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

It is currently 14 Oct 2019, 01:17

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.

Close

Request Expert Reply

Confirm Cancel

If a 3-digit integer is selected at random from the integers 100 throu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58262
If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 26 Nov 2015, 05:47
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (01:37) correct 20% (01:48) wrong based on 163 sessions

HideShow timer Statistics

Verbal Forum Moderator
User avatar
V
Status: Greatness begins beyond your comfort zone
Joined: 08 Dec 2013
Posts: 2401
Location: India
Concentration: General Management, Strategy
Schools: Kelley '20, ISB '19
GPA: 3.2
WE: Information Technology (Consulting)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 26 Nov 2015, 06:37
1
Hundreds digit has to be 1 . So units digit needs to 1 as well
And both Hundreds and Units digit needs to be 1 more than ten's digit
The number is 101
Total numbers between 100 and 199 = (199-100)+1 = 100

Probability = 1/100

Answer D
_________________
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford
The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long
Manager
Manager
User avatar
Joined: 03 May 2014
Posts: 52
Concentration: Operations, Marketing
GMAT 1: 680 Q48 V34
GMAT 2: 700 Q49 V35
GPA: 3.6
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 26 Nov 2015, 13:32
1
Answer-D
Total number of digits=199-100=99+1=100= Number of outcomes
Numbers which fulfill given criteria= only 1 number=101
Probability= Favourable Outcome/Total number of outcomes= 1/100
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 28 Nov 2015, 20:52
Hi All,

The answer choices to this question provide some significant hints as to the possible outcomes that 'fit' the restrictions mentioned in the prompt.

We're told to consider the integers from 100 to 199, inclusive. That is a group of 100 numbers, so any probability question that is based on that range will have a denominator that is either 100 or reduced from 100. Only Answers D and E fit that pattern. With those answers, we know that there is either one number that fits the restrictions (1/100) or two numbers (2/100 = 1/50).

It's actually not too hard to find the integer that fits the description (since we know that the first digit has to be 1): 101. Since there's no other option, we have the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a 3-digit integer is selected at random from the  [#permalink]

Show Tags

New post 31 Mar 2018, 09:45
Hi ALL,

The question uses the phrase "the first digit and the last digit of the integer are EACH EQUAL to "ONE MORE" than the middle digit." This means that the first and third digits are the SAME digit and that each is ONE MORE than the second digit.

Given the range that we have to work with (101 - 199), the ONLY number that fits this description is "101."

Since there are 100 total numbers in that range, the probability is 1/100

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
User avatar
B
Joined: 15 Aug 2018
Posts: 50
GMAT 1: 740 Q47 V45
GPA: 3.5
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 19 Jan 2019, 09:22
EMPOWERgmatRichC wrote:
Hi ALL,

The question uses the phrase "the first digit and the last digit of the integer are EACH EQUAL to "ONE MORE" than the middle digit." This means that the first and third digits are the SAME digit and that each is ONE MORE than the second digit.

Given the range that we have to work with (101 - 199), the ONLY number that fits this description is "101."

Since there are 100 total numbers in that range, the probability is 1/100

Final Answer:

GMAT assassins aren't born, they're made,
Rich

I don't know if I am the only one, but I think the wording here is very weird... would the GMAC provide such a weird phrasing or is it just me?

Best, gota900
_________________
A kudo a day...
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 19 Jan 2019, 17:29
gota900 wrote:
EMPOWERgmatRichC wrote:
Hi ALL,

The question uses the phrase "the first digit and the last digit of the integer are EACH EQUAL to "ONE MORE" than the middle digit." This means that the first and third digits are the SAME digit and that each is ONE MORE than the second digit.

Given the range that we have to work with (101 - 199), the ONLY number that fits this description is "101."

Since there are 100 total numbers in that range, the probability is 1/100

Final Answer:

GMAT assassins aren't born, they're made,
Rich

I don't know if I am the only one, but I think the wording here is very weird... would the GMAC provide such a weird phrasing or is it just me?

Best, gota900


Hi gota900,

When you approached this prompt, did you interpret the wording differently (and if you did, then what 'result' did you end up with?)? One of the great aspects about Quant questions on the Official GMAT is that they are written so that there is little-to-no chance for "interpretational bias." In simple terms, if you interpret a question in a way that is not correct, then the end result that you get to will NOT be among the 5 choices... meaning that you will then be able to deduce that you misinterpreted something.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
User avatar
B
Joined: 15 Aug 2018
Posts: 50
GMAT 1: 740 Q47 V45
GPA: 3.5
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 20 Jan 2019, 05:35
EMPOWERgmatRichC

Hey Rich,

the prompt says:

If a 3-digit integer is selected at random from the integers 100 through 199, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?

