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M19-12

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M19-12 [#permalink]

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51% (01:30) correct 49% (01:30) wrong based on 71 sessions

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An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ?

A. \(\frac{1}{5}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{4}{9}\)
E. \(\frac{1}{2}\)
[Reveal] Spoiler: OA

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Official Solution:

An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at some time between 6:00 and 9:00, what is the probability that he will see the digit 8 ?

A. \(\frac{1}{5}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{4}{9}\)
E. \(\frac{1}{2}\)

The period between 6:00 and 9:00 consists of 180 minutes. During 72 minutes of these 180 the clock will display the digit 8: during 60 minutes of the 8:00-9:00 hour and during 6 minutes of each of the hours 6:00-7:00 and 7:00-8:00 (for example, between 6:00 and 7:00 the clock will show digit 8 only at 06:08, 06:18, 06:28, 06:38, 06:48, and 06:58). The required probability \(= \frac{72}{180} = \frac{2}{5}\).

Answer: C
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Re M19-12 [#permalink]

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New post 22 May 2016, 03:17
I think this is a high-quality question and I agree with explanation. We need to mention " both inclusive" after 6 to 9 in the question ; else denominator may become less than 180 as 6:00 and 9:00 are not included.

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Re M19-12 [#permalink]

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New post 09 Jul 2016, 08:33
I think this is a high-quality question and I agree with explanation. Superb.

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Re: M19-12 [#permalink]

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This question is a good candidate for calculated guessing. From 6:00 to 8:59, at least 1 hour out of the total 3 hours has a 8. So we are looking for a number more than 1/3 or 33%. Hence, options (a) and (b) are out. Options c,d and e translate to 40%, 44% and 50%. Since the number 8 appears very few times in a hour, option (c) must be our best guess.

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Re: M19-12 [#permalink]

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New post 28 Mar 2017, 00:13
hi brunel,

i am unable to understand the point how digit 8 will appear 60 times from time interval 8:00 to 9:00.As per me 8:08 , 8:18 , 8:28 etc will give 8 6 times + 59 times on the hour digit.

kindly clear where i am going wrong

thanks in advance

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Re: M19-12 [#permalink]

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New post 28 Mar 2017, 01:26
sidagar wrote:
hi brunel,

i am unable to understand the point how digit 8 will appear 60 times from time interval 8:00 to 9:00.As per me 8:08 , 8:18 , 8:28 etc will give 8 6 times + 59 times on the hour digit.

kindly clear where i am going wrong

thanks in advance


The probability that he will see the digit 8, does not increase for 8:18, because there are two 8's there. It's still one point in time. Thus 8:18 is still counted once.
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M19-12 [#permalink]

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New post 10 Aug 2017, 11:57
By my math, there are 179 minutes between 6:00 and 9:00. Anyone else getting caught up on that? Yes, it's technical and relatively immaterial.

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Re: M19-12 [#permalink]

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New post 24 Aug 2017, 06:43
Well apparently my rushed mind thinks there are 360 minutes in three hours...

Anyway this is a high quality question.

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Re: M19-12   [#permalink] 24 Aug 2017, 06:43
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