Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 0808:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
16 Sep 2014, 01:46
Kudos
Bookmarks
If \(m^2 < 225\) and \(n - m = -10\), what is the positive difference between the smallest possible integer value of \(3m + 2n\) and the greatest possible integer value of \(3m + 2n\)?
A. 190
B. 188
C. 150
D. 148
E. 40
A. 190
B. 188
C. 150
D. 148
E. 40
16 Sep 2014, 01:46
Kudos
Bookmarks
Official Solution:
If \(m^2 < 225\) and \(n - m = -10\), what is the positive difference between the smallest possible integer value of \(3m + 2n\) and the greatest possible integer value of \(3m + 2n\)?
A. 190
B. 188
C. 150
D. 148
E. 40
This question requires us to perform algebraic manipulations involving inequalities.
Given that \(n - m = -10\), we can deduce that \(n = m - 10\). Consequently, \(3m + 2n = 3m + 2(m - 10) = 5m - 20\). Our goal is to find the positive difference between the smallest possible integer value of \(5m - 20\) and the greatest possible integer value of \(5m - 20\). It's important to note that we are not given any information about whether \(m\) and \(n\) are integers. Keep this in mind when solving the problem.
Next, let's work with the inequality \(m^2 < 225\):
Take the square root of both sides: \(|m| < 15\);
Get rid of the modulus sign: \(-15 < m < 15\);
Multiply all three parts by 5: \(-75 < 5m < 75\);
Subtract 20 from all three parts: \(-95 < 5m - 20 < 55\);
From \(-95 < 5m - 20 < 55\), it follows that the smallest possible integer value of \(5m - 20\) is -94 and the greatest possible integer value of \(5m - 20\) is 54.
Therefore, the positive difference between the smallest and greatest integer values is \(54 - (-94) = 54 + 94 = 148\).
Answer: D
If \(m^2 < 225\) and \(n - m = -10\), what is the positive difference between the smallest possible integer value of \(3m + 2n\) and the greatest possible integer value of \(3m + 2n\)?
A. 190
B. 188
C. 150
D. 148
E. 40
This question requires us to perform algebraic manipulations involving inequalities.
Given that \(n - m = -10\), we can deduce that \(n = m - 10\). Consequently, \(3m + 2n = 3m + 2(m - 10) = 5m - 20\). Our goal is to find the positive difference between the smallest possible integer value of \(5m - 20\) and the greatest possible integer value of \(5m - 20\). It's important to note that we are not given any information about whether \(m\) and \(n\) are integers. Keep this in mind when solving the problem.
Next, let's work with the inequality \(m^2 < 225\):
Take the square root of both sides: \(|m| < 15\);
Get rid of the modulus sign: \(-15 < m < 15\);
Multiply all three parts by 5: \(-75 < 5m < 75\);
Subtract 20 from all three parts: \(-95 < 5m - 20 < 55\);
From \(-95 < 5m - 20 < 55\), it follows that the smallest possible integer value of \(5m - 20\) is -94 and the greatest possible integer value of \(5m - 20\) is 54.
Therefore, the positive difference between the smallest and greatest integer values is \(54 - (-94) = 54 + 94 = 148\).
Answer: D
25 May 2015, 01:53
Kudos
Bookmarks
mahuya78
We are NOT told that m is an integer, hence from -15<m<15 saying that the minimum value of m is -14 and the maximum value of m is 14 is wrong.
