Hey Varun .. Ans is E For function problems of these kind, in LHS sub x by (a+b) and verify if is equal to sum when u sub x by a and b resp .
eg 1. (a+b)^2 + 1 is not equal to a^2 +1 + b^2 + 1 ..incorrect 2 . 2root(a+b) is not equal to 2roota +2rootb ..incorrect . 3. a+b-4 is not equal to a-4 +b-4 ...incorrect 4. 5/(a+b) is not equal to 5/a + 5/b 5. -7(a+b) = -7a-7b ...correct ....Ans E
As a general rule , squares, roots, adding or subtracting constants to variables does not hold true .. Single variate function without any additional operation would hold true .. Hope that helps
Hello Guys out there inspiring to be GMATians, theres a quick question from my side if some one could help please...i dn know the answer but am open to all the suggestions and mind curlings...:-)
here it goes... A function F(X) is defind as the product of all even numbers from 2 to 100 what is the biggest prime factor of F(x)+1.......
wouldnt it be something like this; product of numbers from 1 to 100 is 100!
so the biggest prime number less than 100 would be the highest factor for the factorial..i.e. 97
now 100! + 1 is not 101!... so 101 would not be the highest factor for the function, .. since f(100) + 1 != f(101)..
I believe the answer is 97..
share your thoughts plz.. :drinking:
naa varun ...i have not pinpointed a particular prime no to be a factor of f(x) +1 ...i would be glad if somebody could come up with a technique to find the precise answer ..
i just gave the range, saying it has to be def greater than 50 ...
n i guess u have misinterpreted d question ... its not f(101) ...its not a variable function ..n i never meant 100 ! + 1 = 101 ! ...
function is f(x) = 2*4*6*8*...*100 so, f(x) + 1 = (2*4*6*8*...*100) + 1 hence, f(x) + 1 = 2^50*50! +1
so, why do u say it has to be 97 ?
and my point was , if r is a facor of f(x), it can never be a factor of f(x)+1 ...
I am sure the ans option would be range of nos ...it possibly cannot be definite choices ...
Hello Guys out there inspiring to be GMATians, theres a quick question from my side if some one could help please...i dn know the answer but am open to all the suggestions and mind curlings...:-)
here it goes... A function F(X) is defind as the product of all even numbers from 2 to 100 what is the biggest prime factor of F(x)+1.......
wouldnt it be something like this; product of numbers from 1 to 100 is 100!
so the biggest prime number less than 100 would be the highest factor for the factorial..i.e. 97
now 100! + 1 is not 101!... so 101 would not be the highest factor for the function, .. since f(100) + 1 != f(101)..
I believe the answer is 97..
share your thoughts plz.. :drinking:
naa varun ...i have not pinpointed a particular prime no to be a factor of f(x) +1 ...i would be glad if somebody could come up with a technique to find the precise answer ..
i just gave the range, saying it has to be def greater than 50 ...
n i guess u have misinterpreted d question ... its not f(101) ...its not a variable function ..n i never meant 100 ! + 1 = 101 ! ...
function is f(x) = 2*4*6*8*...*100 so, f(x) + 1 = (2*4*6*8*...*100) + 1 hence, f(x) + 1 = 2^50*50! +1
so, why do u say it has to be 97 ?
and my point was , if r is a facor of f(x), it can never be a factor of f(x)+1 ...
I am sure the ans option would be range of nos ...it possibly cannot be definite choices ...
The reason behind my mistake is simple.. I DID NOT notice EVEN NUMBERSB:oops:
got it now, F(A) = 2 x (2x2) x (2x3) x (2x4) x .. x (2x50) = F(A) + 1 = + 1 = {x (50!)} + 1
I believe that the Biggest primer factor = 47..
why do you say that it would be greater than 50.. the question is to find out prime factor, and not greatest factor..
