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26 Nov 2023, 03:09
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Question Stats:
58% (02:14) correct
42%
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If P is the sum of positive odd numbers which are less than 84 and Q is the sum of the positive even integers that are less than 84, what is the value of Q – P ?
A. - 42
B. - 40
C. 40
D. 41
E. 42
A. - 42
B. - 40
C. 40
D. 41
E. 42
26 Nov 2023, 04:48
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ruis
If P is the sum of positive odd numbers which are less than 84 and Q is the sum of the positive even integers that are less than 84, what is the value of Q – P ?
A. - 42
B. - 40
C. 40
D. 41
E. 42
A. - 42
B. - 40
C. 40
D. 41
E. 42
The sum of first n even numbers = Q = \(n(n+1)\)
Number of terms, n = \(\frac{82-2}{2} + 1 = 41\)
Hence, the sum of the first 41 even numbers= \(41 * 42\)
The sum of the first n odd numbers = R = \(n^2\)
Number of terms, n = \(\frac{83-1}{2} + 1 = 42\)
Hence, the sum of the first 42 odd numbers= \(42 * 42\)
Q - P = 42*41 - 42*42 = 42(41-42) = -42
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26 Nov 2023, 05:48
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Asked: If P is the sum of positive odd numbers which are less than 84 and Q is the sum of the positive even integers that are less than 84, what is the value of Q – P ?
P = 1 + 3 + 5 + .... + 83 = (1+83)/2 *{ (83-1)/2 + 1} = 42*42
Q = 2 + 4 + 6 + .... + 82 = (2+82)/2 * { (82-2)/2 + 1} = 42*41
Q - P = 42*41 - 42*42 = -42
IMO A
P = 1 + 3 + 5 + .... + 83 = (1+83)/2 *{ (83-1)/2 + 1} = 42*42
Q = 2 + 4 + 6 + .... + 82 = (2+82)/2 * { (82-2)/2 + 1} = 42*41
Q - P = 42*41 - 42*42 = -42
IMO A
