Let the two machine rates are x and y and let it takes machine y T days to produce W.
framing equations-
Ty=(T+2)x=W=>w=2xy/(x-y)------1
from second condition-3(x+y)=5/4W......2
solving the above two equations-we get
6x^2-5xy-6y^2=0,solving will give 2x=3y
substitute the value of y in eq-2,
x=w/4
hence if it takes t days to make 2w,tx=2w=t*w/4=2w=>t=8 days
A certain characteristic in a large population has a distribution that is symmetric about the mean
m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent of the distribution is less than m + d ?
A. 16%
B. 32%
C. 48%
D. 84%
E. 92%
For SD, on GMAT we can assume the 34-14-2 probability distribution percentages
So, straigtaway we can say 84 % data is less than m+d
Else, lets takeit this way :
symmetric implies 50 % is above mean and other 50 % is below mean and 68 % within one deviation mean half of the values are above and below mean i.e 34% on each side
So, 50 % below mean and 34 % between mean and m+d, hence 84% below m+d ..Ans D
For SD, on GMAT we can assume the 34-14-2 probability distribution percentages
So, straigtaway we can say 84 % data is less than m+d
Else, lets takeit this way :
symmetric implies 50 % is above mean and other 50 % is below mean and 68 % within one deviation mean half of the values are above and below mean i.e 34% on each side
So, 50 % below mean and 34 % between mean and m+d, hence 84% below m+d ..Ans D
one doubt-34-14-2 means the %ages after mean,
so it should not be-2*(34+14)=96% and since 92 is less then that, opt for 92.
I am still trying to get hand on the sigma and found urs previous post useful.
Q- K is a three digit number such that the ratio of the number to the sum of its digits is least.
i) What is the difference between the hundreds and the tens digit of K?
ii) What can be said about the difference between the tens and the units digit?
iii) For how many values of K will the ratio be highest?
Q- K is a three digit number such that the ratio of the number to the sum of its digits is least.
i) What is the difference between the hundreds and the tens digit of K?
ii) What can be said about the difference between the tens and the units digit?
iii) For how many values of K will the ratio be highest?
Q- K is a three digit number such that the ratio of the number to the sum of its digits is least.
i) What is the difference between the hundreds and the tens digit of K?
ii) What can be said about the difference between the tens and the units digit?
iii) For how many values of K will the ratio be highest?
Interesting question. And I would say it could appear in GMAT, if you are scoring in 750 range. People appearing in GMAT recently have reported that the GMAT is throwing difficult PS/DS questions now a days.
Anybody has any collection of tough PS/DS questions to go through ? Would really appreciate.
Q- K is a three digit number such that the ratio of the number to the sum of its digits is least.
i) What is the difference between the hundreds and the tens digit of K?
ii) What can be said about the difference between the tens and the units digit?
iii) For how many values of K will the ratio be highest?
For any integer n greater than 0, n! denotes the product of all the integers from 1 to n, inclusive. How many multiples of 3 are there between 6!-6 and 6!+6, inclusive ?
A) One
B) Two
C) Three
D) Four
E) Five
For any integer n greater than 0, n! denotes the product of all the integers from 1 to n, inclusive. How many multiples of 3 are there between 6!-6 and 6!+6, inclusive ?
A) One
B) Two
C) Three
D) Four
E) Five
For any integer n greater than 0, n! denotes the product of all the integers from 1 to n, inclusive. How many multiples of 3 are there between 6!-6 and 6!+6, inclusive ?
A) One
B) Two
C) Three
D) Four
E) Five
For any integer n greater than 0, n! denotes the product of all the integers from 1 to n, inclusive. How many multiples of 3 are there between 6!-6 and 6!+6, inclusive ?
A) One
B) Two
C) Three
D) Four
E) Five
OA for "For any integer 'n' greater than 0, n! d..........." is option E)Five.
OA for the 3-digit sum is
1) 8
2) 0
3) 9
Well well ...very interesting question !!
Not really sure if it can be expected on GMAT ..
Let the digits be x,y,z resp .
Hence, no is 100x+10y+z
and sum of digits is x+y+z
ratio = (100x+10y+z)/(x+y+z)
Not really sure what is the quickest way mathematically to calculate the min ratio, but logically ratio is least for lower numerator and higher denominator ...
So ratio would be least when no is in 100's ...for 200 to 999 ratio keeps increasing coz sum of digits cannot increase prop.
SO no should be 199 ..
1) Hence, diff between hundreds and tens is 8
2) diff between tens and units is 0
3) ratio would be highest when sum of digits is least ..so let y=z=0
Then ratio becomes 100x/x= 100
And x can be any no from 1 to 9 ...
Hence for 9 nos ratio is max (100, 200 ,.......900)
Hence , Ans are :
1) 8
2) 0
3) 9
Bhavin: Just one question, when they say SUM : 1 + 9 + 9 = 10 + 9 = 19 = 1+9 = 1?
hence 199 / 1 = 199
IS this not correct, or i summed up too much?
Can someone post some int prblms?