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Is m/n < mn? (1) mn is positive (2) n < -1

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Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 09 Oct 2018, 03:17
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44% (01:50) correct 56% (01:53) wrong based on 70 sessions

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Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post Updated on: 09 Oct 2018, 04:23
1
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


Both values of m & n are either positive or negative.

1- m*n>0 ( it shows moth are either positive or negative )
no other information can be taken out from this.
:. not sufficient

2- n<-1 ( it says n is negative, so m will also be negative)
No other information can be taken out from this.
:. not sufficient

1-2 combined - as n<-1 (n can be = -2,-3,....) and m is also negative,
m/n < m*n always.

:.the correct answer should be, C.

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Originally posted by shiva007 on 09 Oct 2018, 03:42.
Last edited by shiva007 on 09 Oct 2018, 04:23, edited 1 time in total.
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Re: Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 09 Oct 2018, 04:07
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


Question: Is m/n < mn?

In this question we can't further simplify because we do NOT know signs of m and n therefore we straight go to statements to see how useful they may be to determine the answer

Statement 1: mn is positive
i.e. Either both m and n are positive OR both are Negative
Case 1: m = 3 and n = 2, m/n < mn
Case 2: m = 3 and n = 1/2, m/n is NOT less than mn hence
NOT SUFFICIENT

Statement 2: n < -1
No information about m hence
NOT SUFFICIENT

Combining the two statements
Statement 2 says n < -1 i.e. m also is Negative
i.e. Question asked Is m/n < mn may be written as
Is 1/n > n?
But if n < -1 then 1/n is ALWAYS greater than n hence
SUFFICIENT

Answer: Option C
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Re: Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 09 Oct 2018, 04:08
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


Statement 1: insufficient. mn is positive - suggests that the value of both m and n are same, however, the value can vary and thus the statement will not be sufficient.
Statement 2: insufficient: if n is less than -1 than the value of m can be positive and negative. giving us two sets of answers.

Both statement together is sufficient. from info in statement 2 we can rewrite the question as - is m>mn^2, thus we only need to establish that m is negative. statement 1 tells us that mn is positive thus m is negative, hence sufficient.
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Re: Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 09 Oct 2018, 04:13
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


Statement 1:
mn positive means both m and n has same sign.
Let’s take m and n positive

M=2, N=2
Value of m/n<mn ( 2/2<2*2) answer yes

M=0.5 , N=0.5
Value of equation ( 0.5/0.5not < 0.5*0.5) answer no

Statement 1 not sufficient

Statement 2:
N negative, but no information about m
M can be zero then answer is no n can be other values answer will be yes.
Not sufficient.

Combine:
We conclude both m and n is negative with n being less than -1.
Now when we divide or multiply two negative it will give result in positive.
And N being less than -1 it will give a yes answer.
E.g.
M=-0.5, N=-1.1
Equation
0.5/1.1< 0.55


So sufficient
Answer C(IMO)


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Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 09 Oct 2018, 06:07
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


let m = 2 and n = 3

\(\frac{2}{3}\)< 6? yes

let m = 3 and n = \(\frac{1}{3}\)

\(\frac{3}{(1/3)}\) = \(3 * 3 = 9\)

9 < 3 * \(\frac{1}{3}\) no

Two different answers.

1 is insufficient.

2)

we are given n <-1

let m = 2 and n = -2

\(\frac{2}{-2}\)= -1

-1 < -4 no

let m = -9 and n = -3

\(\frac{-9}{-3}\)= 3

3 < 27 yes.

again two different answers not sufficient.

combine (1) and (2)

we know n is negative and mn is positive.

so m has to be negative.

let n = -2 and m = -2

\(\frac{-2}{-2}\) = 1

1 < 4

since n is not between 0 and -1 the left side will never be larger. we get a sufficient answer

\(\frac{m}{n}\) will be > mn only if n lies between 0 and 1 or 0 and -1
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Re: Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 12 Sep 2019, 05:16
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


case 1: m,n=(1,2)…1/2<2:true
case 2: m,n=(3,1)…3/1<3:false
case 3: m,n=(30,-2)…-15<-60:false
case 4: m,n=(-30,-2)…15<60:true

(1) mn is positive: case 1 and 2, insufic.
(2) n < -1: case 3 and 4, insufic.
(1&2) case 4, sufic.

Answer (C)
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Re: Is m/n < mn? (1) mn is positive (2) n < -1  [#permalink]

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New post 12 Sep 2019, 10:56
1
Bunuel wrote:
Is m/n < mn?

(1) mn is positive
(2) n < -1


Analyzing the question:
Note that we cannot simplify this inequality until we know the signs of the variables.

Statement 1:
This means m and n have the same sign, so the left side and right side of "m/n < mn?" are both positive but the magnitude is unknown. Insufficient.

Statement 2:
n is negative, so we can multiply both sides by n to get "m > mn^2?" but we cannot simplify further. If m < 0, then the answer to "1 < n^2?" is yes. If m > 0, we get "1 > n^2?", for which the answer is no, so insufficient.

Combined:
Since n is negative, m must be negative and the question simplifies to "is 1 < n^2?". The answer is yes, so this is sufficient. C
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Re: Is m/n < mn? (1) mn is positive (2) n < -1   [#permalink] 12 Sep 2019, 10:56
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