@jain4444 said:How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200 ?
12 by any chance?
regards
scrabbler
regards
scrabbler
@abhishek.2011 said:let faculty be in middle_ _ _ _ f _ _ _ _now in 8 blanks we arrange them as 8!now let the 2 boys b togetherall can be arranged in 2*7!
How? It should be 2 * 6 * 6!...the two boys have 6 "adjacent" positions which are not allowed (they can sit in the 4th and 5th position you have shown as they will then be on either side of the faculty!)
@abhishek.2011 said:so 8!-2*7!
regards
scrabbler
@jain4444 said:How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200 ?
well if a and b can be only positive
12
a= 200b/b-200
now 200 is 2^3*5^2
(1,2,4,8)(5,25)
6+2+2+2=12
@jain4444 said:How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200 ?
well if a and b can be only positive
12
a= 200b/b-200
now 200 is 2^3*5^2
(1,2,4,8)(5,25)
6+2+2+2=12
i
@jain4444 said:How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200 ?
considering a and b can be positive only
a=200b/200-b
now 200 is 2^3*5^2
(1,2,4,8)(5,25)
6+(3*2)=12
@scrabbler
yes it will be 8!- 2*6*6!
my mistake it is 6*6! and that too for both boys so 2*6*6!
N is a 3-digit number that is a perfect square. When the first digit is increased by 1, the second digit is increased by 2, the third digit is increased by 3, the result is still a perfect square. Determine N.
Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
@jain4444 said:N is a 3-digit number that is a perfect square. When the first digit is increased by 1, the second digit is increased by 2, the third digit is increased by 3, the result is still a perfect square. Determine N.
361.
Basically X^2 -Y^2 = 123 = 41 x 3. So X and Y are 22 and 19
regards
scrabbler
Basically X^2 -Y^2 = 123 = 41 x 3. So X and Y are 22 and 19
regards
scrabbler
@jain4444 said:N is a 3-digit number that is a perfect square. When the first digit is increased by 1, the second digit is increased by 2, the third digit is increased by 3, the result is still a perfect square. Determine N.
361
@jain4444 said:Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
16? Trial and error...
regards
scrabbler
regards
scrabbler
@mohitjain said:ABCD is a parallelogram. A point E is selected on AD such that BE = 2 หลก6 units. Also 2AE = 2AB = BD = 8 units and 5CF = BC where F is a point on BC. Find the ratio of the area of quadrilateral DEFC to the area of parallelogram ABCD.
concepts applied
1. cos formula (b^2 + c^2 - a^2 = 2b*c*cosA
2. Area of the triangles within same parallels are in the ratio of their bases
Apply cos formula
In triangle BAE: cosA = (4^2 + 4^2 - (2rt6)^2))/2*4*4 = 1/4
now use the value of cosA derived above to find the length of AD.
In triangle BAD: cosA = (4^2 + AD^2 - 8^2))/2*AD*4
=>AD = 8
Hence, AE=ED = 4.
Apply area for triangles in same parallels logic
given BF = 4CF
put area(CDF) = A => area(BEF)=4A
area(CDF)+area(BEF) = 0.5*area(parallelogram)
=>area(parallelogram) = 10A
Now easy to see that area(ABE) = area(EDF) = (10A)/4
hence area(DEFC)/area(Parallelogram) = 7/20
ATDH.
@jain4444 said:Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
x=.2 , y=2
x+y=2.2
a/b=11/5
16?
@scrabbler said:361.Basically X^2 -Y^2 = 123 = 41 x 3. So X and Y are 22 and 19regardsscrabbler
hey is it a direct formulae..........
@jain4444 said:N is a 3-digit number that is a perfect square. When the first digit is increased by 1, the second digit is increased by 2, the third digit is increased by 3, the result is still a perfect square. Determine N.
devil_style_007
a b c be 3 digit perfect square number=x^2-------->eq1
a+1 b+2 c+3 digit is also perfect square=y^2-------->eq2
substracting eq1 from eq2
y^2 -x^2 = 123 = 41 x 3.
So X and Y are 22 and 19
a b c be 3 digit perfect square number=x^2-------->eq1
a+1 b+2 c+3 digit is also perfect square=y^2-------->eq2
substracting eq1 from eq2
y^2 -x^2 = 123 = 41 x 3.
So X and Y are 22 and 19
@iLoveTorres said:bhai yeh kaise kiya.. pls explain..
hit and trial
s(2)/s(5*2) = s(2)/s(10) = 2
s(1)/s(5*1) = 1/5 = .2
@devil_style_007 said:hey is it a direct formulae..........
X^2 - Y^2 = 41 * 3 = (X+Y)(X-Y) so X = (41+3)/2 while Y = (41-3)/2.
regards
scrabbler
regards
scrabbler
@IIMAIM said:devil_style_007a b c be 3 digit perfect square number=x^2-------->eq1a+1 b+2 c+3 digit is also perfect square=y^2-------->eq2substracting eq1 from eq2y^2 -x^2 = 123 = 41 x 3. So X and Y are 22 and 19
yeah dats wat i was asking to take 2 no.in terms of a,b,c
@jain4444 said:Let S(n) denote the sum of digits of the integer n. Over all positive integers, the minimum and maximum values of S(n)/S(5n) are X and Y, respectively. The value of X+Y can be written as a/b, where a and b are coprime positive integers. What is the value of a+b?
minimum is when s(5n)=5*s(n)
so minimum is 1/5 = 0.2
maximum is when the number that occurs after 5n gives a digit sum of 1 so any such number like 2 ,10 will do
maximum value = 2
x+y=2+.2=2.2
x+y=11/5 = 16