Yes,the answer is B.raisethebar wrote:Is the Ans B?
only statement B is sufficient to ans.
If ans is correct then I can explain.
1. is not sufficient - for all integer values of nl a^n - b^n is divisible by a - bharsh.champ wrote:Is n odd ?
1. a^n - b^n is divisible by a - b
2. a^n + b^n is not divisible by a + b
Rules for a^n - b^n:can't understand the logic behind why the statement B IS CORRECT. Ajith! can you explain? I can't make a logic to fit in without trying real numbers. Is this some kind of rule in maths.
_____________papgust wrote:Rules for a^n - b^n:can't understand the logic behind why the statement B IS CORRECT. Ajith! can you explain? I can't make a logic to fit in without trying real numbers. Is this some kind of rule in maths.
--> Always divisible by (a-b)
--> Divisible by (a+b), when n is EVEN
--> NOT Divisible by (a+b), when n is ODD
Rules for a^n + b^n:
--> NEVER divisible by (a-b)
--> Divisible by (a+b), when n is ODD
--> NOT Divisible by (a+b), when n is EVEN
---
Coming to the question,
n odd?
A. a^n - b^n is divisible by a - b
when n is ODD/EVEN, (a-b) divides (a^n - b^n)
Insufficient.
B. a^n + b^n is not divisible by a + b
ONLY when n is EVEN. When n is ODD, a^n + b^n is divisible by a + b.
So, n is EVEN. Sufficient.
Hence B
There are so many rules that might show up that it's really not worth seeking out and memorizing the ones unlikely to appear. What's far more important is learning how to answer questions for which you don't remember the rule.harsh.champ wrote: _____________
Thanks papgust,
That was really appreciative of you to post the Rules for a^n - b^n and Rules for a^n - b^n.
Though suppose,I forget any of the 6 rules.Then,it would be impossible to solve the question w/o plugging in numbers.
My question is:what is more worthwhile,remembering all the rules of math or solve by hit-and-trial??
The former can lead to error if misplace any rule with the other.On the other hand,the latter may take up some time during the test.
In the long run,what would prove to be more beneficial.
Seeking advice from experts too!!!
Stuart Kovinsky wrote:Thanks,that was really insightful of you.harsh.champ wrote: _____________
There are so many rules that might show up that it's really not worth seeking out and memorizing the ones unlikely to appear. What's far more important is learning how to answer questions for which you don't remember the rule.
I'd never advocate memorizing the rules related to this question; if you know them, great - but if not, there are far more valuable uses of your time.
The GMAT is less a test of math than of critical thinking, so that's the key skill that you need to master for success.
Picking numbers is invaluable in both problem solving and data sufficiency. Even if you're a math whiz, there will be questions on which it's faster to pick numbers than do the algebra. The key things to work on as you practice are:
1) when can I pick numbers;
2) when should I pick numbers; and
3) what numbers should I pick?
The answer to the first question is pretty much any time there are unknowns in a question.
The answer to the second question is subjective; the trite answer is "any time it's faster than doing algebra", which means you really need to know your own strengths and weaknesses to ensure that you choose the best approach for every question.
How do you do so? Every time you do a question, if you see multiple ways to do it, try it each and every way. These various methods may include algebra, picking numbers, backsolving, logic, intuition and strategic guessing. The only way you're going to become an expert at the methods you're not accustomed to using is to practice them repeatedly; the only way you can determine what's the best way to attack a certain type of question is to try out different approaches.
The answer to the third question depends on the subject matter of the question. Here, for example, we want to try out an odd value of n and an even value of n (odd/even questions are built for picking numbers, since as soon as you try out 1 of each you've usually exhausted all of the possibilities).
Here are some types of numbers you should consider:
1) odd/even
2) positive/negative
3) -1, 0, 1
4) positive fractions
5) primes/non-primes (on prime questions, always pick 2 and an odd prime)
6) integers/non-integers
7) small/big
8) perfect square/non-perfect square
Each time you attack a data sufficiency question, keep track of what the question was testing and what numbers made a difference; the better you get at choosing the right numbers, the less time it will take you to do so.
The effort is really appreciative.
I am sure any community member who looks up this thread will be benefited.
On another note,I had one doubt:-While posting these 3 questions,I was doubtful whether to also post it in the GMAT strategy forum and give the link of this thread,so that it can be helpful both ways.Or should the post belong to the math forum only??
Stuart Kovinsky wrote:There are so many rules that might show up that it's really not worth seeking out and memorizing the ones unlikely to appear. What's far more important is learning how to answer questions for which you don't remember the rule.harsh.champ wrote: _____________
Thanks papgust,
That was really appreciative of you to post the Rules for a^n - b^n and Rules for a^n - b^n.
Though suppose,I forget any of the 6 rules.Then,it would be impossible to solve the question w/o plugging in numbers.
My question is:what is more worthwhile,remembering all the rules of math or solve by hit-and-trial??
