. Directions for Q. 1 to Q. 5: Refer the data:

J, K, L, M and N collected stamps. They collected a total of 100 stamps. None of them collected less than 10.

No two among them collected the same number.

(i) 3 collected the same number as K and M together.

(ii) L collected 3 more than the cube of an integer

(iii) The no. collected by J was the square of an integer.

(iv) Total no. collected by K was either the square or cube of an integer.

1. The no. collected by J was:

(1) 27 (2) 49 (3) 36 (4) 64

2. The no. collected by K was:

(1) 16 (2) 27 (3) 25 (4) 36

3. The difference of numbers collected by L & M was:

(1) 3 (2) 2 (3) 5 (4) 9

• 
  Given,
  
  K+M+J+L+N=100 ———(i)
  
  K,M,J,L,N>10 ———(ii)
  
  K≠M≠N≠J≠L ———(iii)
  
  K+M=J+L+N ———(iv)
  
  L=3 + X^3 , where X is an integer ———(v)
  
  J= Y^3, where Y is an integer (Modify the question here it should be like that) ———(vi)
  
  K=Z^2 or Z^3, where Z is an integer ———(vii)
  
  Now from the ques value of J can be 27 or 64
  
  but if we take 64 then eqn iv would not satisfy so J=27
  
  Again considering eqn ii, iv & ii we can say that L+N = 23 & K+M=50
  
  Now from eqn v the value of L must be 11, thus L=11
  
  That conclude N = 12
  
  Now from the questio part 3,
  
  The difference of numbers collected by L & M was:
  
  (1) 3 (2) 2 (3) 5 (4) 9
  
  Considering the fact M-L=any of those values
  
  Now M=L+any of those values
  
  M=11+any of those values
  
  Now considering each values, M= 14, value =3; K=50-14 =36 which is a square of integer, thus satisfies
  
  again M=13, value = 2; K=37 which is neither square or cube of any integer
  
  M=16, value = 5; K=34 which is neither square or cube of any integer
  
  M=20, value = 9; K=30 which is neither square or cube of any integer
  
  Thus M = 14 & K = 36.
  
• 12 years agoHelpfull: Yes(36) No(7)
• L=12, N=11, J=27, M=14, K=36
• 11 years agoHelpfull: Yes(1) No(1)