. None B. I only C. II only D. III only E. I and II both As the question asks for Must, we can take test with only one set of value  s = 5, m = 4, p,v = 1 Only Statement II Satisfies. Hence, Option B. Yeah I understand. I guess what I'm saying is that picking the right numbers is essential on this one, as if the wrong numbers are picked, III works too. Just realized that there isn't a I and III option though, so it were down to I and III one could pick new numbers Which is why when picking numbers, it's always best to choose at least 2 set. I picked: 1, 2, 3, 9 for easy math and they made B true and everything else false. If you have time, best to verify with a second set of numbers or algebraically.
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Re: If m, p, s and v are positive, and m/p < s/v, which of the following
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