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Difficulty:
15%
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Question Stats:
84% (01:23) correct
16%
(02:06)
wrong
based on 74
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A bag contains 185 cards: 160 “Try Again” cards and 25 “Winner” cards. How many “Try Again” cards must be removed for the probability of selecting a “Winner” card among 25 such cards to be 1/6?
(A) 35
(B) 40
(C) 42
(D) 48
(E) 64
(A) 35
(B) 40
(C) 42
(D) 48
(E) 64
yashikaaggarwal
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The no. of "Try Again" cards to be removed such that \(\frac{Winner}{Winner + Try Again}\) cards become\(\frac{1}{6}\)
\(\frac{Winner}{Winner + Try Again}\)= \(\frac{1}{6}\)
\(\frac{25}{25 + Try Again cards}\) = \(\frac{1}{6}\)
150 = 25 + Try Again cards
125 = Try Again cards
Existing Try Again Cards = 160
Needed Try Again Cards = 125
Try Again Cards to be removed = 160 - 125 = 35
Answer is A
_________________
\(\frac{Winner}{Winner + Try Again}\)= \(\frac{1}{6}\)
\(\frac{25}{25 + Try Again cards}\) = \(\frac{1}{6}\)
150 = 25 + Try Again cards
125 = Try Again cards
Existing Try Again Cards = 160
Needed Try Again Cards = 125
Try Again Cards to be removed = 160 - 125 = 35
Answer is A
_________________
Quote:
For the probability to be 1/6th, 25 must be 1/6th of the total number of cards, i.e., total number of cards including the winner cards has to be 6*25 = 150.
Given the total number of cards - 185
Required Total number of cards - 150
Cards of Try Again to be removed - 35. A is the answer
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25/x=1/6
x=150
185-150= 35
IMO A
Posted from my mobile device
x=150
185-150= 35
IMO A
Posted from my mobile device
IanStewart
Expert
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 09 Sep 2026
Posts: 4,146
Location: United States
GMAT 1: 780 Q51 V47
Expert reply
GMAT 1: 780 Q51 V47
Posts: 4,146
The language is really confusing - when it says "the probability of selecting a “Winner” card among 25 such cards", it sounds like we're picking from a total of 25 cards. We're not. What is the source?
We want to arrive at a situation where the ratio of Winner to Non-winner cards is 1 to 5 (for a 1/6 probability). So with 25 winner cards, we want 125 non-winner cards, and to get that, we must remove 35 non-winner cards.
_________________
We want to arrive at a situation where the ratio of Winner to Non-winner cards is 1 to 5 (for a 1/6 probability). So with 25 winner cards, we want 125 non-winner cards, and to get that, we must remove 35 non-winner cards.
_________________
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