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5: Cannot be x
7: Could be x
9: Cannot be x
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
24% (03:03) correct
76%
(03:12)
wrong
based on 88
sessions
History
Date
Time
Result
Not Attempted Yet
A customer-support center tracked the number of service requests resolved by each of five teams during three consecutive weeks. The actual number resolved by each team was a whole number, but the values shown in the table have been rounded to the nearest multiple of 5.
For each pair of consecutive weeks, a plus sign (+) indicates that the actual number of requests resolved increased by more than x, a minus sign (−) indicates that it decreased by more than x, and a dot (·) indicates that the absolute change was at most x. These classifications are based on the actual numbers before rounding. The value of x is a positive integer.
For each of the following values, select Could be x if that exact value of x is consistent with the information provided. Otherwise, select Cannot be x.
For each pair of consecutive weeks, a plus sign (+) indicates that the actual number of requests resolved increased by more than x, a minus sign (−) indicates that it decreased by more than x, and a dot (·) indicates that the absolute change was at most x. These classifications are based on the actual numbers before rounding. The value of x is a positive integer.
| Team | Week 1 | Week 2 | Week 3 | Week 1 to Week 2 | Week 2 to Week 3 |
|---|---|---|---|---|---|
| A | 40 | 50 | 45 | · | · |
| B | 60 | 65 | 55 | + | − |
| C | 75 | 70 | 75 | · | · |
| D | 50 | 40 | 45 | − | · |
| E | 85 | 90 | 95 | · | + |
For each of the following values, select Could be x if that exact value of x is consistent with the information provided. Otherwise, select Cannot be x.
| Could be x | Cannot be x | |
| 5 | ||
| 7 | ||
| 9 |
ShowHide Answer
Official Answer
5: Cannot be x
7: Could be x
9: Cannot be x
06 Sep 2026, 01:00
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Bunuel
Official Solution:
The value of x determines when the difference between the actual numbers for two consecutive weeks is large enough to be marked + or −.
A + means that the actual number in the second week is more than x greater than the actual number in the first week. For example, if x = 7 and the actual numbers were 77 in Week 1 and 85 in Week 2, the difference would be 8, so the table would show +.
A − means that the actual number in the second week is more than x less than the actual number in the first week. For example, if x = 7 and the actual numbers were 85 in Week 1 and 77 in Week 2, the difference would be 8, so the table would show −.
A · means that the two actual numbers differ by no more than x. For example, if x = 7 and the actual numbers were 77 in Week 1 and 84 in Week 2, they would differ by 7, so the table would show ·.
The numbers shown in the table are rounded to the nearest multiple of 5. Thus, a displayed value of 40 could represent any whole number from 38 through 42, while a displayed value of 45 could represent any whole number from 43 through 47.
We can first determine the possible range of x.
For Team A, the displayed numbers are 40 and 50, and the table shows ·. The smallest possible difference between the actual numbers is:
48 - 42 = 6
Since · means that the actual numbers differ by no more than x:
x >= 6
For Team B, the displayed numbers are 60 and 65, and the table shows +. The greatest possible difference between the actual numbers is:
67 - 58 = 9
Since + means that the second actual number must be more than x greater than the first:
x < 9
Therefore:
6 <= x < 9
Since x is a positive integer, the only possible values of x are 6, 7, and 8.
• 5
Since x must be at least 6, x cannot equal 5.
For Team A, even the closest possible actual values, 42 and 48, differ by 6. If x = 5, these numbers differ by more than x, so they could not be marked ·.
Answer: Cannot be x.
• 7
Since 7 is within the possible range, we need to check whether actual numbers can be chosen so that all of the symbols in the table are satisfied.
One possible set of actual numbers is:
Team A: 42, 48, 44
Team B: 58, 67, 57
Team C: 73, 72, 73
Team D: 52, 42, 43
Team E: 84, 88, 97
All of these numbers round to the values shown in the table.
For every + or −, the relevant actual numbers differ by more than 7:
Team B: 58 to 67 gives +9, and 67 to 57 gives −10
Team D: 52 to 42 gives −10
Team E: 88 to 97 gives +9
For every ·, the relevant actual numbers differ by 7 or less.
Thus, all of the information in the table can be satisfied when x = 7.
Answer: Could be x.
• 9
Since x must be less than 9, x cannot equal 9.
For Team B, the displayed numbers are 60 and 65, and the table shows +. The greatest possible actual increase is obtained with 58 and 67:
67 - 58 = 9
If x = 9, the second actual number would need to be more than 9 greater than the first for the table to show +. That is impossible.
Answer: Cannot be x.
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