The variable x takes on integer values between 1 and 7

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BTGmoderatorLU: Moderator; Posts: 2589; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Tue Aug 28, 2018 2:48 pm

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Source: GMAT Prep

X frequency
1 3
2 1
3 3
4 1
5 3
6 1
7 3

The variable x takes on integer values between 1 and 7 inclusive as shown above. What is the probability that the absolute value of the difference between the mean of the distribution which is 4 and a randomly chosen value of x will be greater than 3/2?

A. 8/15
B. 4/7
C. 4/5
D. 6/7
E. 8/7

The OA is A.

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Source: Beat The GMAT — Problem Solving | Tue Aug 28, 2018 2:48 pm

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by [email protected] » Mon Sep 03, 2018 8:00 pm

Hi All,

We're told that the variable X takes on integer values between 1 and 7 inclusive as shown above (meaning that out of a total of 15 values, there are three 1s, one 2, three 3s, one 4, etc.). We're asked for the probability that the absolute value of the DIFFERENCE between the MEAN (re: 4) and a randomly chosen value of X will be GREATER than 3/2. While this question looks a bit 'thick', it's based on some basic Probability math and some Arithmetic.

To start, for the DIFFERENCE between 4 and a value in the list to be GREATER than 3/2, the value of X would have to be 1, 2, 6 or 7 (for example, 4 - 1 = 3 and 6 - 4 = 2).

Based on the frequencies, we know that there are three 1s, one 2, one 6 and three 7s. That's a total of 8 values out of the 15 total values.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Sep 04, 2018 3:16 am

BTGmoderatorLU wrote:Source: GMAT Prep

X frequency
1 3
2 1
3 3
4 1
5 3
6 1
7 3

The variable x takes on integer values between 1 and 7 inclusive as shown above. What is the probability that the absolute value of the difference between the mean of the distribution which is 4 and a randomly chosen value of x will be greater than 3/2?

A. 8/15
B. 4/7
C. 4/5
D. 6/7
E. 8/7

The only values of x that give us |x - 4| > 3/2 are 1, 2, 6, and 7. Since we have a total of 3 + 1 + 3 + 1 + 3 + 1 + 3 = 15 values in the list and a total of 3 + 1 + 1 + 3 = 8 values that can be x, the probability is 8/15.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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