Aristotle # 5

[oquiella]

5. Five people - Adam, Bob, Craig, Daniel and Evan - are of different ages. Daniel is
younger than both Adam and Craig. Craig is younger than Bob but older than Evan.
Who among the five is the oldest?


(1) The average age of Adam and Bob is less than the average age of Craig and
Evan.
(2) The average age of Bob and Craig is less than the average age of Adam and
Evan.


PLEASE EXPLAIN. BREAK IT DOWN

[GMATGuruNY]

5. Five people - Adam, Bob, Craig, Daniel and Evan - are of different ages. Daniel is
younger than both Adam and Craig. Craig is younger than Bob but older than Evan.
Who among the five is the oldest?

(1) The average age of Adam and Bob is less than the average age of Craig and
Evan.
(2) The average age of Bob and Craig is less than the average age of Adam and
Evan.

From the prompt:
D < A and D < C.
E < C < B.

Statement 1: The average age of Adam and Bob is less than the average age of Craig and Evan.
(A+B)/2 < (C+E)/2
A+B < C+E.

Adding together A+B < C+E and C < B, we get:
(A+B) + C < (C+E) + B
A < E.

Linking together D < A, A < E and E < C < B, we get:
D < A < E < C < B.
B is the oldest.
SUFFICIENT.

Statement 2: The average age of Bob and Craig is less than the average age of Adam and Evan.
(B+C)/2 < (A+E)/2
B+C < A+E.

Adding together B+C < A+E and E < C, we get:
(B+C) + E < (A+E) + C
B < A.

Linking together E < C < B and B < A, we get:
E < C < B < A.
Since D < A, A is the oldest.
SUFFICIENT.

Whereas B is the oldest in statement 1, A is the oldest in statement 2.
This problem is FLAWED.
On the GMAT, the two statements CANNOT contradict each other.
I would ignore this problem.

[oquiella]

5. Five people - Adam, Bob, Craig, Daniel and Evan - are of different ages. Daniel is
younger than both Adam and Craig. Craig is younger than Bob but older than Evan.
Who among the five is the oldest?

(1) The average age of Adam and Bob is less than the average age of Craig and
Evan.
(2) The average age of Bob and Craig is less than the average age of Adam and
Evan.

From the prompt:
D < A and D < C.
E < C < B.

Statement 1: The average age of Adam and Bob is less than the average age of Craig and Evan.
(A+B)/2 < (C+E)/2
A+B < C+E.

Adding together A+B < C+E and C < B, we get:
(A+B) + C < (C+E) + B
A < E.

Linking together D < A, A < E and E < C < B, we get:
D < A < E < C < B.
B is the oldest.
SUFFICIENT.

Statement 2: The average age of Bob and Craig is less than the average age of Adam and Evan.
(B+C)/2 < (A+E)/2
B+C < A+E.

Adding together B+C < A+E and E < C, we get:
(B+C) + E < (A+E) + C
B < A.

Linking together E < C < B and B < A, we get:
E < C < B < A.
Since D < A, A is the oldest.
SUFFICIENT.

Whereas B is the oldest in statement 1, A is the oldest in statement 2.
This problem is FLAWED.
On the GMAT, the two statements CANNOT contradict each other.
I would ignore this problem.

I've never seen this approach Why did you add the given inequalities? Can you give me another problem you've seen that has the same approach?

[GMATGuruNY]

I've never seen this approach Why did you add the given inequalities? Can you give me another problem you've seen that has the same approach?

From the prompt:
D < A
D < C
E < C < B.
Given these relationships, only A or B can be the oldest.

Statement 1:
A+B < C+E
C < B.
I added these inequalities because I could see that the values in red would cancel out, allowing me to determine the relationship between A and E, as shown in my post above.

Statement 2:
B+C < A+E
E < C.
I added these inequalities because I could see that the values in blue would cancel out, allowing me to determine the relationship between B and A, as shown in my post above.

Other problems that can be solved by adding together two inequalities:
https://www.beatthegmat.com/can-i-use-te ... 78286.html
https://www.beatthegmat.com/is-z-between ... 70021.html
https://www.beatthegmat.com/for-the-stud ... 65203.html