Official Quant thread for CAT 2013

ABC is a right triangle with ∠ABC=90∘ with AB=30√3 and BC=30. D is a point on segment BCsuch that AD is the median. E is a point on segment ACsuch that BE is perpendicular to AC. AD and BEintersect at F. If EF=a√b/c, where a and c are positive, coprime integers and b is not divisible by the square of any prime, what is the value of a+b+c?
can anyone explain to me how to solve this problem?
What is the remainder when 25899 is divided by 99?
OPTIONS
1) 4
2) 25
3) 26
4) 0
5) 1

its 25^899/99

@avi11 none of these 60 yr becoz 25839 is divisible
@Tusharrr buddy it's (25^899)/99???
@avi11 ok
@avi11 said:
can anyone explain to me how to solve this problem?What is the remainder when 25899 is divided by 99?OPTIONS 1) 4 2) 25 3) 26 4) 0 5) 1
25^889 / 99
E = 60 (Euler number)

hence , it's equivalent to 25^49 % 99

Using chinese reminder theorem,

it comes out to be

9p - 2 = 11q + 4

i.e; 70..! 😐

Please correct me..!
@blowcat13 said:
in a quadrilateral ABCD, BC=10, CD=14, AD=12 and /_CBD = /_BAD =60. IF AB=a+root b. where a and b are a positive integers then a+b = Options 1) 193 2) 201 3) 204 4) 207 5) none of the above
none of these ?
@avi11 said:
can anyone explain to me how to solve this problem?What is the remainder when 25899 is divided by 99?OPTIONS 1) 4 2) 25 3) 26 4) 0 5) 1
4?
@Tusharrr said:
How many ordered triples (x,y,z) of integer solutions are there to the system of equationsx2+y2+z2=194x2z2+y2z2=194=4225? Here x2 means x sq and y2 means y sq and z2=z sq
second equation clearly likho bhai.
@Tusharrr 4
@pakkapagal said:
4?
Can you explain.??
@zuloo x^2 * z^2 + y^2 * z^2 = 4225
but already got the answer
@sbharadwaj said:
25^889 / 99 E = 60 (Euler number)hence , it's equivalent to 25^49 % 99Using chinese reminder theorem, it comes out to be 9p - 2 = 11q + 4i.e; 70..! Please correct me..!
bhai 49 nhi 59 :P
@pakkapagal said:
bhai 49 nhi 59
@avi11 said:
its 25^899/99
70 ?

25^899 mod 99
99 = 3^2*11
E(3) = 2
25^2k mod 3 = 1
25 mod 3 = 1

E(11) = 10
25^10k mod 11 = 1
25^9 mod 11 = 3^9 mod 11 = 5^3 mod 9 = 4

so 3a + 1 = 11b + 4 = 70

distance PQ should have been given..


@jaspunit ??? is pq a line or else or they are taking turns after reaching end
@Tusharrr
ABC is a right triangle with ∠ABC=90∘ with AB=30√3 and BC=30. D is a point on segment BCsuch that AD is the median. E is a point on segment ACsuch that BE is perpendicular to AC. AD and BEintersect at F. If EF=a√b/c, where a and c are positive, coprime integers and b is not divisible by the square of any prime, what is the value of a+b+c?

hey i just now solved it 55
Number of factors divisible by 12 = 4 x 4 x 3 = 48

koi batao yaar ye 48 kaise aya...help..!