[GMAT math practice question]
If m and n are positive integers, is m^2-n^2 divisible by 4?
1) m^2+n^2 has remainder 2 when it is divided by 4
2) m*n is an odd integer
If m and n are positive integers, is m^2-n^2 divisible by 4?
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]
- 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.
The statement "m^2-n^2 is divisible by 4" means that (m+n)(m-n) is divisible by 4. This is equivalent to the requirement that m and n are either both even integers or both odd integers.
Since condition 2) tells us that both m and n are odd integers, condition 2) is sufficient.
Condition 1)
The square of an odd integer (2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2 + a) + 1 has remainder 1 when it is divided by 4.
The square of an even integer (2b)^2 = 4b^2 has remainder 0 when it is divided by 4.
Thus, if "m^2+n^2 has remainder 2 when it is divided by 4", both m and n must be odd integers.
Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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.
The statement "m^2-n^2 is divisible by 4" means that (m+n)(m-n) is divisible by 4. This is equivalent to the requirement that m and n are either both even integers or both odd integers.
Since condition 2) tells us that both m and n are odd integers, condition 2) is sufficient.
Condition 1)
The square of an odd integer (2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2 + a) + 1 has remainder 1 when it is divided by 4.
The square of an even integer (2b)^2 = 4b^2 has remainder 0 when it is divided by 4.
Thus, if "m^2+n^2 has remainder 2 when it is divided by 4", both m and n must be odd integers.
Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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]
-
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Sun Apr 14, 2019 12:04 am
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Can u please clarify the highlighted portion below ?
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.
The statement "m^2-n^2 is divisible by 4" means that (m+n)(m-n) is divisible by 4. This is equivalent to the requirement that m and n are either both even integers or both odd integers.[/color]
Since condition 2) tells us that both m and n are odd integers, condition 2) is sufficient.
Condition 1)
The square of an odd integer (2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2 + a) + 1 has remainder 1 when it is divided by 4.
The square of an even integer (2b)^2 = 4b^2 has remainder 0 when it is divided by 4.
Thus, if "m^2+n^2 has remainder 2 when it is divided by 4", both m and n must be odd integers.
Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.[/quote] $$$$ $$$$ $$$$ $$$$
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
The statement "m^2-n^2 is divisible by 4" means that (m+n)(m-n) is divisible by 4. This is equivalent to the requirement that m and n are either both even integers or both odd integers.[/color]
Since condition 2) tells us that both m and n are odd integers, condition 2) is sufficient.
Condition 1)
The square of an odd integer (2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2 + a) + 1 has remainder 1 when it is divided by 4.
The square of an even integer (2b)^2 = 4b^2 has remainder 0 when it is divided by 4.
Thus, if "m^2+n^2 has remainder 2 when it is divided by 4", both m and n must be odd integers.
Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.[/quote] $$$$ $$$$ $$$$ $$$$
-
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Sun Apr 14, 2019 12:04 am
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Max@Math Revolution wrote:=>
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.
The statement "m^2-n^2 is divisible by 4" means that (m+n)(m-n) is divisible by 4. This is equivalent to the requirement that m and n are either both even integers or both odd integers.
Since condition 2) tells us that both m and n are odd integers, condition 2) is sufficient.
Condition 1)
The square of an odd integer (2a+1)^2 = 4a^2 + 4a + 1 = 4(a^2 + a) + 1 has remainder 1 when it is divided by 4.
The square of an even integer (2b)^2 = 4b^2 has remainder 0 when it is divided by 4.
Thus, if "m^2+n^2 has remainder 2 when it is divided by 4", both m and n must be odd integers.
Condition 1) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
Can u please clarify the highlighted portion below ?