If m is an integer greater than 9 but less than 20, is n greater than

Question

If m is an integer greater than 9 but less than 20, is n greater than the average (arithmetic mean) of m and 20?

(1) n = 3m
(2) The distance on the number line between n and 20 is less than the distance on the number line between n and m.

US09 · Answer

IMO D

Statement= n>(m+20)/2?
1) If m=10, n=30 & m+20/2=15, therefore n>average of m+20. Stands true for all values. Sufficient.
2) For all values of m, if n is closer to 20 than it is to m on the number line then n>average of m+20, holds true for all values of m from 9 to 19. Therefore Sufficient.

coolnaren · Answer

A is sufficient.

however B can as well be sufficient because distance between n and 20 is less than n and m.

for example m can assume values from 10 to 19. there fore middle value being 14.5. Hence as per option B n has to be greater than 14.5 and less than 20. it cannot exceed 20 or take higher values than 20 because at this point all value of n will not satisfy condition B. Hence 14.5<= n<=20

Answer D

jedit · Answer

It should be  D

From the stem, we know the max and min for  m

9 < m < 20  - so  m  can range between  10  and  19 . Arithmetic mean of m and 20 can be  \frac{10+20}{2} = 15  or  \frac{19+20}{2} = 19.5  at the extremes. Question asks if  n  is greater than these values.

Statement 1: Sufficient 
 n = 3m  so minimum value of  n = 45  and maximum is  57 , which makes it greater than the AM of  m  and  20  in all cases.

Statement 2: Sufficient 
Since  m  is to the left of  20 , and  n  is closer to  20  than it is to  m , this tells us  n  is always to the right of  m . The diagram attached shows both possible cases and arrows represent Arithmetic mean of  m  and  20  and in both cases,  n  shows up as greater than the Arithmetic mean.

techiesam · Answer

Good explanation for statement 2 man.Thanks.

dave13 · Answer

Hi jedit how did you define that m can range between 10 and 19 . ? Did you break this 9 < m < 20 into two inequalities 9 < m --> 1+9 10

m < 20 --> 1+m<20+1 --> 1+m<21 like this ?

thanks!

pushpitkc · Answer

Hey  dave13

The answer to your question has been highlighted. It is clearly mentioned in the 
question stem that m is an integer, greater than 9 and less than 20.

Hope that answers your question!

dave13 · Answer

Hi pushpitkc thanks for your answer

One question when do I need to break this 9 < m < 20 into two inequalities 9 < m --> 1+9 10

m < 20 --> 1+m<20+1 --> 1+m<21 like this ?

i thought i was supposed to do something like this ....or even perhaps subtract +1 from both sides of inequility

niks18 · Answer

Hi dave13 Recall our earlier discussion on inequality and let's try to use the properties in this question. we are given 9\frac{m+20}{2} To know the range of the average add 20 to both sides of the inequality (1) 9+2014.5<\frac{m+20}{2}<20 (dividing both sides of the inequality by a positive number will not change the sign) So from the question stem we got the range of average of m & 20 , which is between 14.5 & 20 Statement 1: n=3m . Now multiply inequality (1) by 3 , we have 9*3<3*m<20*3=>27<3m<60=>27\frac{m+20}{2} . Sufficient Statement 2: Given n is closer to 20 than m . we know the average of m & 20 will be mid point i.e equidistant from both m & 20 and as n is closer to 20 so n>average . Sufficient Option D

dave13 · Answer

Hello niks18

Thanks a lot for taking time to explain

i just have one question

Why do you add +20 to both sides ? Just wanna give you example so as you understand which moment i dont understand ok i googled and found this. please have a look at the question with explanation below (and see my highlighted comment ) ---------------------------------------------------------------------------------------------------------------------------- Technique: Boundary Testing If 2 < x - 6 < 10 and 25 < y + 10 < 45, what inequality represents the range of values of x + y? 1.) Solve each inequality separately. 2 < x - 6 < 10 2 + 6 < x - 6 + 6 < 10 + 6 (see -6 turns positive when adding 6 to both sides, whereas when you add 20 to both sides +20 is still positive and not negative -20, why

Moreover 6 in the middle is canceled out

can you explain the difference between your tecinique and this one 8 < x < 16 25 < y + 10 < 45 25 - 10 < y + 10 - 10 < 45 - 10 15 < y < 35 2.) Combine each inequality by using the boundary of each inequality to find the end of the combined (i.e., summed, x + y) inequality. 2a.) Find the smallest possible value of the inequality. In the first inequality: x is 8.000...0001 In the second inequality: y is 15 23 < x + y 2b.) Find the largest possible value of the inequality. In the first inequality: x is 16 In the second inequality: y is 34.9999... x + y < 51 3.) Combine each value from step 2 to find the inequality that encapsulates x + y. 3a.) Find the smallest possible value of the combined inequality. 8.000...0001 + 15 produces x + y > 23 3b.) Find the largest possible value of the combined inequality. 16 + 34.9999 produces y < 51 Putting these together: 23 < x + y < 51

niks18 · Answer

Hi dave13 , at first there seems to be some formatting issue in my post which somehow I am unable to rectify. Hope you can understand that. Now coming to your question - 2 2+6<(x-6)+6<10+6 =>8 23

niks18 · Answer

Hi  dave13

I am unable to understand why there are so many formatting issues in the forum occurring today, but I hope you got the solution to your queries

If m is an integer greater than 9 but less than 20, is n greater than

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If m is an integer greater than 9 but less than 20, is n greater than

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards