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p, q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr is
  • a)
    ≥ 60 and < 70
  • b)
    ≥ 50 and < 60
  • c)
    ≥ 40 and < 50
  • d)
    ≥ 70 and < 80
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
p, q and r are three non-negative integers such that p + q + r = 10. T...
The product of 2 numbers A and B is maximum when A = B.
If we cannot equate the numbers, then we have to try to minimize the difference between the numbers as much as possible.
pq will be maximum when p=q.
qr will be maximum when q=r.
qr will be maximum when r=p.
Therefore, p, q, and r should be as close to each other as possible.
We know that p,q,and r are integers and p + q + r = 10.
=> p,q, and r should be 3, 3, and 4 in any order.
Substituting the values in the expression, we get,
pq + qr + pr + pqr = 3*3 + 3*4 + 3*4 + 3*3*4
= 9 + 12 + 12 + 36
= 69
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Most Upvoted Answer
p, q and r are three non-negative integers such that p + q + r = 10. T...
To find the maximum value of pq + qr + pr + pqr, we need to maximize each individual term.

Since p, q, and r are non-negative integers, the maximum value for each term occurs when one of the variables is equal to 10 and the others are equal to 0.

Case 1: p = 10, q = 0, r = 0
In this case, pq + qr + pr + pqr = 10*0 + 0*0 + 10*0 + 10*0*0 = 0

Case 2: p = 0, q = 10, r = 0
In this case, pq + qr + pr + pqr = 0*10 + 10*0 + 0*0 + 0*10*0 = 0

Case 3: p = 0, q = 0, r = 10
In this case, pq + qr + pr + pqr = 0*0 + 0*10 + 0*10 + 0*0*10 = 0

Therefore, the maximum value of pq + qr + pr + pqr is 0.
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p, q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr isa)≥ 60 and < 70b)≥ 50 and < 60c)≥ 40 and < 50d)≥ 70 and < 80Correct answer is option 'A'. Can you explain this answer?
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