GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Sep 2018, 12:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If m and n are positive decimals smaller than 1, is m+n>1? 1) All d

Author Message
TAGS:

### Hide Tags

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia
If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

### Show Tags

09 Mar 2017, 22:42
2
2
00:00

Difficulty:

45% (medium)

Question Stats:

56% (01:20) correct 44% (01:21) wrong based on 124 sessions

### HideShow timer Statistics

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

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Senior Manager
Joined: 14 Oct 2015
Posts: 252
GPA: 3.57
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

### Show Tags

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.
_________________

Please hit Kudos if this post helped you inch closer to your GMAT goal.
Procrastination is the termite constantly trying to eat your GMAT tree from the inside.
There is one fix to every problem, working harder!

Manager
Joined: 04 May 2014
Posts: 161
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]

### Show Tags

31 Jul 2017, 05:40
2
0.7X0.7=0.49 hence 2nd statement is sufficient.
Senior Manager
Joined: 15 Jan 2017
Posts: 367
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

### Show Tags

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
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1213
Location: India
GPA: 3.82
If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

### Show Tags

23 Sep 2017, 20:44
3
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
Joined: 28 Dec 2010
Posts: 49
If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

### Show Tags

23 Sep 2017, 21:57
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)

_________________
_________________

_________________________________________

Intern
Joined: 03 Sep 2017
Posts: 9
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d  [#permalink]

### Show Tags

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
Re: If m and n are positive decimals smaller than 1, is m+n>1? 1) All d &nbs [#permalink] 24 Sep 2017, 10:08
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.