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# If x represents a number picked at random from the set

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Senior Manager
Joined: 27 Feb 2014
Posts: 349
Location: India
GMAT 1: 570 Q49 V20
GPA: 3.97
WE: Engineering (Education)
If x represents a number picked at random from the set  [#permalink]

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18 Feb 2020, 04:17
00:00

Difficulty:

5% (low)

Question Stats:

93% (01:15) correct 7% (01:39) wrong based on 29 sessions

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If x is a number picked at random from the set {-4, −3, −2, −1, 0, 1, 2, 3, 4, 5}, what is the probability that x will satisfy the inequality |x-3| ≤ 2?​

a. 1/6​

b. 1/3​

c. ½​

d. 2/3​

e. 3/4​

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Manager
Joined: 22 Sep 2014
Posts: 157
Location: United States (CA)
Re: If x represents a number picked at random from the set  [#permalink]

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18 Feb 2020, 11:20
x must be :

1<= X <= 5

So 5 numbers out of 10

1/2

Posted from my mobile device
Intern
Joined: 03 Jan 2020
Posts: 40
Re: If x represents a number picked at random from the set  [#permalink]

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22 Feb 2020, 02:22
From the set of 10 numbers in {-4, −3, −2, −1, 0, 1, 2, 3, 4, 5}
The numbers which satisfy |x-3| ≤ 2 are {1,2,3,4,5} ie 5 numbers.

Hence probability= 5/10 =1/2
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3337
Re: If x represents a number picked at random from the set  [#permalink]

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22 Feb 2020, 21:34

Solution

Given
In this question, we are given that
• From the set {-4, −3, −2, −1, 0, 1, 2, 3, 4, 5}, a number x is randomly picked

To find
We need to determine
• The probability that x will satisfy the inequality |x – 3| ≤ 2

Approach and Working out
Simplifying the given inequality first, we get
• |x – 3| ≤ 2
Or, -2 ≤ x – 3 ≤ 2
Or, 1 ≤ x ≤ 5

Satisfying this range, the values present in the given set = 1, 2, 3, 4, 5 (5 values)
Therefore, the required probability = 5/10 = 1/2

Thus, option C is the correct answer.

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Re: If x represents a number picked at random from the set   [#permalink] 22 Feb 2020, 21:34
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