a, b, c, and d are positive consecutive odd integers and a < b < c < d.
If you take away the last number from the square of the first number, you get a number that is three more than the sum of the last three numbers. What is the product of ac?
Choose the correct choice from the following answers
A) 35  B) 77  C) 101  D) 39  E) 18
aa - d = b + c + d + 3   Simplify: aa = b + c + 2d + 3   We know that aa is the square of an odd number. Here are some possibilities: 3x3 = 9, 5x5 = 25, 7x7 = 49, 9x9 = 81, 11x11 = 121.   We want to find a sequence where the following odd numbers are very close to the square.   The sequence 11, 13, 15, 17 won't work because 121 is much bigger than 45 (the sum of the other three).   The sequence 3, 5, 7, 9 won't work because 9 is much smaller than 21 (the sum of the other three).   The sequence 7, 9, 11, 13 puts us on the right track: 49 is not that much bigger than 33 (the sum of the other three). So let's try the rest of the equation:   49 = 9 + 11 + 13x2 + 3   Simplify: 49 = 20 + 26 + 3   Add: 49 = 46 + 3   Add: 49 = 49   Done! The sequence is 7, 9, 11, 13. The question asked for the product of ac, or 7x11 = 77 (option 77).
<result>B</result>
a, b, c, and d are positive consecutive odd integers and a < b < c < d.
If you take away the last number from the square of the first number, you get a number that is three more than the sum of the last three numbers. What is the product of ac?