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03 May 2023, 11:14
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D
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Difficulty:
65%
(hard)
Question Stats:
65% (03:08) correct
35%
(03:04)
wrong
based on 165
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A set S contains 6 distinct positive integers. Three of the numbers in the set are consecutive odd integers and the remaining three numbers are even numbers. If the smallest even number is 4 less than the largest even number and the sum of the 6 integers is 507, then what is the sum of the largest odd integer and the 2nd largest even integer?
(A) 164
(B) 167
(C) 169
(D) 171
(E) 173
(A) 164
(B) 167
(C) 169
(D) 171
(E) 173
03 May 2023, 11:34
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ChandlerBong
There is a lot going on in this question, hence, let's break down the information into chunks and process the same.
Quote:
Assume that the three odd integers are : 'y-2', 'y', and 'y+2'
Quote:
Assume that the three even integers are : '2p', '2q', and '2r', such at 2p < 2q < 2r
As this stage, we don't know the exact relationship between these three integers.
Quote:
Inference:
- 2r - 2p = 4, therefore 2r lies 4 units to the right of 2p on a number line.
- As all the numbers in the set are distinct, therefore 2q must lie two units right from 2p on the number line. Hence, we can conclude that 2p, 2q, and 2r are consecutive even numbers.
2p = 2q - 2
2r = 2q + 2
Quote:
y - 2 + y + y + 2 + 2q - 2 + 2q + 2q + 2 = 507
y + 2q = 169
Question: what is the sum of the largest odd integer and the 2nd largest even integer
- largest odd integer = y + 2
- 2nd largest even integer = 2q
Question (Simplified) = 2q + y + 2 = ?
We know 2q + y = 169, therefore 2q + y + 2 = 169 + 2 = 171
Option D
20 Dec 2023, 23:17
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ChandlerBong
Assume , Smallest even number is X, then as per question, the largest even number is X+4 and since 3 Odd numbers has consecutive. we can form a list of consecutive integers as { X, X+1, X+2, X+3, X+4, X+5 }.
Thus sum of the list = 6x+15=507 -> X=82.
Now the list becomes (82,83,84,85,86,87). Sum of Largest odd and 2nd largest even number equals 84+87=171.
Option D is correct.
