4gmat diagnostic test q7 - problem solving - descriptive statistics - range

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GMAT QUANTITATIVE REASONING DESCRIPTIVE STATISTICS PROBLEM SOLVING Diagnostic Test

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Page 1: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

GMAT QUANTITATIVE REASONING

DESCRIPTIVE STATISTICS

PROBLEM SOLVING

Diagnostic Test

Page 2: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Question

7 distinct integers are arranged in ascending order. The range

of the smallest 5 integers is 20 and that of the largest 5

integers is 40. What is the maximum range of the 7 integers?A. 60

B. 59

C. 58

D. 42

E. 43

Page 3: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Part 1

Jot down key data from the question

Page 4: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

What is the maximum range of the 7 integers?

Step 1: Key information

Page 5: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

What is the maximum range of the 7 integers?

7 numbers. All of them integers.

Step 1: Key information

Page 6: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

What is the maximum range of the 7 integers?

7 numbers. All of them integers. Distinct numbers. No two numbers same.

Step 1: Key information

Page 7: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

What is the maximum range of the 7 integers?

7 numbers. All of them integers. Distinct numbers. No two numbers same.

Range of the smallest 5 is 20.

Step 1: Key information

Page 8: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

What is the maximum range of the 7 integers?

7 numbers. All of them integers. Distinct numbers. No two numbers same.

Range of the smallest 5 is 20. Range of the largest 5 is 40.

Step 1: Key information

Page 9: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Page 10: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Page 11: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

Page 12: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

Page 13: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

Page 14: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Page 15: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

Page 16: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

Page 17: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

x1 = x5 - 20

Page 18: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

x1 = x5 - 2003 Range of the largest 5 is 40.

Page 19: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

x1 = x5 - 2003 Range of the largest 5 is 40.

x7 – x3 = 40

Page 20: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

x1 = x5 - 2003 Range of the largest 5 is 40.

x7 – x3 = 40

Alternative ways of expressing:

Page 21: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

x1 = x5 - 2003 Range of the largest 5 is 40.

x7 – x3 = 40

Alternative ways of expressing:

x7 = x3 + 40

Page 22: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

01 7 distinct integers

Step 2: Making sense of the data

What is the maximum range of the 7 integers?

Let the ascending order of the 7 numbers be x1, x2, x3, x4, x5, x6, and x7

x1 < x2 < x3 < x4 < x5 < x6 < x7

02 Range of the smallest 5 is 20.

x5 – x1 = 20

Alternative ways of expressing:

x5 = x1 + 20

x1 = x5 - 2003 Range of the largest 5 is 40.

x7 – x3 = 40

Alternative ways of expressing:

x7 = x3 + 40 x3 = x7 - 40

Page 23: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Part 2

Visually representing to arrive at the answer

Page 24: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Step 3: Visually Presenting Data

Page 25: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

Data as given in the question. x1 to x7 in ascending order

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Step 3: Visually Presenting Data

Page 26: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

Data as given in the question. x1 to x7 in ascending order

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Step 3: Visually Presenting Data

Page 27: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

Data as given in the question. x1 to x7 in ascending order

x3, x4, and x5 common to both ranges - the smallest 5 and the largest 5 numbers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Step 3: Visually Presenting Data

Page 28: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Objective: Maximize range of the 7 integers; maximize (x7 – x1)

Page 29: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Objective: Maximize range of the 7 integers; maximize (x7 – x1)

Page 30: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Objective: Maximize range of the 7 integers; maximize (x7 – x1)

Pushing x1 as much to the left as possible and x7 as much to the right as possible will maximize (x7 – x1)

Page 31: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x3 x4 x5 x6x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

Page 32: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

Page 33: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

Page 34: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

Page 35: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

Page 36: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

Page 37: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x7x5

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

Page 38: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x5 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left

Page 39: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x5 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right.

the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left

Page 40: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x5 x7x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right.

the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left

Page 41: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right.

the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left

Page 42: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right.

the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left

the extent to which x7 can be pushed to the right will be determined by the extent to which x3 can be pushed to the right

Page 43: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x3 x4 x5 x6 x7x5x3

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Push x1 to left extreme and x7 to right extreme

When x1 is pushed to the left, x5 which is x1 + 20 also moves to the left.

