[Math Revolution GMAT math practice question]
If m and n are positive integers, is mn an even number?
1) m/n is an even number.
2) m + n is an even number.
If m and n are positive integers, is mn an even number?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
$$m,n\,\, \ge \,\,1\,\,\,{\rm{ints}}\,\,\,\,\left( * \right)$$Max@Math Revolution wrote:[Math Revolution GMAT math practice question]
If m and n are positive integers, is mn an even number?
1) m/n is an even number.
2) m + n is an even number.
$$mn\,\,\,\mathop = \limits^? \,\,\,{\text{even}}\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\boxed{\,?\,\,\,:\,\,\,m\,\,{\text{or}}\,\,n\,\,{\text{even}}\,\,}$$
$$\left( 1 \right)\,\,{m \over n} = {\rm{even}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,m = n \cdot {\rm{even}}\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,m\,\, = {\mathop{\rm int}} \, \cdot {\rm{even}}\,\,{\rm{ = }}\,\,{\rm{even}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle $$
$$\left( 2 \right)\,\,m + n\,\, = \,\,{\rm{even}}\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {1,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {m,n} \right) = \left( {2,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Some important rules:Max@Math Revolution wrote:If m and n are positive integers, is mn an even number?
1) m/n is an even number.
2) m + n is an even number.
#1. ODD +/- ODD = EVEN
#2. ODD +/- EVEN = ODD
#3. EVEN +/- EVEN = EVEN
#4. (ODD)(ODD) = ODD
#5. (ODD)(EVEN) = EVEN
#6. (EVEN)(EVEN) = EVEN
Target question: Is mn an even number?
Given: m and n are positive integers
Statement 1: m/n is an even number.
m/n = some even integer
Multiply both sides of the equation by n to get: m = (some even integer)(n)
This means m MUST be EVEN
If m is EVEN, then mn must be EVEN
So, the answer to the target question is YES, mn IS an even number
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: m + n is an even number
There are several values of m and n that satisfy statement 2. Here are two:
Case a: m = 2 and n = 2. Notice that 2 + 2 = 4, which is even. In this case, mn = (2)(2) = 4. So, the answer to the target question is YES, mn IS an even number
Case b: m = 1 and n = 1. Notice that 1 + 1 = 2, which is even. In this case, mn = (1)(1) = 1. So, the answer to the target question is NO, mn is NOT an even number
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Modifying the question:
mn is an even number precisely when at least one of m and n is even. So,
the question asks if either m or n is even.
Condition 1:
If m/n = 2k for some integer k, then m = 2kn, which is an even number.
Thus, condition 1) is sufficient.
Condition 2)
If m = 2 and n = 4, then m + n = 6 is even, and mn = 8 is an even number, so the answer is 'yes'.
If m = 1 and n = 3, then m + n = 4 is even, and mn = 3 is not an even number, so the answer is 'no'.
Since it does not give us a unique answer, condition 2) is not sufficient.
Therefore, the correct answer is A.
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Modifying the question:
mn is an even number precisely when at least one of m and n is even. So,
the question asks if either m or n is even.
Condition 1:
If m/n = 2k for some integer k, then m = 2kn, which is an even number.
Thus, condition 1) is sufficient.
Condition 2)
If m = 2 and n = 4, then m + n = 6 is even, and mn = 8 is an even number, so the answer is 'yes'.
If m = 1 and n = 3, then m + n = 4 is even, and mn = 3 is not an even number, so the answer is 'no'.
Since it does not give us a unique answer, condition 2) is not sufficient.
Therefore, the correct answer is A.
Answer: A
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]