4gmat diagnostic test q7 - problem solving - descriptive statistics - range
TRANSCRIPT
GMAT QUANTITATIVE REASONING
DESCRIPTIVE STATISTICS
PROBLEM SOLVING
Diagnostic Test
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
Part 1
Jot down key data from the question
What is the maximum range of the 7 integers?
Step 1: Key information
What is the maximum range of the 7 integers?
7 numbers. All of them integers.
Step 1: Key information
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
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
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
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?
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?
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
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
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.
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
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:
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
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
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.
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
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:
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
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
Part 2
Visually representing to arrive at the answer
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
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
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
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
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)
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)
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Part 3 – Method 1
Solve algebraically to get the answer
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Part 3 – Method 2
Better alternative – assume a value of x1
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?
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?
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.
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
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.
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
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
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.
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
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
For more questions
Visit http://www.4gmat.com
GMAT Classes and GMAT Preparation
Send your comments / feedback to
4GMATWe offer classroom training in Chennai and Bangalore
Tutors include GMAT 98%ilers, US B School graduates and IIM graduates
Call us: +91 95000 48484
Mail us: [email protected]