first, my appologies for not putting up the choices. But i purposefully did that in order to get the explanation. anyway, regarding first, u r missing the question. It says F(n) is product of all even integers between 2 and n inclusive. so F(100) +1 = (2x4x6x8x10.....96x98x100)! + 1 = 2(50!) + 1 now p is a smallest prime factor of 2(50!) + 1. how do we find p now? 😞 too bad in number properties...
2.4.6.8....100 +1 (2^50)(50!) + 1
50! is divisble by 2,3,5,7,11,13,...47 but +1 will spoil it out..
answer shd b greater than 47 but what??
cant go beyond this 8 this moment.. will solve it later when in cool mind..
50! is divisble by 2,3,5,7,11,13,...47 but +1 will spoil it out..
answer shd b greater than 47 but what??
cant go beyond this 8 this moment.. will solve it later when in cool mind..
@dare2 chill man chill... it was a GMATprep question and u already got the answer. Answer is the choice is "greater than 40", but i still didnt get it how it is greater than 40...
@dare2 chill man chill... it was a GMATprep question and u already got the answer. Answer is the choice is "greater than 40", but i still didnt get it how it is greater than 40...
@deepakram, can u help me with this?
if 'greater than 40' is there in da options then this question becomes a very direct question..
as i explained above... (50!) will contain all prime numbers less than 50..
ie 50! will b divisible by prime numbers from 2,3,5,7 to 47. but adding 1 after the factorial will make (50! + 1) not divisible by any of the prime numbers till 47 coz in each case 1 will b da remainder..
the question is asking 4 da smallest prime number which will be a factor of 50! +1.. and as shown above all prime numbers from 2 to 47 cant divide 50!+1.. so da smallest prime number has to be greater than 47..
next prime number is 53.. n 53 may or may not divide (50! + 1)
dats y if option more than 40(even if it is more than 50) then we can directly choose that option..
if 'greater than 40' is there in da options then this question becomes a very direct question..
as i explained above... (50!) will contain all prime numbers less than 50..
ie 50! will b divisible by prime numbers from 2,3,5,7 to 47. but adding 1 after the factorial will make (50! + 1) not divisible by any of the prime numbers till 47 coz in each case 1 will b da remainder..
the question is asking 4 da smallest prime number which will be a factor of 50! +1.. and as shown above all prime numbers from 2 to 47 cant divide 50!+1.. so da smallest prime number has to be greater than 47..
next prime number is 53.. n 53 may or may not divide (50! + 1)
dats y if option more than 40(even if it is more than 50) then we can directly choose that option..
So this teaches us a general rule that n!+1 has the smallest prime number which is greater than n, right?
In the semicircle with origin (0,0) in XY plane point p(-sqrt(3), 1) and Q(s,t) connects with origin at 90 angle. What is the value of s?
Assuming the points P and Q are on semi-circle and making an angle of 90 with origin. then the lenth OP and OQ is 2(from question). OP makes an angle of 30 with origin and 60 with Y axis. OQ makes 30 with Y-axis and 60 with origin. From there, as we know the length of OQ to be 2 's' would be '1' If you draw the semi-circle with all the points, everything would be very clear.
Sorry, wrote incorrectly. It's D that has value 10.
We have x = 1/5 and y = 1/4. so 1/x = 5 and 1/y = 4 Now given A$B = A+B when A > B and B-A when A We will take both the equations seperately. 1. ( 1/X $ 1/Y) = 5$4= 5+4=9. 2. (1/y $ 1/x) = 4$5. now here A=4 and B=5 so the equations follows: 5-4 = 1. So we have the fibal equation as 9$1 which is equal to 9+1 as here A=9 and B=1, that is equal to 10.
THis is the highest value you get when you solve other equations.
Sorry, wrote incorrectly. It's D that has value 10.
We have x = 1/5 and y = 1/4. so 1/x = 5 and 1/y = 4 Now given A$B = A+B when A > B and B-A when A We will take both the equations seperately. 1. ( 1/X $ 1/Y) = 5$4= 5+4=9. 2. (1/y $ 1/x) = 4$5. now here A=4 and B=5 so the equations follows: 5-4 = 1. So we have the fibal equation as 9$1 which is equal to 9+1 as here A=9 and B=1, that is equal to 10.
THis is the highest value you get when you solve other equations.
Thanks, Anurag...
