A is a set containing 7 different numbers...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

A is a set containing 7 different numbers...

by swerve » Thu Jan 18, 2018 10:29 am

A is a set containing 7 different numbers. B is a set containig 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?

A. The range of A is equal to the range of B.
B. The mean of A is greater than the mean of B.
C. The range of A is less than the range of B.
D. The mean of A is equal to the mean of B.
E. The median of A is equal to the median of B.

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Jan 18, 2018 10:29 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Jan 18, 2018 10:18 pm

swerve wrote:A is a set containing 7 different numbers. B is a set containig 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?

A. The range of A is equal to the range of B.
B. The mean of A is greater than the mean of B.
C. The range of A is less than the range of B.
D. The mean of A is equal to the mean of B.
E. The median of A is equal to the median of B.

The OA is C.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

These kinds of questions can be solved taking suitable examples.

Let's take each statement one by one.

A. The range of A is equal to the range of B.

Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 7, 9, 13}; Range of Set A = Range of Set B = 13 - 1 = 12. Can be true.

B. The mean of A is greater than the mean of B.

Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 7, 9, 11}; Mean of Set A = 7; Mean of Set B = (5 + 7)/2 = 6. Can be true.

C. The range of A is less than the range of B.

This is not possible since all the numbers in Set B are there in Set A, thus, it is possible that the range of Set B is less than the range of Set A, but visa-versa is not possible. This is the correct answer.

For the sake of understanding, let's discuss other options too.

D. The mean of A is equal to the mean of B.

Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 9, 11, 13}; Mean of Set A = 7; Mean of Set B = (5 + 9)/2 = 7. Can be true.

E. The median of A is equal to the median of B.

Say Set A: {1, 3, 5, 7, 9, 11, 13} and Set B: {1, 3, 5, 9, 11, 13}; Median of Set A = 7; Median of Set B = (5 + 9)/2 = 7. Can be true.

The correct answer: C

Hope this helps!

-Jay
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Manhattan Review GMAT Prep

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Jan 19, 2018 4:52 am

A is a set containing 7 different numbers. B is a set containing 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?

A) The range of A is equal to the range of B
B) The mean of A is greater than the mean of B
C) The range of A is less than the range of B
D) The mean of A is equal to the mean of B
E) The median of A is equal to the median of B

Let B = {1, 3, 5, 7, 9, 11}

All of the members of B are also members of A.
Since A must include all of the values contained in B, its range cannot be smaller than B's range.

The correct answer is C.

A) The range of A is equal to the range of B
D) The mean of A is equal to the mean of B
E) The median of A is equal to the median of B
These options are possible if A = {1, 3, 5, 6, 7, 9, 11}

B) The mean of A is greater than the mean of B
This option is possible if A = {1, 3, 5, 7, 9, 11, 100}

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sun Jan 21, 2018 6:18 pm

swerve wrote:A is a set containing 7 different numbers. B is a set containig 6 different numbers, all of which are members of A. Which of the following statements CANNOT be true?

A. The range of A is equal to the range of B.
B. The mean of A is greater than the mean of B.
C. The range of A is less than the range of B.
D. The mean of A is equal to the mean of B.
E. The median of A is equal to the median of B.

Since all of the number in set B are in set A, and A has 1 more number than set B, it would be impossible for the range of set A to be any less than set B.

Answer: C

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