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= ?
Hint:2299 is divisible by 11. Choose the correct choice from the following options
A) 292, 306, 270, 282, 289  B) 292, 306, 270, 282, 280  C) 292, 306, 270, 282, 2228  D) 292, 306, 270, 282, 212  E) 292, 306, 270, 282, 210
2299 = 11×11×19×1×1=11×−11×19×−1×1=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= 
<gadget id="calculator">64 + 56 + 86 + 74 + 76</gadget>
<output>356</output>
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   Answer:292, 306, 270, 282, 280
<result>B</result>
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= ?
Hint:2299 is divisible by 11.