ab - cd will be a maximum if ab is as large as possible and cd is as small as possible
I will let d = 1
also we are told that c = a -5, so it is close to a
for a maximum of ab, a = b, but our numbers are to be different, and remember that c is only 5 less than a.
So we know that a,b, and c must be close to each other, and their sum = 99
- so each one is around 33
let's make a chart
A - B - C - D -- AB-CD
35 34 30 1 ---- 1160
34 36 29 1 ---- 1195
33 38 28 1 ---- 1226
..
30 44 25 1 ---- 1296
29 46 24 1 ---- 1310
28 48 26 1 ----- 1318
27 50 22 1 ----- 1328
26 52 21 1 ----- 1331 <------ the highest
25 54 20 1 ----- 1330
24 56 19 1 ----- 1325 - lower than before
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
1 answer