Brent is 18 years younger than Justin. If in 5 years Brent will be

Question

Brent is 18 years younger than Justin. If in 5 years Brent will be half as old as Justin, how old was Justin 5 years ago?

A. 8
B. 18
C. 21
D. 26
E. 31

BrentGMATPrepNow · Accepted Answer

Brent is 18 years younger than Justin.  
Let J = Justin's PRESET AGE
So, J-18 = Brent's PRESENT age

In 5 years, both people will be 5 years older
So, J + 5 = Justin's AGE IN 5 YEARS
And (J-18) + 5 = Brent's AGE IN 5 YEARS
Simplify to get: J - 13 = Brent's AGE IN 5 YEARS

In 5 years Brent will be half as old as Justin.  
In other words, IN 5 YEARS 5 years, (Brent's age) = (1/2)(Justin's age)
We can write: J - 13 = (1/2)(J + 5)
Multiply both sides by 2 to get: 2J - 26 = J + 5
Solve to get: J = 31
So, Justin's PRESENT age = 31

How old was Justin 5 years ago?  
Justin's age 5 years ago = 31 - 5 = 26

Answer:  D

sashiim20 · Answer

Let Brent's age be B and Justin's age be J.
B = J - 18
J - B = 18 ------- (i)

In 5 years; 
B + 5 =  \frac{1}{2} (J + 5)
2B + 10 = J + 5
J - 2B = 5 ------- (ii)

Subtracting (i) from (ii), we get;
B = 13

Substituting Value of B in (i), we get;
J - 13 = 18
J = 18 + 13 = 31

Five years ago, Justin was = 31 - 5 = 26 years. Answer D...

chetan2u · Answer

hi
 a very simple and fast approach would be tackling it logically..

the difference is 18 years. 
so when will the elder be TWICE? :  when the younger one, Brent, is 18 
and then Justin will be 36..
so Justin will be 36 after 5 years, now he will be 36-5=31 and 5 years back, he was 31-5 =26

D

ScottTargetTestPrep · Answer

We can let b = Brent’s current age and j = Justin’s current age.
 
Since Brent is 18 years younger than Justin:
 
b = j - 18
 
In 5 years, Brent will be (b + 5) years old and Justin will be (j + 5) years old, and Brent will be half as old as Justin:
 
b + 5 = (1/2)(j + 5)
 
2b + 10 = j + 5
 
2b + 5 = j
 
We can substitute 2b + 5 for j in the first equation and we have:
 
b = 2b + 5 - 18
 
b = 13
 
Thus, Justin is 18 + 13 = 31 years old, so he was 26 five years ago.
 
Answer: D

EMPOWERgmatRichC · Answer

Hi All,

We're told that Brent is 18 years younger than Justin and in 5 years, Brent will be half as old as Justin. We're asked how old was Justin was 5 YEARS AGO. This is an example of a 'System math' question that involves a 'time shift.' We can solve this with some standard Algebra as long as we properly handle the 'time shift' with the following equations:

B = Brent's age today 
J = Justin's age today

B = J - 18 
(B + 5) = (1/2)(J + 5)

Here, we have a 'system' (2 variable and 2 unique equations), so we can solve it. Since we're focused on the value of J, I'm going to 'substitute in' the value for B...

(J - 18 + 5) = (1/2)(J + 5) 
(J - 13) = (1/2)(J + 5) 
2J - 26 = J + 5 
J = 31

The question asks how old Justin was 5 YEARS AGO. Since he's 31 today, he was 31 - 5 = 26 years old five years ago.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

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Brent is 18 years younger than Justin. If in 5 years Brent will be

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