Let a, b, c, d and e be distinct integers in ascending order such that(76-a)(76-b)(76-c)(76-d)(76-e) = 1127. What is a + b + c + d

• Product of 5 terms equal to 1127. As all the five terms are integers, given product should be a product of 5 numbers. Now factorize 1127.
  1127 = 72 × 23 = 7 × 7 × 23
  But given that all the a, b, c, d, e are distinct. And we are getting only 3 terms with 7 repeats.
  Now the logic is, integers means positive and negative, 7 and - 7 possible and 1, - 1 also possible . As a,b, c, d, e are in ascending order, the factors should be in decreasing order. So (23, 7, 1, -1, -7)
  Now a = 53; b = 69; c = 75; d = 77
  a + b + c + d = 274.
• 8 years agoHelpfull: Yes(44) No(10)
• M4maths.com you should provide correct and of each ques , because here people are answering with different different answers.
• 8 years agoHelpfull: Yes(19) No(1)
• 1127=7*7*23
  so we can say a=69
  b=69
  c=53
  d=75
  e=75
  so that the product remains equal to 1127
  so a+b+c+d = 69+69+53+75=266
• 8 years agoHelpfull: Yes(8) No(31)

•  Product of 5 terms equal to 1127. As all the five terms are integers, given product should be a product of 5 numbers. Now factorize 1127. 1127 = 72 × 23 = 7 × 7 × 23 But given that all the a, b, c, d, e are distinct. And we are getting only 3 terms with 7 repeats. Now the logic is, integers means positive and negative, 7 and - 7 possible and 1, - 1 also possible . As a,b, c, d, e are in ascending order, the factors should be in decreasing order. So (23, 7, 1, -1, -7) Now a = 53; b = 69; c = 75; d = 77 a + b + c + d = 274.

• 8 years agoHelpfull: Yes(3) No(1)
• Product of 5 terms equal to 1127. As all the five terms are integers, given product should be a product of 5 numbers. Now factorize 1127.
  1127 = 7 × 7 × 23
  given that, a,b,c,d,e are distinct integers in ascending order.
  so, (a,b,c,d,e) = (23,7,1,-1,-7)
  then a+b+c+d = 274
  
  If we don't consider the given statement, a,b,c,d,e are distinct integers in ascending order.
  then (a,b,c,d,e) = (53,69,69,75,75)
  then a+b+c+d = 266
• 8 years agoHelpfull: Yes(1) No(0)
• Factorisation of 1127 gives the possible values . Those are 1,-1,7,-7 and 23. on substitution we get a=53, b=69, c=75, d=77, e=83.
• 8 years agoHelpfull: Yes(1) No(1)
• But Ascending order means Increasing order and you all are doing in Descending order why????
• 8 years agoHelpfull: Yes(1) No(0)