If a 3-digit integer is selected at random from the integers 100 through 199, inclusive

Totally fine. We select a 3-digit integer, which will be a random integer that is located between 100 and 199. No problem so far. I'm cool as a cucumber.

Next bit:

what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?

I underlined everything I have problems with.

What this means to me:

the first digit (needless to say that has to be 1, bc every integer between 100 up to 199 will be in the hundreds, so that's that)

reading on: ... and the last digit are each equal to one or more than the middle digit.

This bit is what gets me confused.

If both have to be equal to one or more than the middle digit , why can't the last digit be 2? or 3? or e.g. 6?

In my understanding, if we had, say, 1X2, then both, the first and the last digit could indeed be 1 OR MORE than the middle digit for the case 102, same would apply to 1X3 and 1X4 and so on...

Nothing in the prompt gives me the definitive information (at least from my point of view) that the first and the last integer should be equal to 1.

Best, gota900
_________________
A kudo a day...
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15240
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 20 Jan 2019, 13:35
Hi gota900,

The prompt does NOT state that the two digits are each "one OR more greater"... it states that those digits are "ONE MORE greater" than the middle digit.

What is "one more" than 0?
If there are 5 people in a room, then what would "one more person" be?
If you have $10, but the shirt you want to buy costs "one more dollar" than that, then what is the cost of the shirt?

In all of these examples, the phrase "one more" clearly means "add 1"... and that same meaning applies to this question.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Manager
Manager
User avatar
B
Joined: 15 Aug 2018
Posts: 50
GMAT 1: 740 Q47 V45
GPA: 3.5
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 21 Jan 2019, 05:36
EMPOWERgmatRichC wrote:
Hi gota900,

The prompt does NOT state that the two digits are each "one OR more greater"... it states that those digits are "ONE MORE greater" than the middle digit.

What is "one more" than 0?
If there are 5 people in a room, then what would "one more person" be?
If you have $10, but the shirt you want to buy costs "one more dollar" than that, then what is the cost of the shirt?

In all of these examples, the phrase "one more" clearly means "add 1"... and that same meaning applies to this question.

GMAT assassins aren't born, they're made,
Rich


Thanks mate!
I must have been too exhausted from the studying... I don't know where I took that OR from :-D

Best, gota900
_________________
A kudo a day...
Senior Manager
Senior Manager
User avatar
P
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 433
Premium Member
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 12 Feb 2019, 07:30
This problem could be made harder in various ways by changing the conditions.

For example, "what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?" In this case, p=10/100 = 1/10 {100, 111, 122, 133 ... 199}

An additional change would be increasing the range to something like 100-399. Now we have more than one possibility for the first digit, set with First=2 would be one less {210, 221, 232 ... 298} and First=3 would be 2 less. p=10+9+8/300 = 27/300 = 9/100. It would be even more cumbersome if the range was something like 100-250 because we'd have a partial set of numbers to choose for 200-250.

Another change would be to ask, "what is the probability that the first digit and the last digit of the integer are equal to two or more than the middle digit?" Now p=45/100= 9/20 {101, 102, 103 ... 109} {112, 113, 114 ... 119} etc. Each time First increases by 1 the number of possibilities is reduced by 1, so 9+8+7...+1. You could change the range here too and make it more calculation intensive.

EMPOWERgmatRichC Hope that's all correct.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8040
Location: United States (CA)
Re: If a 3-digit integer is selected at random from the integers 100 throu  [#permalink]

Show Tags

New post 13 Feb 2019, 20:16
Bunuel wrote:
If a 3-digit integer is selected at random from the integers 100 through 199, inclusive, what is the probability that the first digit and the last digit of the integer are each equal to one more than the middle digit?

(A) 2/225
(B) 1/111
(C) 1/110
(D) 1/100
(E) 1/50


Since the first digit (the hundreds digit) must be 1, the second digit (the tens digit) must be 0 and the third digit (the ones digit) must be 1. That is, the number must be 101. The probability of selecting one number (101) from 100 numbers (100 through 199, inclusive) is 1/100.

Answer: D
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If a 3-digit integer is selected at random from the integers 100 throu   [#permalink] 13 Feb 2019, 20:16
Display posts from previous: Sort by

If a 3-digit integer is selected at random from the integers 100 throu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne