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Senior SC Moderator V
Joined: 14 Nov 2016
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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 57% (01:41) correct 43% (01:57) wrong based on 230 sessions

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If m and n are positive decimals smaller than 1, is $$m+n>1$$?

1) All decimal digits of m and n are greater than 5

2) $$mn > \frac{1}{2}$$

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Manager  P
Joined: 14 Oct 2015
Posts: 243
GPA: 3.57
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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ziyuen wrote:
If m and n are positive decimals smaller than 1, is $$m+n>1$$?

1) All decimal digits of m and n are greater than 5

2) $$mn > \frac{1}{2}$$

I chose D.

1- This suggests both m and n are > 0.6 and since we know they are both positive, they can only add up to > 1.

2- I could not find any value where two decimals m and n ending up in a sum less than 1 if their multiple is greater than 0.5. I would greatly appreciate it if someone can provide some mathematical base to this rough calculation.
Manager  B
Joined: 04 May 2014
Posts: 150
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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2
0.7X0.7=0.49 hence 2nd statement is sufficient.
Senior Manager  S
Joined: 15 Jan 2017
Posts: 332
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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gps5441 wrote:
0.7X0.7=0.49 hence 2nd statement is sufficient.

Oh so it could be : 0.7 * 0.9 or 0.7*0.8 --> these give values more than 0.5
so st 2 suff
Ans will be D
Thank you for the hint Retired Moderator D
Joined: 25 Feb 2013
Posts: 1159
Location: India
GPA: 3.82
If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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hazelnut wrote:
If m and n are positive decimals smaller than 1, is $$m+n>1$$?

1) All decimal digits of m and n are greater than 5

2) $$mn > \frac{1}{2}$$

Statement 1: implies $$m>0.5$$ & $$n>0.5$$ Add the two you will get $$m+n>1$$. Hence Sufficient

Statement 2: $$mn>0.5$$ here you can logically deduce the values of $$m$$ & $$n$$ to know that both will be greater than $$0.5$$, hence $$m+n>1$$

Alternatively, $$m>\frac{0.5}{n}$$, it is given that $$m$$ & $$n$$ are decimals, so $$n>0.5$$ because if $$n<0.5$$, then $$\frac{0.5}{n}>1$$, which is not possible

similarly $$m>\frac{0.5}{n}$$, hence $$m>0.5$$. this is equivalent to our statement 1. Hence Sufficient

Option D
Intern  B
Joined: 28 Dec 2010
Posts: 48
If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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1
1. Each decimal digit is greater than 5
m,n >0.6
This is sufficient.
Note: Give attention to "greater than". If it was greater than equal to 5, we could have m=n=0.5. In that scenario, m+n=1, not >1

2. For second statement, you should know this
AM >= GM

Arithmetic Mean of 2 numbers is greater than equal to Geometric Mean of 2 numbers.
So,
$$\frac{(m+n)}{2}$$ >= $$\sqrt{mn}$$

We know that mn > $$\frac{1}{2}$$
So $$\sqrt{mn}$$ > $$\frac{1}{\sqrt{2}}$$

Substitute this in our original equation
$$\frac{(m+n)}{2}$$ >= $$\frac{1}{\sqrt{2}}$$

m+n >= $$\sqrt{2}$$
Hence, m+n >1
This is sufficient.

D.

Additional Lesson: AM >= GM >= HM (Harmonic Mean)

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Intern  B
Joined: 03 Sep 2017
Posts: 13
GMAT 1: 650 Q46 V34 Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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jedit wrote:
ziyuen wrote:
If m and n are positive decimals smaller than 1, is $$m+n>1$$?

1) All decimal digits of m and n are greater than 5

2) $$mn > \frac{1}{2}$$

I chose D.

1- This suggests both m and n are > 0.6 and since we know they are both positive, they can only add up to > 1.

2- I could not find any value where two decimals m and n ending up in a sum less than 1 if their multiple is greater than 0.5. I would greatly appreciate it if someone can provide some mathematical base to this rough calculation.

For the second part > 0.5 so let's say 0.63 which is 0.9 and 0.7
Intern  B
Joined: 14 Dec 2018
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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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hazelnut wrote:
If m and n are positive decimals smaller than 1, is $$m+n>1$$?

1) All decimal digits of m and n are greater than 5

2) $$mn > \frac{1}{2}$$

(1) the least decimal with digits greater than 5 is 0,6. If m and n are equal than 0.6, m+n=1,2>1. SUFFICIENT

(2) If m is the greatest decimal less than 1, we can write it like (99...9)/(10^x) where 99...9 has "x" digits.
If mn were at least 1/2, n should be (10^x)/(2*99...9) or (5000...0000)/(99...9) where each number has "x digits. Hence n>1/2.
According to these premises m and n are greater than 1/2. Hence m+n>1. SUFFICIENT

Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

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hazelnut wrote:
If m and n are positive decimals smaller than 1, is $$m+n>1$$?

1) All decimal digits of m and n are greater than 5

2) $$mn > \frac{1}{2}$$

Multiply carefully

Statement 1 is sufficient alone
All decimal digits of m and n are greater than 5

0.66 + 0.6 => 1.26

Statement 2 i sufficient alone
$$mn > \frac{1}{2}$$

mn > 0.5

0.8 * 0.7
0.8 * 0.8
0.9 * 0.7

D
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Many of life's failures happen with people who do not realize how close they were to success when they gave up. If m and n are positive decimals smaller than 1, is m+n>1? 1) All d   [#permalink] 25 Jan 2019, 20:45
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