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In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24.

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by BTGModeratorVI » Thu Jul 23, 2020 6:30 am

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C

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Difficulty—

In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7 ?

A. 3/24

B. 4/24

C. 7/24

D. 8/24

E. 17/24

Answer: C
Source: Official guide
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Re: In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24.

by Scott@TargetTestPrep » Sun Jul 26, 2020 9:03 am
BTGModeratorVI wrote: ↑
Thu Jul 23, 2020 6:30 am
 In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7 ?

A. 3/24

B. 4/24

C. 7/24

D. 8/24

E. 17/24

Answer: C
Source: Official guide
Solution:

The numbers that are divisible by both 2 and 3 are 6, 12, 18, and 24.

The numbers that are divisible by 7 are 7, 14, and 21.

So the probability is 7/24.

Answer: C

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Re: In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24.

by Brent@GMATPrepNow » Mon Jul 27, 2020 5:53 am
BTGModeratorVI wrote: ↑
Thu Jul 23, 2020 6:30 am
 In a set of 24 cards, each card is numbered with a different positive integer from 1 to 24. One card will be drawn at random from the set. What is the probability that the card drawn will have either a number that is divisible by both 2 and 3 or a number that is divisible by 7 ?

A. 3/24

B. 4/24

C. 7/24

D. 8/24

E. 17/24

Answer: C
Source: Official guide
P(event) = (number of outcomes that meet the given condition)/(total number of possible outcomes)

So, P(selected number is divisible by both 2 and 3 OR is divisible by 7) = number of integers that are divisible by both 2 and 3 OR are divisible by 7/24

number of integers that are divisible by both 2 and 3 OR are divisible by 7
The integers that meet this condition are: 6, 7, 12, 14, 18, 21, 24
There are 7 such numbers

So, P(selected number is divisible by both 2 and 3 OR is divisible by 7) = 7/24

Answer: C

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Brent Hanneson - Creator of GMATPrepNow.com
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