a,b,c,d,e are distinct numbers. if (75-a)(75-b)(75-c)(75-d)(75-e)=2299 then a+b+c+d= ?

• 2299 = (-11)*11*19*(-1)*1
  75-a= -11
  75-b=11
  75-c=19
  75-d= -1
  75-e=1
  a=86,b=64,c=56,d=76,e=74
  a+b+c+d+e=356
  a+b+c+d=270 or 292 or 300 or 280 or 182
  since any one of the 5 numbers can be a,b,c,d
• 9 years agoHelpfull: Yes(19) No(3)
• 2299=11*11*19*1*1
  75-a=11; a=64
  75-b=11; b=64
  75-c=19; c=56
  75-d=1; d=74
  75-e=1; e=74
  a+b+c+d=258
  
  ans=258
• 9 years agoHelpfull: Yes(18) No(8)
• ADWAIT SATHE, brother do the LCM of that given number and u get 11 * 11 * 19 * 1. And since distinct numbers are told in qstn you can give negative sign to one of the same numbers occuring twice. Hope that answered your question.
• 9 years agoHelpfull: Yes(6) No(1)
• 2299 = (-11)*11*19*(-1)*1
  
  how did this come ? please explain . which book to refer for these kind of problems ?
  
• 9 years agoHelpfull: Yes(3) No(0)
• Ans is:280
  (75-a)(75-b)(75-c)(75-d)(75-e)=2299
  a,b,c,d, are distinct numbers
  11,-11,19,1
  64+86+56+74=280
• 9 years agoHelpfull: Yes(3) No(2)
• 2299 = 11×11×19×1×1=11×−11×19×−1×1=
  Two of the terms in the given expression should equal to 1. As all the digits are distinct, two of the terms should be negative.
  One possible solution = (75 - 64)(75 - 56)(75 - 86)(75 - 74)(75 - 76)
  Then a + b + c + d + e = 64 + 56 + 86 + 74 + 76 = 356
  But as the sum of only 4 terms was asked, we have to subtract one term.
  So given answer can be one of 292, 306, 270, 282, 280.I just copied the solution from campusgate.com..hope its useful
• 9 years agoHelpfull: Yes(2) No(1)
• how 11,-11,19,-1 and 1 are taken.anybody please reply
• 9 years agoHelpfull: Yes(1) No(0)
• 2299=11*11*19*1*1
  
• 9 years agoHelpfull: Yes(0) No(1)