The former can lead to error if misplace any rule with the other.On the other hand,the latter may take up some time during the test.
In the long run,what would prove to be more beneficial.
Seeking advice from experts too!!!
I'd never advocate memorizing the rules related to this question; if you know them, great - but if not, there are far more valuable uses of your time.
The GMAT is less a test of math than of critical thinking, so that's the key skill that you need to master for success.
Picking numbers is invaluable in both problem solving and data sufficiency. Even if you're a math whiz, there will be questions on which it's faster to pick numbers than do the algebra. The key things to work on as you practice are:
1) when can I pick numbers;
2) when should I pick numbers; and
3) what numbers should I pick?
The answer to the first question is pretty much any time there are unknowns in a question.
The answer to the second question is subjective; the trite answer is "any time it's faster than doing algebra", which means you really need to know your own strengths and weaknesses to ensure that you choose the best approach for every question.
How do you do so? Every time you do a question, if you see multiple ways to do it, try it each and every way. These various methods may include algebra, picking numbers, backsolving, logic, intuition and strategic guessing. The only way you're going to become an expert at the methods you're not accustomed to using is to practice them repeatedly; the only way you can determine what's the best way to attack a certain type of question is to try out different approaches.
The answer to the third question depends on the subject matter of the question. Here, for example, we want to try out an odd value of n and an even value of n (odd/even questions are built for picking numbers, since as soon as you try out 1 of each you've usually exhausted all of the possibilities).
Here are some types of numbers you should consider:
1) odd/even
2) positive/negative
3) -1, 0, 1
4) positive fractions
5) primes/non-primes (on prime questions, always pick 2 and an odd prime)
6) integers/non-integers
7) small/big
8) perfect square/non-perfect square
Each time you attack a data sufficiency question, keep track of what the question was testing and what numbers made a difference; the better you get at choosing the right numbers, the less time it will take you to do so.
I'm concerned that some readers might find the above 'rules' misleading. These are rules about algebraic factoring; it is not correct to use any of the "NOT" or "NEVER" 'rules' in questions about divisibility. If we take, for example, the 'rule'papgust wrote:
Rules for a^n - b^n:
--> Always divisible by (a-b)
--> Divisible by (a+b), when n is EVEN
--> NOT Divisible by (a+b), when n is ODD
Rules for a^n + b^n:
--> NEVER divisible by (a-b)
--> Divisible by (a+b), when n is ODD
--> NOT Divisible by (a+b), when n is EVEN
and, for simplicity, we let n=2, this would say that a^2 + b^2 is not divisible by a+b. What you mean is that it is impossible to factor out (a+b) from (a^2 + b^2); that is certainly true. It is *not*, however, correct to interpret this as a rule about divisibility of numbers. If, say, a=20 and b=5, then 20^2 + 5^2 most certainly *is* divisible by 20+5. That we cannot factor (a+b) from (a^2 + b^2) *only* tells us that a^2 + b^2 is not *always* divisible by a+b; it sometimes is, and it sometimes is not. There are similar examples one can give for any of the 'NEVER' rules above:papgust wrote: Rules for a^n + b^n:
--> NOT Divisible by (a+b), when n is EVEN
If you let a=3 and b=2, for example, then a^n + b^n will always be divisible by a-b = 1, no matter what the value of n.papgust wrote: Rules for a^n + b^n:
--> NEVER divisible by (a-b)
Again you can use a=20, b=5 and n=3; 20^3 - 5^3 is divisible by 25.papgust wrote: Rules for a^n - b^n:
--> NOT Divisible by (a+b), when n is ODD
Nice xplantn dude...thankspapgust wrote:Rules for a^n - b^n:can't understand the logic behind why the statement B IS CORRECT. Ajith! can you explain? I can't make a logic to fit in without trying real numbers. Is this some kind of rule in maths.
--> Always divisible by (a-b)
--> Divisible by (a+b), when n is EVEN
--> NOT Divisible by (a+b), when n is ODD
Rules for a^n + b^n:
--> NEVER divisible by (a-b)
--> Divisible by (a+b), when n is ODD
--> NOT Divisible by (a+b), when n is EVEN
---
Coming to the question,
n odd?
A. a^n - b^n is divisible by a - b
when n is ODD/EVEN, (a-b) divides (a^n - b^n)
Insufficient.
B. a^n + b^n is not divisible by a + b
ONLY when n is EVEN. When n is ODD, a^n + b^n is divisible by a + b.
So, n is EVEN. Sufficient.
Hence B
an easy entry; it tests a^n - b^n reformation --> every time n={n is integer, 2,3,4, ... +infinity} (a-b) is one factor present ahead of the reformationIs n odd ?
1. a^n - b^n is divisible by a - b
2. a^n + b^n is not divisible by a + b
rohu27 wrote:re-opening an old thread (this was todays BTG ath question)
can someone explain the solution wth exact steps? unable to figure out