:nono::nono::nono::nono: Christ !!!! i am so careless .. i was solving this entire while taking 1/x and 1/y to be 1/5 and 1/4 , no wonder messed up such a question. .. !!!! thanks anyway dude \m/
:nono::nono::nono::nono: Christ !!!! i am so careless .. i was solving this entire while taking 1/x and 1/y to be 1/5 and 1/4 , no wonder messed up such a question. .. !!!! thanks anyway dude \m/
Yeah, i know that...this is where one commits mistake. Otherwise, this is not the type of question to lose scores...but this is what makes GMAT quant problem...
For this kind of a question there is no hard and fast rule, however after seeing the question, X and Y should be as close as it could be and must be the highest available options in this case it turns out to be 4 and 5. If there is option for 6 and 7 we have to gor for that as the difference of two adjacent no.s is always one and to maximize the given answer, there is only one difference operation be there. The answer would (5+4)+(5-4)=10 D
yes rite.. this is da beauty of maths - we can derive our own formulae..
but juz a small correction of the theorem u've define above.. the prime number(bold text) shd be 'prime factor'.. ie
Mission's Theorem : the smallest prime factor of (n! +1) should be greater than n.
Its all yours man.... anyway, can you clarify that relationship between average and standard deviation? For example, 100 numbers having average 6 and std deviation d, we have to add two number more, which numbers will make standard deviation less than d?
i believe that the farther you move from average, the higher your standard deviation. So the two numbers shoud be 6 and 6. right? but how??
Its all yours man.... anyway, can you clarify that relationship between average and standard deviation? For example, 100 numbers having average 6 and std deviation d, we have to add two number more, which numbers will make standard deviation less than d?
i believe that the farther you move from average, the higher your standard deviation. So the two numbers shoud be 6 and 6. right? but how??
look at the formula for standard deviation.. if u add two numbers which has the value same as dat of average, the numerator in the standard deviation formula wont change, but the denominator will increase by 2.. so in a fraction if the numerator remains the same but the denominator increases then the value of the fraction decreases.. so the SD has to decrease..
also take note of da square part(difference of mean n the numbers).. the square will make the numerator always postive.. even if the number is greater than the average or smaller, its square will have the same impact on the SD formula.. but if the number is equal to the mean then difference will b zero and it will have no impact on the numerator coz numerator(summation) will remain the same.. but the denominator will increase by 1(if u add 1 number in da data) n hence the SD will decrease..
look at the SD formula 2 make my explanation clearer..
The residents of Town X participated in a survey to determine the no. of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 Hrs. and a standard deviation of 6 Hrs.. The no. of hrs that pat, a resident of town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the no. of hrs that Pat watched television last week.
The residents of Town X participated in a survey to determine the no. of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 Hrs. and a standard deviation of 6 Hrs.. The no. of that pat, a resident of town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the no. of hrs that Pat watched television last week.
30,20,18,12,6
Is the answer to this question 12?
Mean is 21 and pat's no. of hours is between 1 and 2 S.D. S.D. is 6. So mathmatically the expression can be formed as: 21 - 1*6 > p > 21 - 2*6 That is between 15 and 9.
Mean is 21 and pat's no. of hours is between 1 and 2 S.D. S.D. is 6. So mathmatically the expression can be formed as: 21 - 1*6 > p > 21 - 2*6 That is between 15 and 9.
Thanks, Anurag...
Yes, the answer is 12, could you please elaborate on the explanation as I am naive in statistics.
The residents of Town X participated in a survey to determine the no. of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 Hrs. and a standard deviation of 6 Hrs.. The no. of hrs that pat, a resident of town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the no. of hrs that Pat watched television last week.
30,20,18,12,6
This has nothing much to do with statistics. Lets forget statistics. You could actually call the mean and the SD , X and Y respectively. X= 21, Y=6.
"no. of hrs that pat, a resident of town X, watched television last week was between 1 and 2 standard deviations below the mean"
Lets call Pat's hours Z. All the values are positive integers so X-2Y => X-2Y Substituting the values of X and Y => 9 Only one values above satisfies the value of Z here i.e. 12
The residents of Town X participated in a survey to determine the no. of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 Hrs. and a standard deviation of 6 Hrs.. The no. of hrs that pat, a resident of town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the no. of hrs that Pat watched television last week.
30,20,18,12,6
Mean = 21 hrs. Let no. of hours Pat watched TV be X. Acc. to condition, 21-(2XS.D) which mean, 21-(2X6) 21-12 9 Only option is 12. :)