Abcd are four whole numbers such that a>b>c>d>0.the average of a &d is 7 and average of b & c is 4.5.how many such combinations are possible.

• a+d=14,b+c=9
  (a,d)=(13,1),(12,2),(11,3),(10,4),(9,5),(8,6)
  (b,c)=(8,1),(7,2),(6,3),(5,4)
  a>b>c>d>0
  13>7>2>1
  13>6>3>1
  13>5>4>1
  12>6>3>2
  12>5>4>2
  11>5>4>3
  so only 6 combinations.
• 11 years agoHelpfull: Yes(56) No(0)
• b+c=9;
  a+d=14;
  
  1. 13>7>2>1
  2. 13>6>3>1
  3. 13>5>4>1
  4. 12>6>3>2
  5. 12>5>4>2
  6. 11>5>4>3
• 11 years agoHelpfull: Yes(15) No(2)
• 6 such combinations are possible.
  since average of a and d is 7 so, a+d=14
  average of b and c is 4.5 so, b+c=9;
  possible values for b and c are 5,4; 6,3; 7;2
  8,1 is not possible coz d cannot be equal to 0
  taking values of a and d, where d=1, a=13 it is possible for all 3 cases before.
  for d=2, a=12 it is not possible for last case where b=7, c=2 coz c!=d.
  So it is possible for only 2 case
  Similarly for d=3, a=11, it is only possible for case 1, where b=5, c=4.
  So total of 3+2+1= 6 cases are possible.
• 11 years agoHelpfull: Yes(7) No(0)
• correct answer is 4
  a+d/2 = 7
  a+d=14
  similarly
  b+c=9
  now apply we see that a is greatest and d is smallest and their sum is 14
  so take a=13 and d=1
  13+1=14 similarly take b=5 and c=4 5+4=9 this satisfies a>b>c>d>0
  now
  a=12 and d=12
  12+2=14 similarly take b=6 and c=3 6+3=9 this satisfies a>b>c>d>0
  and no other solution is possible so ans is 4.
  
• 11 years agoHelpfull: Yes(2) No(6)
• 4 wasnt der in the options.. 3 6 8 n sumthing was the option...
• 11 years agoHelpfull: Yes(2) No(1)
• 3 is the correct answer
• 11 years agoHelpfull: Yes(1) No(2)
• correct answer is 4
  a+d/2 = 7
  a+d=14
  similarly
  b+c=9
  now apply we see that a is greatest and d is smallest and their sum is 14
  so take a=13 and d=1
  13+1=14 similarly take b=5 and c=4 5+4=9 this satisfies a>b>c>d>0
  now
  a=12 and d=2
  12+2=14 similarly take b=6 and c=3 6+3=9 this satisfies a>b>c>d>0
  and no other solution is possible so ans is 4.
• 11 years agoHelpfull: Yes(1) No(3)
• Though answer 4 is correct but explaination is not adequate.
  Try to understand the question.
  a,b,c,d are whole numbers greater than 0 where a>b>c>d>0.
  Given, (a+d)/2=7
  and (b+c)/2=4.5
  With condition a>d and average = 7, the possibilities are..
  a d avg
  9 5 (9+5)/2=7
  8 6 (8+6)/2=7
  With condition b>c and average = 4.5, the possibilities are..
  b c avg
  8 1 (6+3)/2=4.5
  7 2 (7+2)/2=4.5
  6 3 (6+3)/2=4.5
  5 4 (5+4)/2=4.5
  Now...
  keeping in mind a>b>c>d>0 , the possibilities of 4 digit number abcd are..
  9851
  9752
  9653
  8564
  Therefore, only 4 possibilities.
  
• 11 years agoHelpfull: Yes(1) No(3)
• go by options ..
  since a+d=7*2(14) and b+c=(9)..
  
• 11 years agoHelpfull: Yes(0) No(1)
• wht is the procedure to solve this..
  
• 11 years agoHelpfull: Yes(0) No(1)
• 13>6>3>1
  12>5>4>2
  11>5>4>3 a>b>c>d>0 only these three posbl soln
• 11 years agoHelpfull: Yes(0) No(2)
• There can be five solutions
  13>6>3>1
  13>5>4>1
  12>6>3>2
  12>5>4>2
  11>5>4>3
• 11 years agoHelpfull: Yes(0) No(0)