If $a$, $b$, $c$, and $d$ are replaced by four distinct digits from $1$ to $9$, inclusive, then what's the largest possible value of the difference $a. b - c. d$ ?

Step-by-step explanation:

Correct answer

Given that a, b, c, and d are different numbers (from 1 to 9), we are to find the largest possible value of a.b + c.d.

This problem can be answered by trial and error and with some logic. Clearly, a to d cannot be at the lower end of the values (1 to 5). Since the digits must be different, it can be a combination of digits from 6 to 9.

It is rather tempting to say that the 9.8 + 7.6 would yield the highest possible sum (=17.4) but this is incorrect. Since it is the sum of two numbers with a decimal, we have to maximize on the one-digit first before maximizing the tenths digit. Therefore: the combination of numbers must then be:

9.7 + 8.6 which results to 18.3

9.6 + 8.7 yields 18.3 as well.

Dollar replacement

For the value of the 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 the 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

Hence, the difference = 72-2 = 70

Thus,  the largest possible value of the difference $a.b - c.d$ = 70

both the histogram and the stem and leaf plot will visually show how many shoppers were of various ages within each range of data.   the histogram does not give us the specific ages of these shoppers unlike the stem and leaf plot.a histogram does not give us a true range of the data because we do not know exactly how old the shoppers were. a stem and leaf plot will give exact ages, so we can determine the exact range along with all measures of center and the others measures of center.   with the histogram, we cannot find any of these.

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