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12 Jan 2024, 22:58
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D
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Difficulty:
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Question Stats:
46% (02:50) correct
54%
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Rounded to the nearest 10,000, the populations of San Pepe and of its suburb Maple Beach are 140,000 and 80,000, respectively. What is the combined population of San Pepe and Maple Beach, rounded to the nearest 10,000 ?
(1) The exact population figures of San Pepe and Maple Beach are each within 2% of the rounded figures above.
(2) The approximate population figure for San Pepe was rounded up, whereas the figure for Maple Beach was rounded down.
Screenshot 2024-01-13 112600.png [ 306.58 KiB | Viewed 9458 times ]
(1) The exact population figures of San Pepe and Maple Beach are each within 2% of the rounded figures above.
(2) The approximate population figure for San Pepe was rounded up, whereas the figure for Maple Beach was rounded down.
Attachment:
Screenshot 2024-01-13 112600.png [ 306.58 KiB | Viewed 9458 times ]
03 Oct 2024, 02:51
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MalachiKeti
Keep it simple.
Rounded to the nearest 10,000, the populations of San Pepe and of its suburb Maple Beach are 140,000 and 80,000, respectively. What is the combined population of San Pepe and Maple Beach, rounded to the nearest 10,000 ?
Given:
135 < SP < 145
75 < MB < 85
75 < MB < 85
Thus:
210 < SP + MB < 230
So, SP + MB, rounded to the nearest 10, could be 210, 220, or 230.
(1) The exact population figures of San Pepe and Maple Beach are each within 2% of the rounded figures above.
Since SP rounded to the nearest 10 is 140, its exact population is approximately from 137 (a little more than that) to 143 (a little less than that) (2% of 140 is less than 3).
Since MB rounded to the nearest 10 is 80, its exact population is approximately from 78 (a little more than that) to 82 (a little less than that) (2% of 80 is less than 2).
Thus:
137 + 78 < SP + MB < 143 + 82
215 < SP + MB < 225
215 < SP + MB < 225
Rounded to the nearest 10, the combined population is 220. Sufficient.
(2) The approximate population figure for San Pepe was rounded up, whereas the figure for Maple Beach was rounded down.
135 < SP < 140
80 < MB < 85
80 < MB < 85
Thus:
215 < SP + MB < 225
Rounded to the nearest 10, the combined population is 220. Sufficient.
Answer: D.
General Discussion
14 Jan 2024, 08:58
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gmatophobia
Sharing some thoughts on this question
Rounded to the nearest 10,000, the populations of San Pepe and of its suburb Maple Beach are 140,000 and 80,000
M.B ⇒ Maple Beach
S.P ⇒ San Pepe
Actual Population
- \(135,000 \leq \text{S.P} < 145,000 \)
- \(75,000 \leq \text{M.B} < 85,000 \)
Adding the above inequalities
\(135,000 + 75,000 \leq \text{S.P + M.B} < 145,000 + 85,000 \)
\(210,000 \leq \text{S.P + M.B} < 230,000 \)
Hence, the rounded population can be either 210,000; 220,000 ; or 230,000
As we are rounding to the nearest 10,000, the maximum possible difference between the actual value and the rounded value can be 5,000.
Statement 1
(1) The exact population figures of San Pepe and Maple Beach are each within 2% of the rounded figures above.
- 2% of 140,000 = 2,800
- 2% of 80,000 = 1,600
Actual Population
- \(140,000 - 2,800 \leq \text{S.P} < 140,000 + 2,800 \)
- \(80,000 - 1,600 \leq \text{M.B} < 80,000 + 1,600 \)
Adding the above inequalities
\(220,000 - 4,000 \leq \text{S.P + M.B} < 220,000 + 4,000 \)
As the difference is less than 5,000 the rounded value will be 220,000
The statement is sufficient to answer the question. Eliminate B, C, and E.
Statement 2
(2) The approximate population figure for San Pepe was rounded up, whereas the figure for Maple Beach was rounded down.
Inference about San Pepe:
- As the population figure for San Pepe was rounded up, the actual population of San Pepe is less than or equal to the rounded population
- The maximum difference between the actual population and the rounded population = -5000
Note: We are indicating the difference as negative, as the actual population is less than the rounded population.
Inference about Maple Beach:
- As the population figure for Maple Beach was rounded down, the actual population of Maple Beach is greater than or equal to the rounded population
- The maximum difference between the actual population and the rounded population = +4999
Note: We are indicating the difference as positive, as the actual population is greater than the rounded population.
When we add the two values, the maximum difference between the actual and the rounded population will not exceed 5000.
Greatest possible rounding difference = -5000 - 0 = -5000 ⇒ When the actual population of San Pepe is 135,000 and the population of Maple Beach is 80,000. The combined population of San Pepe and Maple Beach = 135,000 + 80,000 = 215,000
Least possible rounding difference = 0 - 0 = 0 ⇒ When the actual population of San Pepe is 140,000 and the population of Maple Beach is 80,000. The combined population of San Pepe and Maple Beach = 140,000 + 80,000 = 220,000
In both the above cases, the rounded population to the nearest 10,000 is 220,000.
Hence, this statement is also sufficient to answer the question.
Option D
