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Let X represent a segment on a number line such that 1 < x < 5. Let Y
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12 Jan 2023, 07:53
12 Jan 2023, 07:53
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Question Stats:
55% (01:14) correct
44% (01:08) wrong based on 9 sessions
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Let X represent a segment on a number line such that −1 < x < 5. Let Y represent a segment on a number line such that 6 ≤ y ≤ 10. If X were shifted by 5 in the positive direction and Y were shifted by 2 in the positive direction, how many common integers would the new X and the new Y share?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
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Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: Let X represent a segment on a number line such that 1 < x < 5. Let Y
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21 Jan 2023, 10:50
21 Jan 2023, 10:50
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Re: Let X represent a segment on a number line such that 1 < x < 5. Let Y
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05 Feb 2023, 10:26
05 Feb 2023, 10:26
1
Expert Reply
OE
X originally contains the integers 0, 1, 2, 3, and 4. (Note that you do not include the endpoints −1 and 5, because x must be strictly larger than −1 and strictly less than 5.) Y originally contains the integers 6, 7, 8, 9, and 10
When X is shifted by 5 in the positive direction, it now contains the integers 5, 6, 7, 8, and 9. (Note again that you do include the endpoints 4 and 10.) When Y is shifted by 2 in the positive direction, it now contains the integers 8, 9, 10, 11, and 12
Only the integers 8 and 9 are found in both the new X and the new Y. The answer is 2, which is choice (B).
X originally contains the integers 0, 1, 2, 3, and 4. (Note that you do not include the endpoints −1 and 5, because x must be strictly larger than −1 and strictly less than 5.) Y originally contains the integers 6, 7, 8, 9, and 10
When X is shifted by 5 in the positive direction, it now contains the integers 5, 6, 7, 8, and 9. (Note again that you do include the endpoints 4 and 10.) When Y is shifted by 2 in the positive direction, it now contains the integers 8, 9, 10, 11, and 12
Only the integers 8 and 9 are found in both the new X and the new Y. The answer is 2, which is choice (B).
