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

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Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139709 [0], given: 12794

If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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04 Jan 2018, 22:47
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Question Stats:

69% (01:26) correct 31% (01:00) wrong based on 16 sessions

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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?

A. (48 + z - p)/2
B. (38 - z + p)/2
C. (38 + z + p)/2
D. (38 + z - p)/2
E. (48 + z + p)/2
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139709 [0], given: 12794

Math Expert
Joined: 02 Sep 2009
Posts: 43348

Kudos [?]: 139709 [0], given: 12794

Re: If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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04 Jan 2018, 22:48
Bunuel wrote:
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?

A. (48 + z - p)/2
B. (38 - z + p)/2
C. (38 + z + p)/2
D. (38 + z - p)/2
E. (48 + z + p)/2

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_________________

Kudos [?]: 139709 [0], given: 12794

VP
Joined: 22 May 2016
Posts: 1258

Kudos [?]: 467 [1], given: 683

If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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05 Jan 2018, 15:35
1
KUDOS
Bunuel wrote:
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?

A. (48 + z - p)/2
B. (38 - z + p)/2
C. (38 + z + p)/2
D. (38 + z - p)/2
E. (48 + z + p)/2

Assign values that make the equations easy.
Let Janice = 30 now, z years ago she was 25
z = 5
Let Lisa = 20 now, in p years she will be 23
p = 3

Average of their ages 5 years ago? Five years ago
Janice: (30 - 5) = 25
Lisa: (20 - 5) = 15
Average 5 yrs ago $$\frac{25+15}{2}=20$$

All the answers are divided by 2.
With z = 5, p = 3, find the answer with a numerator of 40, because 40/2 = 20 = average of their ages

A. (48 + z - p)/2
48 + 5 - 3 = 50 NOT A MATCH

B. (38 - z + p)/2
38 - 5 + 3 = 36 NOT A MATCH

C. (38 + z + p)/2
38 + 5 + 3 = 46 NOT A MATCH

D. (38 + z - p)/2
38 + 5 - 3 = 40 MATCH

E. (48 + z + p)/2
48 + 5 + 3 = 56 NOT A MATCH

[Reveal] Spoiler:
D

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Kudos [?]: 467 [1], given: 683

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Joined: 12 Oct 2017
Posts: 39

Kudos [?]: 2 [0], given: 15

Re: If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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05 Jan 2018, 19:05
If Janice was 25 years old z years ago => Janice's age now = 25 + z => 5years ago = 25+ z - 5
Lisa will be 23 years old in p years => Lisa's age now = 23 - p => 5 years ago = 23 - p - 5
Hence, the average (arithmetic mean) of their ages 5 years ago = (25+z-5 + 23-p -5)/2 = (38 + z - p)/2. the answer is D
-----
Please +1 kudos if the explanation is clear.
Thank you!

Kudos [?]: 2 [0], given: 15

Manager
Joined: 22 May 2015
Posts: 97

Kudos [?]: 48 [0], given: 22

Re: If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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05 Jan 2018, 21:04
Straight forward classic algebra problem.

Assume present ages are j and p
Eq 1 : 25 = j-z
Eq 2 : 23 = l+p

Need to find avg of there ages 5 years ago ie (j-5+l-5) / 2 = (j+l-10)/2
substituting j and l from eq 1 and eq 2 we get the answer as D
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Consistency is the Key

Kudos [?]: 48 [0], given: 22

Manager
Joined: 23 Oct 2017
Posts: 63

Kudos [?]: 4 [0], given: 4

Re: If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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06 Jan 2018, 04:40
Bunuel wrote:
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?

A. (48 + z - p)/2
B. (38 - z + p)/2
C. (38 + z + p)/2
D. (38 + z - p)/2
E. (48 + z + p)/2

------------
Janice's age z years ago = 25 years old, so as of now age of janice = 25 +z
Since Lisa will be 23 years old in p years, so as of now age of lisa = 23- p
Now average of both their 5 years beack will be:
(25+z-5 + 23-p -5)/2
= (38 + z - p)/2

Kudos [?]: 4 [0], given: 4

Re: If Janice was 25 years old z years ago and Lisa will be 23 years old   [#permalink] 06 Jan 2018, 04:40
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# If Janice was 25 years old z years ago and Lisa will be 23 years old

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