This one is a data sufficiency question in Averages - Descriptive Statistics. What is the maximum possible average of the ages of 3 people A, B, and C if each of them is at least 1 year old? Statement 1: The sum of the ages of A and B is 28. Statement 2: B is 8 years younger than C.

1. GMAT QUANTITATIVE REASONING
DESCRIPTIVE STATISTICS –
AVERAGES
DATA SUFFICIENCY
Diagnostic Test

2. Question
What is the maximum possible average of the ages of 3
people A, B, and C if each of them is at least 1 year old?
Statement 1: The sum of the ages of A and B is 28.
Statement 2: B is 8 years younger than C.

3. Step 1
Get clarity on when the data is sufficient

4. What is the maximum possible average of the ages of 3 people A, B, & C?
We will not even look at the statements while answering the following questions
When is the data sufficient and when not?

5. What is the maximum possible average of the ages of 3 people A, B, & C?
We will not even look at the statements while answering the following questions
When is the data sufficient and when not?
The data is sufficient if we are able to
compute one single value as the
maximum possible average of the ages.

6. What is the maximum possible average of the ages of 3 people A, B, & C?
We will not even look at the statements while answering the following questions
When is the data sufficient and when not?
The data is sufficient if we are able to
compute one single value as the
maximum possible average of the ages.
If the information in the statement(s)
results in more than one value, data is
NOT sufficient.

7. What is the maximum possible average of the ages of 3 people A, B, & C?
We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What expression will give the average?
The data is sufficient if we are able to
compute one single value as the
maximum possible average of the ages.
If the information in the statement(s)
results in more than one value, data is
NOT sufficient.

8. What is the maximum possible average of the ages of 3 people A, B, & C?
We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What expression will give the average?
The data is sufficient if we are able to
compute one single value as the
maximum possible average of the ages.
If the information in the statement(s)
results in more than one value, data is
NOT sufficient.
Let A, B and C be the ages of the 3
people.

9. What is the maximum possible average of the ages of 3 people A, B, & C?
We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What expression will give the average?
The data is sufficient if we are able to
compute one single value as the
maximum possible average of the ages.
If the information in the statement(s)
results in more than one value, data is
NOT sufficient.
Let A, B and C be the ages of the 3
people.
We have to compute max
A + B + C
3

10. Step 2
Let’s evaluate statement 1 alone

11. Statement 1: The sum of the ages of A and B is 28.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28

12. Statement 1: The sum of the ages of A and B is 28.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
If C = 40, A + B + C = 28 + 40 = 68

13. Statement 1: The sum of the ages of A and B is 28.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
If C = 40, A + B + C = 28 + 40 = 68
If C = 20, A + B + C = 28 + 20 = 48

14. Statement 1: The sum of the ages of A and B is 28.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
If C = 40, A + B + C = 28 + 40 = 68
If C = 20, A + B + C = 28 + 20 = 48
We get different answer for A + B + C
for different values of C. Any one of
these could be the maximum value.
We are not able to get a unique value
for max (A + B + C) from statement 1.

15. Statement 1: The sum of the ages of A and B is 28.
Statement 1 alone is NOT sufficient
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
If C = 40, A + B + C = 28 + 40 = 68
If C = 20, A + B + C = 28 + 20 = 48
We get different answer for A + B + C
for different values of C. Any one of
these could be the maximum value.
We are not able to get a unique value
for max (A + B + C) from statement 1.

16. Statement 1: The sum of the ages of A and B is 28.
Eliminate choices A and D
Statement 1 alone is NOT sufficient
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
If C = 40, A + B + C = 28 + 40 = 68
If C = 20, A + B + C = 28 + 20 = 48
We get different answer for A + B + C
for different values of C. Any one of
these could be the maximum value.
We are not able to get a unique value
for max (A + B + C) from statement 1.