The reason behind my mistake is simple.. I DID NOT notice EVEN NUMBERSB:oops:
got it now, F(A) = 2 x (2x2) x (2x3) x (2x4) x .. x (2x50) = F(A) + 1 = + 1 = {x (50!)} + 1
I believe that the Biggest primer factor = 47..
why do you say that it would be greater than 50.. the question is to find out prime factor, and not greatest factor..
now.. am I confused, or am I just drunk.. :drinking:
he he varun ...u r so close ...again a simple mistake out here ... Yes, 47 is the highest prime factor of 2^50*50! , so if u add 1 to this no, 47 is no longer a factor of this new no ...
Its like 2^50*50! = 47*p (where p is some integer)
So, 47 is not a factor of 47p+1 ...
The biggest challenge really would be to find which is the highest prime factor of 2^50*50! +1 ...it could be 53, 97 or watever ...(I am not aware of the technique to deduce this ) .... If somebody has a way to come to the precise value, please share your thoughts !!
Cheers !! (Varun: I am sure your doubt is cleared now)
Hello Guys out there inspiring to be GMATians, theres a quick question from my side if some one could help please...i dn know the answer but am open to all the suggestions and mind curlings...:-)
here it goes... A function F(X) is defind as the product of all even numbers from 2 to 100 what is the biggest prime factor of F(x)+1.......
This is a question from one of the GMAt testPrep.and the options given are->50 and so on
Bhavin has clearly explained the highest prime factor will be greater than 50
ha haa.. laugh one laugh all.. public forum pe izzat ki dash dash ho gayi.. shucks!!
btw got it now.. thanks man.. ;)
he he varun ...u r so close ...again a simple mistake out here ... Yes, 47 is the highest prime factor of 2^50*50! , so if u add 1 to this no, 47 is no longer a factor of this new no ...
Its like 2^50*50! = 47*p (where p is some integer)
So, 47 is not a factor of 47p+1 ...
The biggest challenge really would be to find which is the highest prime factor of 2^50*50! +1 ...it could be 53, 97 or watever ...(I am not aware of the technique to deduce this ) .... If somebody has a way to come to the precise value, please share your thoughts !!
Cheers !! (Varun: I am sure your doubt is cleared now)
ha haa.. laugh one laugh all.. public forum pe izzat ki dash dash ho gayi.. shucks!!
btw got it now.. thanks man.. ;)
arre koi baat nahi dost ...evrbdy has a bad day ...sabse galtiyaan hoti hain ...aur izzat ki parva kisko hai ...we are here to learn from each other, even at the expense of committing few errors
arre koi baat nahi dost ...evrbdy has a bad day ...sabse galtiyaan hoti hain ...aur izzat ki parva kisko hai ...we are here to learn from each other, even at the expense of committing few errors
Theek Bola. btw bhavin , I have seen u more active on maths sections?any reasons
Theek Bola. btw bhavin , I have seen u more active on maths sections?any reasons
ya buddy ...am a second year MBA grad of NMIMS, Mumbai . Solving maths problems is my passion. No particular intensions of writing GMAT in the near future, though i have given n no of mock tests. Hence, u would never spot me on the verbal thread
hello bhavin,,i also thought on the same terms but then...if a number n has a prime factor 'r' then n+1 may or may not have a factor greater than r...so even though 2*4*6..100 has the highest prime factor 47, then ( 2*4*6...100) +1 may or may not have the greatest prime factor > 47....ur thoughts...
hello ravish, sorry, i am not able to interpret your statement properly, are u hinting that ( 2*4*6...100) +1 could be a prime number ? well, that is a possibility, however if it has a prime factor it has to be 53 or higher ...
getting back to your previous thought, well, i dont think there is any particular method or formula to determine whether a no is prime or not ...though there are many approximations....
Its just that ( 2*4*6...100) +1 is a very huge number,so we bank on our normal logic and say well it should have some factors
Guys, I have a GMAT scheduled for next month and I am short of Math practice. I wanted to know the level of maths being asked here. THe problems you guys are being discussing here seem to be simple. As compared to CAT of course, though a few are tricky... Simply, how many questions out of 37 could be difficult and how many will be sitters ? any estimate ?
