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01 Jun 2022, 23:00
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C
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Difficulty:
75%
(hard)
Question Stats:
61% (02:53) correct
39%
(02:50)
wrong
based on 122
sessions
History
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Time
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Not Attempted Yet
Mr. Smith has 30 currency notes consisting of 1 dollar and 1-euro notes. If the euros were dollars and dollars were euros, he would have 78 euros more than he has now. If one dollar is equal to 40 euros, the number of dollars he has, is
A. 12
B. 13
C. 14
D. 15
E. 21
A. 12
B. 13
C. 14
D. 15
E. 21
Given: Mr. Smith has 30 currency notes consisting of 1 dollar and 1-euro notes. If the euros were dollars and dollars were euros, he would have 78 euros more than he has now.
Asked: If one dollar is equal to 40 euros, the number of dollars he has, is
Let the number of dollar notes Mr Smith has be x.
Number of Euro notes = 30 - x
Number of Euros after converting dollars to euros = 40x + (30-x) = 39x + 30
If the euros were dollars and dollars were euros
The number of dollar notes = 30 - x.
The number of Euro notes = x
Number of Euros after converting dollars to euros = 40(30-x) + x = 1200 - 39x
Difference = (1200-39x) - (39x + 30) = 78
1170 - 78x = 78
78x = 1170 - 78 = 1092
x = 1092/78 = 14
IMO C
Asked: If one dollar is equal to 40 euros, the number of dollars he has, is
Let the number of dollar notes Mr Smith has be x.
Number of Euro notes = 30 - x
Number of Euros after converting dollars to euros = 40x + (30-x) = 39x + 30
If the euros were dollars and dollars were euros
The number of dollar notes = 30 - x.
The number of Euro notes = x
Number of Euros after converting dollars to euros = 40(30-x) + x = 1200 - 39x
Difference = (1200-39x) - (39x + 30) = 78
1170 - 78x = 78
78x = 1170 - 78 = 1092
x = 1092/78 = 14
IMO C
02 Jun 2022, 09:17
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Shivanshsm
30-second solution: Hello, everyone. To avoid unnecessary algebra or calculations with large numbers, you can consider that the difference for every extra dollar, according to the exchange provided, is +40 - 1, or +39, since Mr. Smith would be gaining 40 euros while losing the 1 euro that was converted to a dollar. Since 39 * 2 = 78, our target value, we know that Mr. Smith must currently have two fewer dollars than euros. To illustrate:
14D + 16E
--convert--
16D + 14E
----------
+2D - 2E
+(80E) - 2E = +78E
The answer must be (C).
Good luck with your studies.
- Andrew