Effects: Notice the following effects of pushing x1 to the left and x7 to the right

When x7 is pushed to the right, x3 which is x7 - 40 also moves to the right.

the extent to which x1 can be pushed to the left will be determined by the extent to which x5 can be pushed to the left

the extent to which x7 can be pushed to the right will be determined by the extent to which x3 can be pushed to the left

Page 44: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x6

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Page 45: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x6 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Page 46: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x1 x2 x6 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

To maximize the range between x1 and x7

Page 47: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x6

To maximize the range between x1 and x7

x1 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Page 48: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x6

To maximize the range between x1 and x7

Minimize range between x3 and x5

x1 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Page 49: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x3 x5 x6

To maximize the range between x1 and x7

Minimize range between x3 and x5

x1 x7

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Page 50: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x6

To maximize the range between x1 and x7

Minimize range between x3 and x5

x1 x7x3 x5

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Page 51: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

x2 x4 x6

To maximize the range between x1 and x7

Minimize range between x3 and x5

x1 x7x3 x5

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

What should you do? Push x5 as much to the left and x3 as much to the right as possible

Make x3, x4, and x5 three consecutive integers

Page 52: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Part 3 – Method 1

Solve algebraically to get the answer

Page 53: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 54: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 55: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 56: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 57: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 58: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

We also know x7 = x3 + 40 (range of largest 5 is 40)

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 59: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

We also know x7 = x3 + 40 (range of largest 5 is 40)

x7 = x1 + 18 + 40 from eqn (2)

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 60: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

We also know x7 = x3 + 40 (range of largest 5 is 40)

x7 = x1 + 18 + 40 from eqn (2)

Or x7 = x1 + 58

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 61: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

We also know x7 = x3 + 40 (range of largest 5 is 40)

x7 = x1 + 18 + 40 from eqn (2)

Or x7 = x1 + 58

Or x7 - x1 = 58

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 62: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

We also know x7 = x3 + 40 (range of largest 5 is 40)

x7 = x1 + 18 + 40 from eqn (2)

Or x7 = x1 + 58

Or x7 - x1 = 58

Maximum range is 58

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 63: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

x5 = x3 + 2 …. eqn(1)

We know x5 = x1 + 20 (range of smallest 5 is 20)

By replacing x5 as (x3 + 2) from eqn (1) we get (x3 + 2) = x1 + 20 or x3 = x1 + 18 … eqn (2)

We also know x7 = x3 + 40 (range of largest 5 is 40)

x7 = x1 + 18 + 40 from eqn (2)

Or x7 = x1 + 58

Or x7 - x1 = 58 Correct answer is choice C

Maximum range is 58

Approach: Express x7 in terms of x1 – the link is x3 and x5.

Page 64: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Part 3 – Method 2

Better alternative – assume a value of x1

Page 65: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Page 66: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Page 67: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

Page 68: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

Page 69: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

x3, x4, and x5 are consecutive integers.

Page 70: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

x3, x4, and x5 are consecutive integers.

So, x3 = 40 – 2 = 38

Page 71: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

x3, x4, and x5 are consecutive integers.

So, x3 = 40 – 2 = 38

So, x7 = x3 + 40 = 38 + 40 = 78

Page 72: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

x3, x4, and x5 are consecutive integers.

So, x3 = 40 – 2 = 38

So, x7 = x3 + 40 = 38 + 40 = 78

x7 – x1 = 78 – 20 = 58.

Page 73: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

x3, x4, and x5 are consecutive integers.

So, x3 = 40 – 2 = 38

So, x7 = x3 + 40 = 38 + 40 = 78

x7 – x1 = 78 – 20 = 58.

Maximum range is 58

Page 74: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

Inference: x3, x4, and x5 should be 3 consecutive integers in order to maximize the range of the 7 integers

Approach: Assume a value of x1

7 distinct integers; range of smallest 5 is 20; range of largest 5 is 40

What is the maximum range of the 7 integers?

Let x1 be 20.

x5 = x1 + 20 = 20 + 20 = 40

x3, x4, and x5 are consecutive integers.

So, x3 = 40 – 2 = 38

So, x7 = x3 + 40 = 38 + 40 = 78

x7 – x1 = 78 – 20 = 58.

Correct answer is choice C

Maximum range is 58

Page 75: 4GMAT Diagnostic Test Q7 - Problem Solving - Descriptive Statistics - Range

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