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a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc – (a + b + c)]?
- a)524
- b)693
- c)970
- d)731
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 1...
|a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10
Expression: [abc - (a + b + c)]
For maximum value, two of a,b and c should be negative, as all three negative will make abc negative.
Thus, max value will occur if a= -10, b = -9, c = 8
⇒ Max value = [(-10 × 9 × 8)-(-10-9+8)]
= 720 + 11 = 731
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Community Answer
a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 1...
Explanation:
Finding the Maximum Value:
- To find the maximum possible value of the expression [abc - (a + b + c)], we need to consider the maximum and minimum values of a, b, and c.
- Since -10 ≤ a, b, c ≤ 10, the maximum possible value for each integer is 10.
Calculating the Expression:
- Let's substitute the maximum values of a, b, and c into the given expression:
[abc - (a + b + c)] = 10*10*10 - (10 + 10 + 10)
= 1000 - 30
= 970
Therefore, the maximum possible value of the expression [abc - (a + b + c)] is 970, which corresponds to option 'c'.
Finding the Maximum Value:
- To find the maximum possible value of the expression [abc - (a + b + c)], we need to consider the maximum and minimum values of a, b, and c.
- Since -10 ≤ a, b, c ≤ 10, the maximum possible value for each integer is 10.
Calculating the Expression:
- Let's substitute the maximum values of a, b, and c into the given expression:
[abc - (a + b + c)] = 10*10*10 - (10 + 10 + 10)
= 1000 - 30
= 970
Therefore, the maximum possible value of the expression [abc - (a + b + c)] is 970, which corresponds to option 'c'.
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