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16 Feb 2022, 05:00
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If Phil’s age is exactly half of Jan’s age, what is Jan’s age?
(1) In 24 years, Jan’s age will be 25% greater than Phil’s.
(2) 6 years ago, Phil’s age was 1/5 Jan’s age.
(1) In 24 years, Jan’s age will be 25% greater than Phil’s.
(2) 6 years ago, Phil’s age was 1/5 Jan’s age.
16 Feb 2022, 08:22
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Bunuel
If Phil’s age is exactly half of Jan’s age, what is Jan’s age?
(1) In 24 years, Jan’s age will be 25% greater than Phil’s.
(2) 6 years ago, Phil’s age was 1/5 Jan’s age.
(1) In 24 years, Jan’s age will be 25% greater than Phil’s.
(2) 6 years ago, Phil’s age was 1/5 Jan’s age.
Let P = Phil's PRESENT age
Let J = Jan's PRESENT age
Given: Phil’s age is exactly half of Jan’s age
We can write: P = 0.5J
Target question: What is Jan’s (PRESENT) age?
Statement 1: In 24 years, Jan’s age will be 25% greater than Phil’s.
In 24 years...
J + 24 = Jan's age
P + 24 = Phil's age
So, we can write: J + 24 = 1.25(P + 24) [a linear equation with two variables]
We also have: P = 0.5J [a different linear equation with the same two variables]
Since we have a system of two linear equations with two variables, we COULD solve the system for P and J, which means we COULD answer the target question with certainty.
So, statement 1 is SUFFICIENT
Statement 2: 6 years ago, Phil’s age was 1/5 Jan’s age.
6 years ago,...
J - 6 = Jan's age
P - 6 = Phil's age
We can write: J - 6 = (1/5)(P - 6) [a linear equation with two variables]
We also have: P = 0.5J [a different linear equation with the same two variables]
Since we have a system of two linear equations with two variables, we COULD solve the system for P and J (although we would never waste precious time on test day actually solving the system), which means we COULD answer the target question with certainty.
So, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
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16 Feb 2022, 12:47
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Let Jan's present age be J
Therefore, Phil's present age = J/2
(1) \(\frac{5}{4}*(\frac{J}{2}+24)=(J+24)\)
\(5(\frac{J}{2}+24)=4(J+24)\)
\(\frac{5J}{2}+120=4J+96\)
\(\frac{3J}{2}=24\)
\(J=16\) Sufficient
(2) \(5*(\frac{J}{2}-6)=(J-6)\)
\(\frac{5J}{2}-30=J-6\)
\(\frac{3J}{2}=24\)
\(J=16\) Sufficient
Hence, D.
Posted from my mobile device
Therefore, Phil's present age = J/2
(1) \(\frac{5}{4}*(\frac{J}{2}+24)=(J+24)\)
\(5(\frac{J}{2}+24)=4(J+24)\)
\(\frac{5J}{2}+120=4J+96\)
\(\frac{3J}{2}=24\)
\(J=16\) Sufficient
(2) \(5*(\frac{J}{2}-6)=(J-6)\)
\(\frac{5J}{2}-30=J-6\)
\(\frac{3J}{2}=24\)
\(J=16\) Sufficient
Hence, D.
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