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

 It is currently 22 Mar 2019, 15:31

### 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

# If a bowl contains numbered tiles labeled with integers from 1 – 100,

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53792
If a bowl contains numbered tiles labeled with integers from 1 – 100,  [#permalink]

### Show Tags

31 Jan 2017, 09:58
00:00

Difficulty:

35% (medium)

Question Stats:

65% (01:14) correct 35% (01:01) wrong based on 110 sessions

### HideShow timer Statistics

If a bowl contains numbered tiles labeled with integers from 1 – 100, inclusive, what is the probability of selecting a tile with a three on it?

A. 1/5
B. 19/101
C. 19/100
D. 1/10
E. 1/100

_________________
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: If a bowl contains numbered tiles labeled with integers from 1 – 100,  [#permalink]

### Show Tags

31 Jan 2017, 10:59
Bunuel wrote:
If a bowl contains numbered tiles labeled with integers from 1 – 100, inclusive, what is the probability of selecting a tile with a three on it?

A. 1/5
B. 19/101
C. 19/100
D. 1/10
E. 1/100

Total # of tiles = 100

1 - 9 - one (3)
10 - 19 - one (13)
20 - 29 - 1
30 - 39 - all 10
40 - 49 - 1
...
90 - 100 - 1

All clusters of 10 (with exception of 30's) has one number with 3 (3 or X3). In the case of 30's we have all 10 numbers with 3 (9 with one 3 and one with two 3's - 33).

Our probability = (9 + 10/ 100 = 19/100

Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 132
If a bowl contains numbered tiles labeled with integers from 1 – 100,  [#permalink]

### Show Tags

Updated on: 19 Feb 2019, 07:05
There's 2 Cases for getting a 3:
1) 3 in units digit {03, 13, 23, 33, 43 ... 93} = 10 ways
2) 3 in tens digit: {31, 32, 33, 34 ... 39} 9 ways, remove 33 as it repeats

10+9 = 19/100

Originally posted by energetics on 18 Feb 2019, 11:10.
Last edited by energetics on 19 Feb 2019, 07:05, edited 1 time in total.
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2722
Re: If a bowl contains numbered tiles labeled with integers from 1 – 100,  [#permalink]

### Show Tags

18 Feb 2019, 19:24

Solution

Given:
• A bowl contains numbered tiles labelled with integers from 1 to 100, inclusive.

To find:
• The probability of selecting a tile with a three on it

Approach and Working:
In the range between 1 to 100, inclusive, we have either 1-digit numbers or 2-digit numbers of 3-digit number.

Considering all the 1-digit numbers,
• Number of numbers with the digit 3 = 1

Considering all the 2-digit numbers,
• Number of numbers with digit 3 only in the units place = 8 (13, 23, 43, 53, 63, 73, 83, 93)
• Number of numbers with digit 3 only in the tens place = 9 (30, 31, 32, 34, 35, 36, 37, 38, 39)
• Number of numbers with digit 3 in both units and tens place = 1 (33)

Considering all the 3-digit numbers, there is no such number in the given range with the digit 3.

So, total number of instances = 1 + 8 + 9 + 1 = 19
Therefore, the required probability = $$\frac{19}{100}$$

Hence, the correct answer is option C.

_________________

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

Re: If a bowl contains numbered tiles labeled with integers from 1 – 100,   [#permalink] 18 Feb 2019, 19:24
Display posts from previous: Sort by