If Janice was 25 years old z years ago and Lisa will be 23

Question

If Janice was 25 years old z years ago and Lisa will be 23 years old in p years, what was the average (arithmetic mean) of their ages 5 years ago?

(z + p)/2

(z - p + 38)/4

(z - p + 28)/4

(z + p + 48)/2

(z - p + 38)/2

padukaprasad · Answer

For the sake of simplicity let us assume z=10 and p=13

So Janice's current age = 25+10=35
 Lisa's current age= 23-13=10

Janice's age before 5 years = 35-5=30
Lisa's age before 5 years=10-5=5

Average age =35/2=17.5

Now substituting the values of z and p in the options a) ruled out(as z+p/2 is not equal to 17.5)
b) ruled out
c) ruled out
d) ruled out

None of the options are satisfying the condition..so I feel that either b can be the correct answer if the option is (z-p+38)/2.

rxs0005 · Answer

can someone do this algebraically i cant seem to quite get any of the AC using algebra

padukaprasad · Answer

Let me try...
Current age of Janice =z+25
Current age of Lisa=23-p
Age of Janice 5 years ago =z+20
Age of Lisa 5 years ago=23-p-5=18-p

Avearage(Arithmetic mean)=(z+20+18-p)/2=(z-p+38)/2

I feel that the option B is wrong..It should be (z-p+38)/2 as I had derived before...

Bunuel · Answer

Janice was 25 years old z years ago -->  J-z=25 , so  J=25+z ;
Lisa will be 23 years old in p years -->  L+p=23 , so  L=23-p ;

5 years ago Janice was  J-5=25+z-5=20+z  and Lisa was  L-5=23-p-5=18-p , so the average (arithmetic mean) of their ages was  \frac{20+z+18-p}{2}=\frac{38+z-p}{2} .

No correct answer among answer choices.

rxs0005 · Answer

thanks i had a typo AC E had 2 in the denominator

KarishmaB · Answer

I would still suggest, the fastest way to do it is by assuming values for z and p. Say z = 0 so Janice is 25 yrs old now. p = 0 so Lisa is 23 yrs old now. They were 20 and 18 respectively 5 yrs back so their average age was 19. So you are looking for the option that gives you 19. (When you are putting values, make sure you are very clear about what value you want from the options) 
Put z = 0, p =0, you get 19 from option (E).

TeamGMATIFY · Answer

Since Janice was 25 years old z years ago,
Hence current Age of Janice = 25 + z
Age 5 years before = 20 + z (i)

Since Lisa will be 23 years old in p years.
Hence current age of Lisa = 23 - p
Age 5 years before = 18 - p (ii)

Average of (i) and (ii) =  \frac{{20 + z + 18 - p}}{2}  =  \frac{{z - p + 38}}{2}

Option E

Abhishek009 · Answer

Avergae (arithmetic mean) =  \frac{{(18-p) +( 20+z)}}{2}

Avergae (arithmetic mean) =  \frac{(38+z-p)}{2} 
  
Hence IMHO (E)

ajdse22 · Answer

I solved this question using algebra, but as others have suggested, choosing smart numbers is a better approach.
Let z=0 and p=0. With this extreme case, can we eliminate choices?
This means Janice is 25 years now while Lisa is 23 years now. 5 years ago, Janice was 20 and Lisa was 18. Ok average = 38/2. Looking at the choices and substituting zero values for both p and z, we can see E work! . Rest others dont work at all
So E

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If Janice was 25 years old z years ago and Lisa will be 23

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If Janice was 25 years old z years ago and Lisa will be 23

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