It is currently 20 Mar 2018, 14:43

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Are positive integers j and k both greater than m?

Author Message
TAGS:

### Hide Tags

Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1471
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Are positive integers j and k both greater than m? [#permalink]

### Show Tags

14 Dec 2011, 09:31
1
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

66% (01:33) correct 34% (01:30) wrong based on 86 sessions

### HideShow timer Statistics

Are positive integers j and k both greater than m?

(1) $$m + k - j$$ is negative.
(2) $$k - j - m$$ is positive.

Can we solve it algebraicaly?
[Reveal] Spoiler: OA

_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 12 Oct 2011
Posts: 241
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

14 Dec 2011, 12:20
2
KUDOS
3
This post was
BOOKMARKED
I do not know if this is the right approach but this is how I solved it (after quite some time though).

Given: j > 0; k > 0

Statement 1: m + k - j < 0
Thus m + k < j or j > (k + m)
Now, j and k are both positive. So this inequality shows that j is greater than the sum of a positive number k and m(the sign of m does not matter). Thus, j > m

Statement 2: k - j - m > 0
Thus, k > (j + m)
Using similar logic as above, we can understand that k is also greater than the sum of a positive number j and m. Thus k > m

Thus the individual statements answer about each j and m, and together they answer the question. That is why the correct answer should be C.

Please suggest a more efficient method to solve.
Retired Moderator
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1471
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

14 Dec 2011, 14:03
siddharthmuzumdar wrote:
I do not know if this is the right approach but this is how I solved it (after quite some time though).

Given: j > 0; k > 0

Statement 1: m + k - j < 0
Thus m + k < j or j > (k + m)
Now, j and k are both positive. So this inequality shows that j is greater than the sum of a positive number k and m(the sign of m does not matter). Thus, j > m

Statement 2: k - j - m > 0
Thus, k > (j + m)
Using similar logic as above, we can understand that k is also greater than the sum of a positive number j and m. Thus k > m

Thus the individual statements answer about each j and m, and together they answer the question. That is why the correct answer should be C.

Please suggest a more efficient method to solve.

Wonderful! I think it is a good approach.
Thank you. Kudos to you!
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

14 Dec 2011, 18:21
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
metallicafan wrote:
Are positive integers j and k both greater than m?

(1) $$m + k - j$$ is negative.
(2) $$k - j - m$$ is positive.

Can we solve it algebraicaly?

Neither statement is sufficient alone here (there's no way to say which of m or k is larger in statement 1, and no way to say which of m and j is larger in statement 2). We can combine the statements directly: if two inequalities face the same way, we can *add* them (but note that we cannot subtract them) just as we do with equations. So writing the inequalities so they face the same way and adding them we find:

\begin{align*} 0 &> m + k - j \\ k -j - m &> 0 \\ k - j - m &> m + k - j \\ 0 &> 2m \\ 0 &> m \end{align*}

If m is negative, it's definitely smaller than any positive number, so it's smaller than j and k, and the answer is C.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Manager
Joined: 12 Oct 2011
Posts: 241
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

15 Dec 2011, 02:52
IanStewart wrote:
Neither statement is sufficient alone here (there's no way to say which of m or k is larger in statement 1, and no way to say which of m and j is larger in statement 2). We can combine the statements directly: if two inequalities face the same way, we can *add* them (but note that we cannot subtract them) just as we do with equations. So writing the inequalities so they face the same way and adding them we find:

\begin{align*} 0 &> m + k - j \\ k -j - m &> 0 \\ k - j - m &> m + k - j \\ 0 &> 2m \\ 0 &> m \end{align*}

If m is negative, it's definitely smaller than any positive number, so it's smaller than j and k, and the answer is C.

I guess this is the best approach.

metallicafan, I guess you found your best answer now. My method also works but is than the one mentioned here.
_________________

Consider KUDOS if you feel the effort's worth it

GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

15 Dec 2011, 06:18
siddharthmuzumdar wrote:

I guess this is the best approach.

metallicafan, I guess you found your best answer now. My method also works but is than the one mentioned here.

Your approach is also very good - if the question asked something different, you might need to use an approach similar to yours. For example, if the question had asked if j > m, then you would need to analyze each statement in the way you've done. As with many higher level questions, there are often several ways to get to an answer.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Senior Manager
Joined: 15 Jan 2017
Posts: 360
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

13 Nov 2017, 01:33
Thought of this way. Kudos, if you felt it was useful

1) m + k - j = -1 (as answer is negative)
m = j- 1-k
m = j - k -1
m = j -1(k+1)
Thus j > m (cause j minus values = m)
K we don't know about --> m + 1=k +1 (if we remove j), so m = K. But we don't know for sure.

2) k - j - m = 1
k = 1 + j + m
k - 1(j +1) = m.
Thus K > m. J we are not sure.

1) + 2) j, k > m. Thus C.
Manager
Joined: 12 Nov 2017
Posts: 95
Location: India
GMAT 1: 650 Q50 V28
GMAT 2: 710 Q50 V35
GPA: 2.8
WE: Information Technology (Computer Software)
Re: Are positive integers j and k both greater than m? [#permalink]

### Show Tags

13 Nov 2017, 06:53
metallicafan wrote:
Are positive integers j and k both greater than m?

(1) $$m + k - j$$ is negative.
(2) $$k - j - m$$ is positive.

Can we solve it algebraicaly?

As we can not solve it with statements 1 &2 individually:

Just subtract the statement 1 from statement 2 (Positive-(Negative)) will always be positive.After subtraction, we get
-2m >0, so m is negative.

As J & K are mentioned as positives, they will always be greater than m.

Re: Are positive integers j and k both greater than m?   [#permalink] 13 Nov 2017, 06:53
Display posts from previous: Sort by