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02 May 2025, 02:31
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:24) correct
31%
(01:15)
wrong
based on 88
sessions
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Not Attempted Yet
In an archery contest, each arrow fired by a contestant earns exactly 0, 3, or 6 points: 3 points if it hits the outer ring, 6 points if it hits the bullseye, and 0 points if it misses the target completely. Alexandra scored a total of T points in the contest. Is T an even number?
(1) Exactly five of Alexandra’s arrows hit the bullseye.
(2) Exactly three of Alexandra’s arrows hit the outer ring.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
(1) Exactly five of Alexandra’s arrows hit the bullseye.
(2) Exactly three of Alexandra’s arrows hit the outer ring.
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
11 May 2025, 05:30
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Official Solution:
In an archery contest, each arrow fired by a contestant earns exactly 0, 3, or 6 points: 3 points if it hits the outer ring, 6 points if it hits the bullseye, and 0 points if it misses the target completely. Alexandra scored a total of T points in the contest. Is T an even number?
Assuming Alexandra hit the outer ring with \(m\) arrows and the bullseye with \(n\) arrows, her total score is \(T = 3m + 6n\). Since \(6n\) is always even, whether \(T\) is even or odd depends only on \(3m\). If \(m\) is even, then \(T\) is even; if \(m\) is odd, then \(T\) is odd.
(1) Exactly five of Alexandra’s arrows hit the bullseye.
This gives \(n = 5\). As established, the value of \(n\) has no effect on whether \(T\) is even or odd. Not sufficient.
(2) Exactly three of Alexandra’s arrows hit the outer ring.
This gives \(m = 3\). Since \(m\) is odd, \(T\) is odd. Thus, the answer to the question is NO. Sufficient.
Answer: B
In an archery contest, each arrow fired by a contestant earns exactly 0, 3, or 6 points: 3 points if it hits the outer ring, 6 points if it hits the bullseye, and 0 points if it misses the target completely. Alexandra scored a total of T points in the contest. Is T an even number?
Assuming Alexandra hit the outer ring with \(m\) arrows and the bullseye with \(n\) arrows, her total score is \(T = 3m + 6n\). Since \(6n\) is always even, whether \(T\) is even or odd depends only on \(3m\). If \(m\) is even, then \(T\) is even; if \(m\) is odd, then \(T\) is odd.
(1) Exactly five of Alexandra’s arrows hit the bullseye.
This gives \(n = 5\). As established, the value of \(n\) has no effect on whether \(T\) is even or odd. Not sufficient.
(2) Exactly three of Alexandra’s arrows hit the outer ring.
This gives \(m = 3\). Since \(m\) is odd, \(T\) is odd. Thus, the answer to the question is NO. Sufficient.
Answer: B
General Discussion
Bunuel
In an archery context. every arrow fired by the contestant earns EXACTLY 0,3,6 points.
Outer ring = 3 points.
Bulls eye = 6 points.
Miss. = 0 points.
Alexandra scored a total of T points. Is T even ?
Statement 1:
(1) Exactly five of Alexandra’s arrows hit the bullseye.
5 arrows hit bulls eye. So the score is 5*6 = 30.
Since, we don’t know how many arrows hit outer ring. Insufficient
Statement 2:
(2) Exactly three of Alexandra’s arrows hit the outer ring.
Exactly 3 strikes the outer ring = 3*3 = 9.
This is an odd number.
We know the points of bulls eye is an even number (6). Irrespective of the shots taken, the outcome is always even.
With misses providing 0 points.
Total score = odd + even + 0 = odd number only.
Hence, Sufficient.
Option B
* Edited after correcting my previous error *
