GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Sep 2018, 07:53

### 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

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

# A certain circular stopwatch has exactly 60-second marks and a single

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49320
A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 21:34
00:00

Difficulty:

75% (hard)

Question Stats:

33% (02:12) correct 68% (01:58) wrong based on 39 sessions

### HideShow timer Statistics

A certain circular stopwatch has exactly 60-second marks and a single hand. If the hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds, what is the probability that the hand will stop less than 10 marks from the 53-second mark?

A. $$\frac{1}{6}$$

B. $$\frac{19}{60}$$

C. $$\frac{1}{3}$$

D. $$\frac{29}{60}$$

E. $$\frac{1}{2}$$

_________________
Senior Manager
Joined: 14 Dec 2017
Posts: 478
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 22:49
Bunuel wrote:
A certain circular stopwatch has exactly 60-second marks and a single hand. If the hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds, what is the probability that the hand will stop less than 10 marks from the 53-second mark?

A. $$\frac{1}{6}$$

B. $$\frac{19}{60}$$

C. $$\frac{1}{3}$$

D. $$\frac{29}{60}$$

E. $$\frac{1}{2}$$

Less than 10 marks from the 53-second mark, means the hand stops at {53, 52, 51, 50, 49, 48, 47, 46, 45, 44}

Since the hand is allowed to move exactly 10 marks from its starting position, hence the starting positions can be {43, 42, 41, 40, 39, 38, 37, 36, 35, 34}

Hence we have 10 available marks out of 60 marks.

Required Probability = 10/60 = 1/6

Thanks,
GyM
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 23:11

Solution

Given:
• A certain circular stopwatch has exactly 60-second marks and a single hand
• The hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds

To find:
• The probability that the hand will stop less than 10 marks from the 53-second mark

Approach and Working:
Considering less than 10 marks from 53, we have two limits to consider
• More than 43
• Less than 3

Therefore, the possible values are = 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 00, 01, and 02 = total 19 favourable cases
• The probability = $$\frac{19}{60}$$

We can count the favourable cases in other way:
From 43 to 03, total cases excluding both = 20 – 1 = 19

Hence, the correct answer is option B.

_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior Manager
Joined: 14 Dec 2017
Posts: 478
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 23:30
EgmatQuantExpert wrote:

Solution

Given:
• A certain circular stopwatch has exactly 60-second marks and a single hand
• The hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds

To find:
• The probability that the hand will stop less than 10 marks from the 53-second mark

Approach and Working:
Considering less than 10 marks from 53, we have two limits to consider
• More than 43
• Less than 3

Therefore, the possible values are = 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 00, 01, and 02 = total 19 favourable cases
• The probability = $$\frac{19}{60}$$

We can count the favourable cases in other way:
From 43 to 03, total cases excluding both = 20 – 1 = 19

Hence, the correct answer is option B.

Is there a stopwatch that goes in anti-clockwise direction as well?

On the GMAT, are we supposed to be strictly literal about whats specifically mentioned or are we at liberty to use normal logic, for normal everyday items?

Thanks,
GyM
_________________
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2014
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 23:34
1
GyMrAT wrote:
Is there a stopwatch that goes in anti-clockwise direction as well?

On the GMAT, are we supposed to be strictly literal about whats specifically mentioned or are we at liberty to use normal logic, for normal everyday items?

Thanks,
GyM

We are not assuming anti-clockwise movement. Assume that you are starting to count from 54 only - then also it can stop anywhere between 54 and 2, making a situation where the hand is in less than 10 marks from 53.
_________________

Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Math Expert
Joined: 02 Aug 2009
Posts: 6799
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 23:41
2
1
Bunuel wrote:
A certain circular stopwatch has exactly 60-second marks and a single hand. If the hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds, what is the probability that the hand will stop less than 10 marks from the 53-second mark?

A. $$\frac{1}{6}$$

B. $$\frac{19}{60}$$

C. $$\frac{1}{3}$$

D. $$\frac{29}{60}$$

E. $$\frac{1}{2}$$

Seems it is a Kaplan question and the wording is a bit confusing..
1) Easy to infer that " the hand will stop less than 10 marks from the 53-second mark " and then answer will be 43 to 53 = 10 as also solved by GyMrAT

2) But here it seems to be trying to say " WITHIN 10 marks from 53-second mark"
so two cases
a) TEN below 53 that is 43 to 53 and
b) TEN above 53 that is 53 to 63 (or 03)

ans $$10+10-1=19....$$ MINUS 1 is because 53 is common in both the list
so probability = $$\frac{19}{60}$$

B

Bunuel, I know although the original question says "10 marks LESS than", the question would be better saying " WITHIN 10 marks from"
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Senior Manager
Joined: 14 Dec 2017
Posts: 478
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 23:42
EgmatQuantExpert wrote:
GyMrAT wrote:
Is there a stopwatch that goes in anti-clockwise direction as well?

On the GMAT, are we supposed to be strictly literal about whats specifically mentioned or are we at liberty to use normal logic, for normal everyday items?

Thanks,
GyM

We are not assuming anti-clockwise movement. Assume that you are starting to count from 54 only - then also it can stop anywhere between 54 and 2, making a situation where the hand is in less than 10 marks from 53.

Ahhh! got it!!

Thanks,
GyM
_________________
Senior Manager
Joined: 14 Dec 2017
Posts: 478
Re: A certain circular stopwatch has exactly 60-second marks and a single  [#permalink]

### Show Tags

08 Jul 2018, 23:45
chetan2u wrote:
Bunuel wrote:
A certain circular stopwatch has exactly 60-second marks and a single hand. If the hand of the watch is randomly set to one of the marks and allowed to count exactly 10 seconds, what is the probability that the hand will stop less than 10 marks from the 53-second mark?

A. $$\frac{1}{6}$$

B. $$\frac{19}{60}$$

C. $$\frac{1}{3}$$

D. $$\frac{29}{60}$$

E. $$\frac{1}{2}$$

Seems it is a Kaplan question and the wording is a bit confusing..
1) Easy to infer that " the hand will stop less than 10 marks from the 53-second mark " and then answer will be 43 to 53 = 10 as also solved by GyMrAT

2) But here it seems to be trying to say " WITHIN 10 marks from 53-second mark"
so two cases
a) TEN below 53 that is 43 to 53 and
b) TEN above 53 that is 53 to 63 (or 03)

ans $$10+10-1=19....$$ MINUS 1 is because 53 is common in both the list
so probability = $$\frac{19}{60}$$

B

Bunuel, I know although the original question says "10 marks LESS than", the question would be better saying " WITHIN 10 marks from"

Nice Explanation!! I agree "within" will be more clear.

Thanks,
GyM
_________________
Re: A certain circular stopwatch has exactly 60-second marks and a single &nbs [#permalink] 08 Jul 2018, 23:45
Display posts from previous: Sort by

# A certain circular stopwatch has exactly 60-second marks and a single

## Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.