The average of 13 numbers is 60. Average of the first 7 of them is 55 and that of the last 7 is 61. Find the 8th number?
Options:
(A) 32
(B) 83
(C) 45
(D) 53
(E) 64
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Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 55 = 385
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 385 - 780 = 32. So the answer is: (A).
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Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 88 players took part in that tournament. How many matches were played?
Options:
(A) 90 matches
(B) 95 matches
(C) 99 matches
(D) 85 matches
(E) 87 matches
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E 87 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 87 matches were played. So the answer is: (E).
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For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 99 Θ (33 Θ 17)) ?
Options:
(A) 10
(B) 8
(C) 6
(D) 4
(E) 2
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Show your work and conclude with the exact phrasing "Therefore, the final answer is [answer]." where [answer] is just the final number or expression that solves the problem.
user
(( 90 Θ 33 ) Θ 17 )
The remainder of 90 divided by 33 is 24;
The remainder of 24 divided by 17 is 7;
( 99 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
7 - 3 = 4. So the answer is: (D).
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