Last visit was: 19 Sep 2024, 23:34 It is currently 19 Sep 2024, 23:34
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A reality show has four answer choices for each question - A, B, C, an

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
S
Abhibarua
Joined: 31 Jan 2021
Posts: 45
Own Kudos [?]: 35 [3]
Given Kudos: 99
Location: Bangladesh
GMAT 1: 760 Q50 V44
Send PM
A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   Updated on: 25 Jul 2021, 05:54
3
Bookmarks
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

13% (01:43) correct 87% (01:31) wrong based on 87 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
A show has four answer choices for each question - A, B, C, and D. The participant, John, correctly knows that the right answer is either A or D. The show has a '50:50' option by using which participants can eliminate two wrong answer choices. What is the probability that John uses the '50:50' option and is still left with both A and D?

A. 1/2
B. 1/3
C. 1/4
D. 1/5
E. 1/ 6
ShowHide Answer
Official Answer
B

Originally posted by Abhibarua on 24 Jun 2021, 04:24.
Last edited by Abhibarua on 25 Jul 2021, 05:54, edited 2 times in total.
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9624 [1]
Given Kudos: 96
 Q51  V47
Send PM
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   24 Jun 2021, 05:23
1
Kudos
Expert Reply
Abhibarua
A reality show has four answer choices for each question - A, B, C, and D. The participant, John, correctly knows that the right answer is between A and D. The show has a '50:50' option by using which participants can eliminate two wrong answer choices. What is the probability that John uses the '50:50' option and is still left with answer choices A and D?

A. 1/4
B. 1/5
C. 1/6
D. 1/10
E. 1/ 12

This is a good question concept, but there are several problems with the question as written. Most importantly, the right answer isn't among the choices. When the game show eliminates two answers, it must eliminate two of the three wrong answers. So it must leave one of the three wrong answers 'on the board'. So there's a 1/3 chance they'll leave up the wrong answer John is worried about, and a 2/3 chance they'll leave up one of the other two wrong answers, and the answer is 1/3. If that's a bit conceptual, you can imagine that the right answer is actually A. Then the game show is obligated to leave exactly one of B, C or D on the board, so there's a 1/3 chance they leave D up. The same is true when the right answer is D; then there is a 1/3 chance they leave A up. So no matter what answer is right, there's a 1/3 chance A and D are still available after the 50-50 is used.

But I think the question means to describe a "game show" (not a "reality show") and they really shouldn't say "between A and D" after listing the options in order. If we say "x is an integer between 1 and 4", we mean "x is either 2 or 3". We do not mean "x is one of the two numbers 1 or 4", but that is (I assume) the intended meaning in this question. What is the source?
avatar
S
Abhibarua
Joined: 31 Jan 2021
Posts: 45
Own Kudos [?]: 35 [0]
Given Kudos: 99
Location: Bangladesh
GMAT 1: 760 Q50 V44
Send PM
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   25 Jul 2021, 04:55
IanStewart
Abhibarua
A reality show has four answer choices for each question - A, B, C, and D. The participant, John, correctly knows that the right answer is between A and D. The show has a '50:50' option by using which participants can eliminate two wrong answer choices. What is the probability that John uses the '50:50' option and is still left with answer choices A and D?

A. 1/4
B. 1/5
C. 1/6
D. 1/10
E. 1/ 12

This is a good question concept, but there are several problems with the question as written. Most importantly, the right answer isn't among the choices. When the game show eliminates two answers, it must eliminate two of the three wrong answers. So it must leave one of the three wrong answers 'on the board'. So there's a 1/3 chance they'll leave up the wrong answer John is worried about, and a 2/3 chance they'll leave up one of the other two wrong answers, and the answer is 1/3. If that's a bit conceptual, you can imagine that the right answer is actually A. Then the game show is obligated to leave exactly one of B, C or D on the board, so there's a 1/3 chance they leave D up. The same is true when the right answer is D; then there is a 1/3 chance they leave A up. So no matter what answer is right, there's a 1/3 chance A and D are still available after the 50-50 is used.

But I think the question means to describe a "game show" (not a "reality show") and they really shouldn't say "between A and D" after listing the options in order. If we say "x is an integer between 1 and 4", we mean "x is either 2 or 3". We do not mean "x is one of the two numbers 1 or 4", but that is (I assume) the intended meaning in this question. What is the source?

Thanks for your feedback. I edited the question for better clarity.
avatar
S
Abhibarua
Joined: 31 Jan 2021
Posts: 45
Own Kudos [?]: 35 [1]
Given Kudos: 99
Location: Bangladesh
GMAT 1: 760 Q50 V44
Send PM
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   25 Jul 2021, 05:12
1
Kudos
Abhibarua
A show has four answer choices for each question - A, B, C, and D. The participant, John, correctly knows that the right answer is either A or D. The show has a '50:50' option by using which participants can eliminate two wrong answer choices. What is the probability that John uses the '50:50' option and is still left with both A and D?

