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How old will Fred be in 3 years?

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How old will Fred be in 3 years?  [#permalink]

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New post 26 Jun 2018, 07:34
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C
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E

Difficulty:

  15% (low)

Question Stats:

95% (00:42) correct 5% (00:53) wrong based on 21 sessions

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How old will Fred be in 3 years?

(1) Presently, Fred is 4 times as old as Gary.
(2) In 10 years, Fred will be 3 times as old as Gary.

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Brent Hanneson – Founder of gmatprepnow.com

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How old will Fred be in 3 years?  [#permalink]

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New post 26 Jun 2018, 07:56
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GMATPrepNow wrote:
How old will Fred be in 3 years?

(1) Presently, Fred is 4 times as old as Gary.
(2) In 10 years, Fred will be 3 times as old as Gary.



If I am short of time, I will mark C just after reading the question as statement I gives a ratio between TWO variables and statement II gives a linear equation with some term without any variables ( there is 10)

Let the ages be F and G

1) F=4G
Just aratio..
Insufficient

2) F+10=3(G+10)..
So a linear equation in two variables..
Insufficient

Combined
4G+10=3(G+10)....G=20
So Far is 4*20=80
And after 3 years he will be 83
Sufficient

C
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: How old will Fred be in 3 years?  [#permalink]

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New post 30 Jun 2018, 07:34
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GMATPrepNow wrote:
How old will Fred be in 3 years?

(1) Presently, Fred is 4 times as old as Gary.
(2) In 10 years, Fred will be 3 times as old as Gary.


Let's solve the question using 2 variables
Let F = Fred's PRESENT age
Let G = Gary's PRESENT age

Target question: What is the value of F+3 ?

Statement 1: Presently, Fred is 4 times as old as Gary.
In other words, F = 4G
There are several values of F and G that satisfy the equation F = 4G. Here are two:
Case a: F = 4 and G = 1. In this case, the answer to the target question is F+3 = 4+3 = 7
Case b: F = 8 and G = 2. In this case, the answer to the target question is F+3 = 8+3 = 11
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: In 10 years, Fred will be 3 times as old as Gary.
IN 10 YEARS, Fred's age = F + 10
IN 10 YEARS, Gary's age = G + 10
If Fred will be 3 times as old as Gary, we can write: F + 10 = 3(G + 10)
Expand: F + 10 = 3G + 30
Rearrange to get: F = 3G + 20
There are several values of F and G that satisfy the equation F = 3G + 20. Here are two:
Case a: F = 23 and G = 1. In this case, the answer to the target question is F+3 = 23+3 = 26
Case b: F = 26 and G = 2. In this case, the answer to the target question is F+3 = 26+3 = 29
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that F = 4G
Statement 2 tells us that F = 3G + 20
At this point, we should recognize that we have a system of 2 linear equations with 2 variables. As such, we COULD solve this system for G and F, which means we COULD answer the target question.
ASIDE: Although we COULD solve the system of equations, we would never waste valuable time on test day doing so. We need only determine that we COULD answer the target question.
Since we COULD answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

ASIDE: If we were to solve the system, we'd get: G = 20 and F = 80, which means Fred will be 83 years old in 3 years.

Cheers,
Brent
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Re: How old will Fred be in 3 years? &nbs [#permalink] 30 Jun 2018, 07:34
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