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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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09 Mar 2017, 22:42
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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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Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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10 Mar 2017, 00:19
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.



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Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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31 Jul 2017, 05:40
0.7X0.7=0.49 hence 2nd statement is sufficient.



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Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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23 Sep 2017, 11:36
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



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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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23 Sep 2017, 20:44
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 SufficientStatement 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 SufficientOption D



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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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23 Sep 2017, 21:57
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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Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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24 Sep 2017, 10:08
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



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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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25 Jan 2019, 19:38
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. SUFFICIENTANSWER (D) Thanks for reading!



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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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25 Jan 2019, 20:45
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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If m and n are positive decimals smaller than 1, is m+n>1? 1) All d
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25 Jan 2019, 20:45