A. 1/4
B. 1/5
C. 1/6
D. 1/10
E. 1/ 12

There are 6 ways to pick 2 from 4 answer choices [4!/(2!*2!)].

These six combinations are AB, AC, AD, BC, BD, CD. However, BC is not an allowed combination because it does not contain the right answer, which is either A or D.

So, the number of desired outcomes (AD) = 1

the number of possible outcomes = 5

So, the probability that John uses the '50:50' option and is still left with both A and D = 1/5 [Option: B]
User avatar
L
IanStewart
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4127
Own Kudos [?]: 9624 [0]
Given Kudos: 96
 Q51  V47
Send PM
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   25 Jul 2021, 05:32
Expert Reply
Abhibarua
There are 6 ways to pick 2 from 4 answer choices [4!/(2!*2!)].

These six combinations are AB, AC, AD, BC, BD, CD. However, BC is not an allowed combination because it does not contain the right answer, which is either A or D.

So, the number of desired outcomes (AD) = 1

the number of possible outcomes = 5

So, the probability that John uses the '50:50' option and is still left with both A and D = 1/5 [Option: B]

That solution is not correct. It's true that BC cannot be the remaining two answers. But when the correct answer is A, it is also true that BD and CD cannot be the remaining two answers. And when the correct answer is D, then AB and AC cannot be the two remaining answers. You haven't accounted for that anywhere.

The game show is obligated to leave the right answer available after the 50-50 is used. The game show is always choosing 2 wrong answers from the 3 wrong answers to the question. So from the game show's point of view, when it randomly eliminates two wrong answers, it doesn't have six choices. It only has three choices (3C2 = 3).
avatar
S
Abhibarua
Joined: 31 Jan 2021
Posts: 45
Own Kudos [?]: 35 [0]
Given Kudos: 99
Location: Bangladesh
GMAT 1: 760 Q50 V44
Send PM
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   25 Jul 2021, 05:53
IanStewart
Abhibarua
There are 6 ways to pick 2 from 4 answer choices [4!/(2!*2!)].

These six combinations are AB, AC, AD, BC, BD, CD. However, BC is not an allowed combination because it does not contain the right answer, which is either A or D.

So, the number of desired outcomes (AD) = 1

the number of possible outcomes = 5

So, the probability that John uses the '50:50' option and is still left with both A and D = 1/5 [Option: B]

That solution is not correct. It's true that BC cannot be the remaining two answers. But when the correct answer is A, it is also true that BD and CD cannot be the remaining two answers. And when the correct answer is D, then AB and AC cannot be the two remaining answers. You haven't accounted for that anywhere.

The game show is obligated to leave the right answer available after the 50-50 is used. The game show is always choosing 2 wrong answers from the 3 wrong answers to the question. So from the game show's point of view, when it randomly eliminates two wrong answers, it doesn't have six choices. It only has three choices (3C2 = 3).

You are right. After the '50:50', the answer choices can only have 3 possible combinations. (1 way to choose the right answer * 3 ways to choose 1 from 3 wrong answers) [1 * (3!/1!*2!)]

For example, if the right answer is A, the possible combinations are AB, AC, and AD.
If the right answer is D, the possible combinations are AD, BD, CD.

Either way, the number of desired outcomes (AD) is 1 and the number of possible outcomes is 3. So the probability should be 1/3.

Thanks again.
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5367
Own Kudos [?]: 4383 [2]
Given Kudos: 161
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink] A reality show has four answer choices for each question - A, B, C, an   25 Jul 2021, 08:57
2
Kudos
Given: A show has four answer choices for each question - A, B, C, and D. The participant, John, correctly knows that the right answer is either A or D. The show has a '50:50' option by using which participants can eliminate two wrong answer choices.
Asked: What is the probability that John uses the '50:50' option and is still left with both A and D?

There is exactly 1 correct answer choice and 3 incorrect answer choices.
Answer choices B & C are incorrect.
Right answer is either A or D.

Selecting 2 out of 3 incorrect answer choices: -
Total ways = 3C2 = 3
Favorable ways = 1
The probability that John uses the '50:50' option and is still left with both A and D = 1/3

IMO B
GMAT Club Bot
gmatclubot
Re: A reality show has four answer choices for each question - A, B, C, an [#permalink]
25 Jul 2021, 08:57
Moderator:
Bunuel
Math Expert
95674 posts