17. Statement 1: The sum of the ages of A and B is 28.
Choices narrow down to B, C or E.
Eliminate choices A and D
Statement 1 alone is NOT sufficient
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
If C = 40, A + B + C = 28 + 40 = 68
If C = 20, A + B + C = 28 + 20 = 48
We get different answer for A + B + C
for different values of C. Any one of
these could be the maximum value.
We are not able to get a unique value
for max (A + B + C) from statement 1.

18. Step 3
Let’s evaluate statement 2 alone.

19. Statement 2 : B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 2, B = C - 8.

20. Statement 2 : B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 2, B = C - 8.
There is no information about the age of A

21. Statement 2 : B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 2, B = C - 8.
There is no information about the age of A
We will not able to get a unique value
for max (A + B + C) from statement 2.

22. Statement 2 : B is 8 years younger than C.
Statement 2 alone is also NOT sufficient
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 2, B = C - 8.
There is no information about the age of A
We will not able to get a unique value
for max (A + B + C) from statement 2.

23. Statement 2 : B is 8 years younger than C.
Eliminate choice B
Statement 2 alone is also NOT sufficient
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 2, B = C - 8.
There is no information about the age of A
We will not able to get a unique value
for max (A + B + C) from statement 2.

24. Statement 2 : B is 8 years younger than C.
Choices narrow down to C or E.
Eliminate choice B
Statement 2 alone is also NOT sufficient
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 2, B = C - 8.
There is no information about the age of A
We will not able to get a unique value
for max (A + B + C) from statement 2.

25. Step 4
Let’s combine data from both the
statements.

26. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28

27. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8

28. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.

29. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We have to find max
A + B + C
3

30. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3

31. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3
Because the expression contains 2B and an A, the
expression will get maximized if we maximize B.

32. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3
Because the expression contains 2B and an A, the
expression will get maximized if we maximize B.
A + B = 28. B will be maximized when A is minimized.
Minimum value for A is 1. So, maximum for B is 27.

33. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We are able to get a unique value for max(A + B + C)
from statements 1 and 2 together.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3
Because the expression contains 2B and an A, the
expression will get maximized if we maximize B.
A + B = 28. B will be maximized when A is minimized.
Minimum value for A is 1. So, maximum for B is 27.

34. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
Statements together are SUFFICIENT
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We are able to get a unique value for max(A + B + C)
from statements 1 and 2 together.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3
Because the expression contains 2B and an A, the
expression will get maximized if we maximize B.
A + B = 28. B will be maximized when A is minimized.
Minimum value for A is 1. So, maximum for B is 27.

35. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
Eliminate choice E
Statements together are SUFFICIENT
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We are able to get a unique value for max(A + B + C)
from statements 1 and 2 together.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3
Because the expression contains 2B and an A, the
expression will get maximized if we maximize B.
A + B = 28. B will be maximized when A is minimized.
Minimum value for A is 1. So, maximum for B is 27.

36. Statements Together : The sum of the ages of A and B is 28; B is 8 years younger than C.
Answer is choice C
Eliminate choice E
Statements together are SUFFICIENT
What is the maximum possible average of the ages of 3 people A, B, & C?
From statement 1, A + B = 28
From statement 2, B = C – 8 or C = B + 8
From question stem, we know each is at least a year old.
We are able to get a unique value for max(A + B + C)
from statements 1 and 2 together.
We have to find max
A + B + C
3
Because C = B + 8, we can rewrite what we need to find
as max
A + B + B + 8
3 or as max
A + 2B + 8
3
Because the expression contains 2B and an A, the
expression will get maximized if we maximize B.
A + B = 28. B will be maximized when A is minimized.
Minimum value for A is 1. So, maximum for B is 27.

37. Try this
Here is a variant. Try it yourself

38. Question
What is the average of the ages of 3 people A, B, and C
if each of them is at least 1 year old?
Statement 1: The sum of the ages of A and B is 28.
Statement 2: B is 8 years younger than C.

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