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31 May 2024, 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:
35%
(medium)
Question Stats:
75% (01:33) correct
25%
(02:09)
wrong
based on 44
sessions
History
Date
Time
Result
Not Attempted Yet
The population of Town X on January 1, 2010, was 56 percent greater than the population of the same town on January 1, 2005. The population of Town X on January 1, 2015, was 75 percent greater than the population of the same town on January 1, 2010. What was the population of Town X on January 1, 2005?
(1) The population of Town X on January 1, 2015, was 21,840.
(2) The increase in the population of Town X from January 1, 2010, to January 1, 2015, was 4,880 greater than the increase in the population of Town X from January 1, 2005, to January 1, 2010.
(1) The population of Town X on January 1, 2015, was 21,840.
(2) The increase in the population of Town X from January 1, 2010, to January 1, 2015, was 4,880 greater than the increase in the population of Town X from January 1, 2005, to January 1, 2010.
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Schools: ISB '27 (A) INSEAD '26 Tuck '27
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31 May 2024, 02:36
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Answer is Option D.
Let's assume population of Town X on January 1, 2005 as P
and
population in 2010 as P(2010), population in 2015 as P(2015)
Given -
P(2010) = 1.56 P
P(2015) = 1.75*P(2010) = 1.75*1.56P = 2.73P
Statement 1:
We know that P(2015) = 21840 = 2.73P. Hence, we can deduce "P". So statement 1 is sufficient.
Statement 2:
We are given that
P(2015) - P(2010) = P(2010) - P(2005) + 4880
2.73P - 1.56P = 1.56P - P + 4880
From here too, we can deduce "P". So statement 2 is sufficient.
Hence, both statements alone are sufficient.
Let's assume population of Town X on January 1, 2005 as P
and
population in 2010 as P(2010), population in 2015 as P(2015)
Given -
P(2010) = 1.56 P
P(2015) = 1.75*P(2010) = 1.75*1.56P = 2.73P
Statement 1:
We know that P(2015) = 21840 = 2.73P. Hence, we can deduce "P". So statement 1 is sufficient.
Statement 2:
We are given that
P(2015) - P(2010) = P(2010) - P(2005) + 4880
2.73P - 1.56P = 1.56P - P + 4880
From here too, we can deduce "P". So statement 2 is sufficient.
Hence, both statements alone are sufficient.
31 May 2024, 02:49
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Bunuel
IMO D,
Assuming population of village X at the start of Jan 1, 2005 as 100x.
Jan 2005 Jan 2010(56% greater than 2005) Jan 2015(75% greater than 2010)
100x 100x + 56% of 100x = 156x 156x + 75% of 156x = 273x.
Now,
1st - The population of Town X on January 1, 2015, was 21,840.
273x = 21840 after solving we will get x = 80
So, the population of Town X on January 1, 2005 = 100x = 80*100 = 8000. Hence Sufficient.
2nd - The increase in the population of Town X from January 1, 2010, to January 1, 2015, was 4,880 greater than the increase in the population of Town X from January 1, 2005, to January 1, 2010.
Increase in population from jan1, 2010 to jan1, 2015 is 75% of 156x which is equal to 117x
increase in population from jan1, 2005 to jan1, 2010 is 56% of 100x which is equal to 56x.
forming equation as per given statement,
117x = 4880 + 56x
117x - 56x = 4880
61x = 4880
x=80
So, the population of Town X on January 1, 2005 = 100x = 80*100 = 8000. Hence Sufficient.
Both alone sufficient Hence D.
