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

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

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New post 04 Jan 2018, 23:47
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Question Stats:

73% (01:46) correct 27% (00:54) wrong based on 26 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

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

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New post 04 Jan 2018, 23:48
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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 05 Jan 2018, 16:35
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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

Answer
[Reveal] Spoiler:
D

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

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New post 05 Jan 2018, 20:05
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
-----
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Re: If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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New post 05 Jan 2018, 22:04
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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Re: If Janice was 25 years old z years ago and Lisa will be 23 years old [#permalink]

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New post 06 Jan 2018, 05:40
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
Re: If Janice was 25 years old z years ago and Lisa will be 23 years old   [#permalink] 06 Jan 2018, 05:40
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If Janice was 25 years old z years ago and Lisa will be 23 years old

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