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GMAT Official Guide 2019 In a set of 24 cards, each

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by BTGmoderatorDC » Fri Jul 06, 2018 12:41 am

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Answers

A

B

C

D

E

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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
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by GMATGuruNY » Fri Jul 06, 2018 2:03 am
BTGmoderatorDC wrote: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
P = (good outcomes)/(all possible outcomes)

All possible outcomes:
Since there are 24 cards, there are 24 possible outcomes.

Good outcomes:
For a number to be divisible by 2 and 3, it must be a multiple of 6.
Multiples of 6 between 1 and 24, inclusive:
6, 12, 18, 24
For a number to be divisible by 7, it must be a multiple of 7.
Multiples of 7 between 1 and 24, inclusive:
7, 14, 21
Since a good outcome will be yielded by either the 4 blue options or the 3 red options, we get:
Good outcomes = blue options + red options = 4+3 = 7.

Resulting probability:
(good outcomes)/(all possible outcomes) = 7/24.

The correct answer is C.
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by Shahrukh@mbabreakspace » Fri Jul 06, 2018 5:29 am
Total outcomes possible= 24
Favourable outcome= Number divisible by 6(both by 2 and 3) or 7
So, possible multiples of 6 + multiples of 7 - Multiples of 6*7
= 4+3-0=7

So, probablity= 7/24
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by Scott@TargetTestPrep » Sun Jul 22, 2018 5:37 pm
BTGmoderatorDC wrote: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
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: GMAT Official Guide 2019 In a set of 24 cards, each

by Bijaya Krushna Mohapatra » Fri Jan 17, 2020 8:06 pm
from 1 to 24: div by 2 and 3 means divisible by 6 = 6,12,18,24

Div by 7 = 7, 14, 21

So total number div by 2,3 or 7 = 4+3 =7

And total number of cards = 24

So probably = number of success/ total number = 7/24
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