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14 Jun 2023, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
62% (02:17) correct
38%
(02:29)
wrong
based on 227
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When x is rounded to the nearest tenth the result is 1.5, and when y is rounded to the nearest tenth the result is 7.5. If z = y − x, which of the following inequalities gives all of the possible values of z?
A. 5 < z < 7
B. 5.5 < z < 6.5
C. 5.9 < z < 6.0
D. 5.9 < z < 6.1
E. 5.95 < z < 6.05
A. 5 < z < 7
B. 5.5 < z < 6.5
C. 5.9 < z < 6.0
D. 5.9 < z < 6.1
E. 5.95 < z < 6.05
14 Jun 2023, 10:16
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Bunuel
According to the conventional rule of rounding, x and y must be in the following intervals:
1.45 ≤ x < 1.55
7.45 ≤ y < 7.55
If we multiply the first inequality by -1, we get:
-1.45 ≥ -x > -1.55, or -1.55 < -x ≤ -1.45
Since the directions of the inequality signs now face the same directions, we can add the inequality for y and the transformed inequality for x:
7.45 ≤ y < 7.55
-1.55 < -x ≤ -1.45
To get:
5.9 < y- x < 6.1, or 5.9 < z < 6.1
Answer: D
(Note: adding ≤ and < always results in <.)
15 Jun 2023, 16:44
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I think the wording of this question needs to be edited. Would request the experts to confirm. Bunuel yashikaaggarwal
The question states that "which of the following inequalities gives all of the possible values of z".
We get the range to be 5.9<z<6.1.
Based on this range even option A and option B give all the possible values of z. The question needs to be reframed to prevent this ambiguity.
The question states that "which of the following inequalities gives all of the possible values of z".
We get the range to be 5.9<z<6.1.
Based on this range even option A and option B give all the possible values of z. The question needs to be reframed to prevent this ambiguity.
