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16 Sep 2014, 00:14
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Today, John is three times as old as Mark. If, in 13 years, John will be one year younger than twice Mark's age at that time, how old is John today?
A. 13
B. 33
C. 36
D. 38
E. 39
A. 13
B. 33
C. 36
D. 38
E. 39
16 Sep 2014, 00:14
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Official Solution:
Today, John is three times as old as Mark. If, in 13 years, John will be one year younger than twice Mark's age at that time, how old is John today?
A. 13
B. 33
C. 36
D. 38
E. 39
Let J represent John's age and M represent Mark's age.
Since John is three times as old as Mark, we have: \(J = 3M\).
In 13 years, John will be one year younger than twice Mark's age at that time: \(J + 13 = 2(M + 13) - 1\).
Substituting \(J\) with \(3M\) in the second equation, we get:
\(3M+13=2(M+13)-1\);
From this, \(M = 12\).
Thus, Mark is 12 years old today, which means John is \(J = 3M = 3*12 = 36\) years old today.
Answer: C
Today, John is three times as old as Mark. If, in 13 years, John will be one year younger than twice Mark's age at that time, how old is John today?
A. 13
B. 33
C. 36
D. 38
E. 39
Let J represent John's age and M represent Mark's age.
Since John is three times as old as Mark, we have: \(J = 3M\).
In 13 years, John will be one year younger than twice Mark's age at that time: \(J + 13 = 2(M + 13) - 1\).
Substituting \(J\) with \(3M\) in the second equation, we get:
\(3M+13=2(M+13)-1\);
From this, \(M = 12\).
Thus, Mark is 12 years old today, which means John is \(J = 3M = 3*12 = 36\) years old today.
Answer: C
07 Jul 2019, 04:52
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We can back track also this question
With backtracking we can eliminate 2 options A and D
because in question stem it is provided that John is 3 times old than Mark.
If John is 13 or 38 then mark will have age in decimals and word problem questions generally deals with positive integers.
Now lets see other three options
B - 33 lets back track if
John is 33 then Mark will be 11
Add 13 to each ages
46 will be John's and 24 will be Mark's age and it is given John is 1 year younger..
not matching.
C - 36 lets back track if
John is 36 then Mark will be 12
Add 13 to each ages
49 will be John's and 25 will be Mark's age and it is given John is 1 year younger..
so C is the answer.
we don't need to check for E here. I solved this question without paper pen.
With backtracking we can eliminate 2 options A and D
because in question stem it is provided that John is 3 times old than Mark.
If John is 13 or 38 then mark will have age in decimals and word problem questions generally deals with positive integers.
Now lets see other three options
B - 33 lets back track if
John is 33 then Mark will be 11
Add 13 to each ages
46 will be John's and 24 will be Mark's age and it is given John is 1 year younger..
not matching.
C - 36 lets back track if
John is 36 then Mark will be 12
Add 13 to each ages
49 will be John's and 25 will be Mark's age and it is given John is 1 year younger..
so C is the answer.
we don't need to check for E here. I solved this question without paper pen.
