[MaskedMenace]

Originally Posted by michaeldouglas

1) how many right-angled triangles have one of their sides (not the hypotenuse) equal to 60 cm?

11 ??

2)the sum of a certain number of positive integers is 31. What is the largest value of their product?

3^9 * 2^2 = 78732

[seba_catrpillar]

puys check this out

Q...For how many pairs of (X,Y) is square root (X) + square root (Y) = square root (1332)?
options: a. 5
b. 7
c. 9
d. 3

[kawan84]

puys, plz help me solving 3-4 ques based on number sys....
1) find remainder when 53^1111 is divided by 51?
2) find last 3 digits 10!+11!+12!...50! ?
3) find unit's digit of 7^23^12^9 ?

[jigar_p_civil]

Originally Posted by kawan84

puys, plz help me solving 3-4 ques based on number sys....
1) find remainder when 53^1111 is divided by 51?
2) find last 3 digits 10!+11!+12!...50! ?
3) find unit's digit of 7^23^12^9 ?

53^1111

53 & 51 prime to each other so

53^50K gives reminder=1

1111=50*k+11

so now need to find 53^11/51

so 2^11/51

2^11=1024*2=2048

2048/51=8

so ans is 8


2) find last 3 digits 10!+11!+12!...50! ?


here u know that 10!=3628800

11!=800*11=*800
12!=*800*12=*600
13!=*600*13=*800
14!=*800*14=*200

now from 15! add one more zero means all last 3 digit are zero

so last 3 digit of 10!+11!+12!...50!=800+800+600+800+200=3200

means last 3 digit=200

[seba_catrpillar]

one more ques from total gadha.....

the product P of 3 posetive integers is 9 times their sum and one of the integers is the sum of the other two. The sum of all posible values of P is
1. 1404
2. 702
3. 540
4. 336...

Cud not solve it
My approach was

let one num be X and the second be Y
so the third X + Y
now 9(X + Y + X + Y) = XY(X + Y)

Now on the left 18(X + Y)
......the ans shud be multiple of 18.......eliminates option 4
Then....??????

[seba_catrpillar]

Puys....is there anyway we can get the solution for ques @ totalgadha

[shashank3012]

Originally Posted by michaeldouglas

1) How many right-angled triangles have one of their sides (not the hypotenuse) equal to 60 cm?

2)The sum of a certain number of positive integers is 31. What is the largest value of their product?

3)How many integers can be expressed as a sum of three distinct numbers chosen from the set {4, 7, 10, 13..., 46}?

4) Blue + Blue = Red, Red + Blue = Blue, Then Red × Blue = ?

1)60^2+a^2=b^2
3600=(a+b)(a-b)
3600 is 2^4*3^2*5^2 so,45 factors, one of which is 60.so,remaining 44 factors are possible.
so,22 triangles possible???
approach might be right,but answer

for 2nd one,tallying options would be good,btw,is there any approach for such problems.menace bhai's answer looks good.

3)minimum sum is 4+7+10=21 to maximum=>129 with difference of 3.
so,129=21+(n-1)3
n=37 terms.

4)should not be as easy as it seems...but still,0 it seems????
what does the answer say??

[shashank3012]

Originally Posted by seba_catrpillar

one more ques from total gadha.....

the product P of 3 posetive integers is 9 times their sum and one of the integers is the sum of the other two. The sum of all posible values of P is
1. 1404
2. 702
3. 540
4. 336...

Cud not solve it
My approach was

let one num be X and the second be Y
so the third X + Y
now 9(X + Y + X + Y) = XY(X + Y)

Now on the left 18(X + Y)
......the ans shud be multiple of 18.......eliminates option 4
Then....??????

let they be a,b,c

a+b=c

abc=9(a+b+c)

ab(a+b)=18a+18b

ab=18.

(a,b,c)=(1,18,19)(2,9,11)(3,6,9)

342+198+162

702.

option (B)

[MaskedMenace]

Originally Posted by seba_catrpillar

puys check this out

Q...For how many pairs of (X,Y) is square root (X) + square root (Y) = square root (1332)?
options: a. 5
b. 7
c. 9
d. 3

sqrt(x) + sqrt(y) = sqrt(1332)

x = y = 333 is one pair

Now,

sqrt(1332) = sqrt(36*37) = 6*sqrt(37)

5*sqrt(37) + sqrt(37) => 2nd pair

4*sqrt(37) + 2*sqrt(37) => 3rd pair

two more pairs as (x,0) (0,y)

Total seven pairs .. !!!

[shashank3012]

Originally Posted by kawan84

puys, plz help me solving 3-4 ques based on number sys....

3) find unit's digit of 7^23^12^9 ?

first consider 23^12^9 mod 4

(-1)^12^9 mod 4

so,remainder is 1.

digit is 7^1 is 7.