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If m, p, s and v are positive, and m/p<s/v, which of the fol

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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 19 Sep 2015, 06:26
reto 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



I agree with jlgdr, plugging in makes this question a sub 600 question.

Let's say:

\(\frac{m}{p} <\frac{s}{v}\) = \(\frac{1}{10} <\frac{5}{10}\)

Then I. = 0.3, which is between the two values
Then II. = 0.05, which is not between the two values
Then III. = -0.05, which is not between the two values


Not necessarily. A sub-600 question can be categorized as a 650-700 level question if you end up taking more than usual time for solving it. Some people might not see the value of plugging in different numbers for this question and spend time on using algebra for the same. As you can see out of 443 attempts, only 50% people were able to answer this correctly. Alternately, this question might be a difficult question for people who are not gfood with inequalities in general.

So, the current categorization is somewhat accurate.
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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 11 Oct 2015, 20:45
VeritasPrepKarishma wrote:
Cee0612 wrote:

I make the plug in as follows but it does not work: 1/2 < 3/4

1. (1+3)/(2+4) = 4/6 = 2/3 so in between
2. (1*3)/(2*4) = 3/8 less than 1/2
3. (3-1)/(4-2) = 1 > 3/4

So this problem cannot solve by using plugin?? Please help to correct me if I went wrong.

Thanks!


Statement 3 is (s/v) - (m/p)
When you take values as 1, 2, 3 and 4, it becomes (3/4) - (1/2) = 1/4 (This is not between 1/2 and 3/4 and hence you know that statement 3 may not hold always)

Plugging in numbers is not the best strategy for 'must be true' questions. You know that statement 1 holds for these particular values of m , p, s and v (1, 2, 3 and 4) but how do you know that it will be true for every set of valid values of m, p, s and v? You cannot try every set. You can certainly ignore statements II and III since you have already got values for which they are not satisfied. But you must focus more on statement I and try to figure out using logic whether it must always hold.



I tried 2/4 < 3/4 (I avoided typical 1/2 and matched the denominators)

I.- With the numbers I chose, this gives me 5/8. I multiply my initial numbers by 2/2 and I get:

4/8 < 5/8 < 6/8

By having the numbers nicely and tightly between them, Isn't it a good indication that it must be true?

They didn't mention, however, that m,p,s and v must be integers. If they had, then this approach must certainly be sufficient, since you can divide everything by 8 and end up with 4<5<6. Am I right?

And by the way, once you get I.- to hold true, you end up between B and E and you can forget about testing III.-. Once you find II.- does not hold true, you know It's B

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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 03 Jan 2016, 11:31
I picked m =10, p =5,s =20, v = 4.
And using this, I and III satisfy as they give 3. something for I and 3 for III. Hence it satisfies values between 2 and 5.

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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 01 Aug 2016, 10:28
geometric wrote:
mau5 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


Given that \(\frac{m}{p}<\frac{s}{v} \to \frac{m}{s}<\frac{p}{v}\)Adding 1 on both sides we have \(\frac{m+s}{s}<\frac{p+v}{v} \to \frac{m+s}{p+v}<\frac{s}{v}\)

Again,\(\frac{m}{p}<\frac{s}{v} \to \frac{v}{p}<\frac{s}{m}\) Adding 1 on both sides, we have \(\frac{v+p}{p}<\frac{s+m}{m} \to \frac{m}{p}<\frac{s+m}{v+p}\) . Thus, I is always true. We just have to check for Option II now.

Assming it to be true, we should have\(\frac{ms}{pv}<\frac{s}{v} \to \frac{m}{p}<1\) Which is not always true. Thus the answer is B.


You have the best approach in this thread, but I would never have thought of your solution to #1. I think you made it more complicated than it needed to be.

This is actually a very easy problem once you spend a few moments understanding what you need to do.

You're told the following:
1) m, p, s and v are positive
2) \(\frac{m}{p} <\frac{s}{v}\)

So, you need to know whether each option is both less than \(\frac{s}{v}\) and greater than \(\frac{m}{p}\). That's it. Once that clicks, it's very easy.

I. \(\frac{m+s}{p+v}\)

So part A:

Is \(\frac{m+s}{p+v} < \frac{s}{v}\) ?
Is \(mv+sv < sp + sv\) ?
Is \(mv < sp\) ?
Hmmm, that looks familar. In fact, it's the second thing they gave us: \(\frac{m}{p} <\frac{s}{v}\).
So yes!

Part B:

Is \(\frac{m+s}{p+v} > \frac{m}{p}\) ?
Is \(mp+sp > mp + mv\) ?
Is \(sp > mv\) ?
Hmmm, that looks familar too. In fact, it's also the second thing they gave us: \(\frac{m}{p} <\frac{s}{v}\).
So yes!

Then you perform the same (quicker) process for II.


above approach was good. can someone help to apply the same for II
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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 28 Aug 2016, 08:08
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:

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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 27 Sep 2017, 05:07
Nowhere it says m,p,s and v can't be same numbers. Therefore I plugged in numbers to disprove the statements.
Shall they not mention that the numbers are distict.

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Re: If m, p, s and v are positive, and m/p<s/v, which of the fol [#permalink]

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New post 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=4/5-1/2=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 fol   [#permalink] 01 Oct 2017, 05:19

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