Guys, I have a GMAT scheduled for next month and I am short of Math practice. I wanted to know the level of maths being asked here. THe problems you guys are being discussing here seem to be simple. As compared to CAT of course, though a few are tricky... Simply, how many questions out of 37 could be difficult and how many will be sitters ? any estimate ?
Haha...evidently you are new to this forum waiwai. I suggest you to go through as many problems on this thread as possible, and time them for ~2-3 min, and I am positive, you will encounter few questions, that will prove to be nerve racking.
In your straightforward question, you have brought up a subtle but very important point...Taming the CAT is the niche that one has to gain, rather than just practicing questions, even under timed conditions. That is the basis for GMAT success and is one of the pillars on which GMAT heavily relies on.
"How many questions out of 37 ..." I guess it depends on the gmat algo...which is a highly proclaimed topic in discussions at various places for aspirants. Rather than thinking and wasting time about that...I suggest to concentrate on "Attaining your peak level of difficulty quickly in CAT...and try to hold on there as much as possible"
PS: Do Visit the Query Center as thats the appropriate place for discussions like this. You will find a lot more valuable posts there, in this regard.
Did u type this question or pasted it from some doc..??..
the reason why I ask is.. bcoz either this question is incomplete..or not very good.. If x is positive, which of the following could be the coorect ordering of 1/x, 2x, and x2?
x is paositive what?? If x is a positive real number then the results can vary from the case where x is a positive integer..
Now since integer is not mentioned.. lets assume x is a positive real number.. lets take a value.. say, x = 0.5 1/x = 2 2x = 1 x^2 = 0.25 I. x2
but if x = 1 1/x = 1 2x = 2 x^2 = 1 Qualifies for none of the 3 options
but if x = 2 1/x = 0.5 2x = 4 x^2 = 4 Qualifies for none of the 3 options
but if x = 5 1/x = 0.2 2x = 10 x^2 = 25 Qualifies for none of the 3 options
but if x = 10 1/x = 0.1 2x = 20 x^2 = 100 Qualifies for none of the 3 options
so for real postive numbers, the answer would have been I only. I would have marked option B
HOWEVER, if the positive number would have been integer, then none of the 3 eqns would have worked and the answer would have been NONE. In case of positive integer defined/marked, I would have marked option A
If x is positive, which of the following could be the coorect ordering of 1/x, 2x, and x2?
I. x2 II. x2 III. 2x a. None b. I only c. III only d. I and II only e. I, II and III only
Did u type this question or pasted it from some doc..??..
the reason why I ask is.. bcoz either this question is incomplete..or not very good.. If x is positive, which of the following could be the coorect ordering of 1/x, 2x, and x2?
x is paositive what?? If x is a positive real number then the results can vary from the case where x is a positive integer..
Now since integer is not mentioned.. lets assume x is a positive real number.. lets take a value.. say, x = 0.5 1/x = 2 2x = 1 x^2 = 0.25 I. x2
but if x = 1 1/x = 1 2x = 2 x^2 = 1 Qualifies for none of the 3 options
but if x = 2 1/x = 0.5 2x = 4 x^2 = 4 Qualifies for none of the 3 options
but if x = 5 1/x = 0.2 2x = 10 x^2 = 25 Qualifies for none of the 3 options
but if x = 10 1/x = 0.1 2x = 20 x^2 = 100 Qualifies for none of the 3 options so for real postive numbers, the answer would have been I only. I would have marked option B
HOWEVER, if the positive number would have been integer, then none of the 3 eqns would have worked and the answer would have been NONE. In case of positive integer defined/marked, I would have marked option A
Hey varun ...Statement in red is incorrect ...For all postive real nos I does not hold true ...you have only tried 0.5, try 1.5 ...it wud change ...
Ans is A..none of the options ..
And on a GMAT , unless otherwise mentioned you cannot assume variables to be integers ...it has to be real nos only...
