If $a$, $b$, $c$, and $d$ are replaced by four distinct digits from $1$ to $9$, inclusive, then what's the largest possible valu

Question

2 years ago

10

e of the difference $a.b - c.d$ ?

1 answer:

Alexxx [7] · Answer 1 · 2023-12-27T18:23:56+03:00

Answer:

70

Step-by-step explanation:

for the value of difference to be largest, the minuend should be maximum(most possibly) and the subtrahend should be minimum

[in A-B=X, A is minuend and B is subtrahend ]

so, $a.b should be maximum. as there is a condition that 4 digits should be distinct, the product will be maximum if we choose 2 maximum valued numbers from the given numbers. so, one of them should be 9 and the other should be 8.

therefore, $a.b=9*8=72

as mentioned above, c.d$ should be minimum. this will be possible only when we choose 2 minimum valued numbers from the given numbers. so, one of them should be 1 and the other should be 2.

therefore, c.d$ = 1*2 = 2