GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 Mar 2020, 10:39

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

On writing first 252 positive integers in a straight line, how many ti

  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: 62287
On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 00:24
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

40% (02:15) correct 60% (02:32) wrong based on 40 sessions

HideShow timer Statistics

HEC & IMD School Moderator
User avatar
P
Status: Preparing for GMAT
Joined: 16 Dec 2018
Posts: 828
Location: Italy
Concentration: Leadership, Operations
WE: Engineering (Manufacturing)
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 01:50
1
I do not know the trick for this solution but I counted like this:

From 0-100 -> 9 (leaving 40-49)
100-120 -> 9 (leaving 140-149)
200-252 -> 4 (leaving 240-249)

From (40-49), (140-149) and (240-249) - We get 30 more with '4' at Tens place (40, 41 ... 140, 141 ... 240, 241 ...) + 3 more for Unit place (44, 144 and 244)

in Total, we have - 9 + 9 + 4 + 30 + 3 = 55
I would appreciate a trick :)
_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6057
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 02:14
count the digit 4 values from 1-10 ; 1
10-39 ; 3
40-49;11
50-99; 5
total ; 20
same for 100-199 ; 20
now from 200-252 ; 15
total ; 20+20+15 ; 55
IMO D


On writing first 252 positive integers in a straight line, how many times digit 4 appears?

A. 50
B. 52
C. 54
D. 55
E. 56
Director
Director
avatar
V
Joined: 30 Sep 2017
Posts: 800
GMAT 1: 720 Q49 V40
GPA: 3.8
Premium Member Reviews Badge
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 02:37
1
04,14,24,34, 54,...,94 = 9 nos of 4.
40,41,42,43,44,...,49 = 11 nos of 4.
104,114,124,134, 154,...,194 = 9 nos of 4.
140,141,142,143,144,...,149 = 11 nos of 4.
204,214,224,234 = 4 nos of 4.
240,241,242,243,244,...,249 = 11 nos of 4.

Total 4s = 9+11+9+11+4+11=55 nos

FINAL ANSWER IS (D)

Posted from my mobile device
Intern
Intern
avatar
B
Joined: 02 Jan 2020
Posts: 5
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 05:03
1
To solve the question, I just counted all possible 4's, like from 1 to 100 there are ten 4's. likewise from 100 to 200 there are ten 4's. then there are five 4's between 200 and 252. However, there are the numbers beginning with 4, such as 40, 41, 42,... and 140, 141, 142,... as well as 240, 241, 242,.... These all amount for thirty 4's. Finally, we need to sum all 4's up.
10+10+5+10+10+10=55
Senior Manager
Senior Manager
avatar
G
Joined: 14 Dec 2019
Posts: 460
Location: Poland
GMAT 1: 570 Q41 V27
WE: Engineering (Consumer Electronics)
Premium Member CAT Tests
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 06:03
1
4,14,24,34,40-49,54,64,74,84,94
There is an extra 4 in 44

So total 20 in (1-100), Similarly 20 in (101-200) and 15 in 201-252 => 55

Answer - D
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 902
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 09:11
1
On writing first 252 positive integers in a straight line, how many times digit 4 appears?

A. 50
B. 52
C. 54
D. 55
E. 56

Hundred's place can be taken by three digits i.e. 0,1 and 2.
For 0's and 1's at hundred place possibilities are
2 * 10 * 1 = 20 where 2 is for 0 and 1 and 10 is for 0 to 9
For 2's at hundred place, possibilities are
1 * 5 * 1 = 5

For 4 at tens place possibilities are
3 * 1 * 10 = 30 where 3 is for 0, 1 and 2 at hundred's place and 10 is for 0 to 9 for unit's place

Hence total appearances = 20 + 5 + 30 = 55

Answer D.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Manager
Manager
avatar
B
Joined: 14 Sep 2019
Posts: 220
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 11:05
On writing first 252 positive integers in a straight line, how many times digit 4 appears?

A. 50
B. 52
C. 54
D. 55
E. 56
From 1 to 10 ----------1 times 4
From 11 to 20……….....1 times 4
From 21 to 30 ---------1 times 4
From 31 to 39 ---------1 times 4
From 40 to 49 ---------10 times 4
From 50 to 99 ---------5 times 4

Total 20 times 4 from 1 to 100

In the same way, 20 times 4 from 101 to 200 and
14 times 4 from 201 to 252.
Total 54 times 4 on writing 252 positive integers in a straight line.

Answer: C
VP
VP
avatar
P
Joined: 24 Nov 2016
Posts: 1342
Location: United States
CAT Tests
On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 17:13
1
Quote:
On writing first 252 positive integers in a straight line, how many times digit 4 appears?

A. 50
B. 52
C. 54
D. 55
E. 56


1 to 252;
4 appears?
04,44,94=10+([4]4)=11
104,144,194=10+(1[4]4)=11
204,244=5+(2[4]4)=6
40,49=10-(44)=9
140,149=10-(144)=9
240,249=10-(244)=9
total: 11+11+6+9(3)=55

Ans (D)
Director
Director
avatar
P
Joined: 25 Jul 2018
Posts: 645
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 20 Feb 2020, 23:28
1
001, 002, 003, 004, ... 009, 010.. ... 250, 251, 252

————252 ————
From 1 to 100 —> 20 times digit 4 is used
From 101 to 200 —> 20 times digit 4 is used
From 201 to 252:
—> from 240 to 249 — 11 times
—> 204, 214, 224, 234 —4 times

In total, 20+20+11+4= 55

The answer is D


Posted from my mobile device
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 902
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 21 Feb 2020, 00:27
Leadership wrote:
I do not know the trick for this solution but I counted like this:

From 0-100 -> 9 (leaving 40-49)
100-120 -> 9 (leaving 140-149)
200-252 -> 4 (leaving 240-249)

From (40-49), (140-149) and (240-249) - We get 30 more with '4' at Tens place (40, 41 ... 140, 141 ... 240, 241 ...) + 3 more for Unit place (44, 144 and 244)

in Total, we have - 9 + 9 + 4 + 30 + 3 = 55
I would appreciate a trick :)


I tried one although i can't say that that is a definite one. ;)
See the combinations i did if you are okay with it.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
HEC & IMD School Moderator
User avatar
P
Status: Preparing for GMAT
Joined: 16 Dec 2018
Posts: 828
Location: Italy
Concentration: Leadership, Operations
WE: Engineering (Manufacturing)
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 21 Feb 2020, 01:05
Thank you lnm87 for explanation but I have not understood :lol: Might be your way is correct but P&C are my weaknesses :lol:

lnm87 wrote:
I tried one although i can't say that that is a definite one. ;)
See the combinations i did if you are okay with it.

_________________
Director
Director
User avatar
D
Joined: 07 Mar 2019
Posts: 902
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 21 Feb 2020, 01:39
Leadership wrote:
Thank you lnm87 for explanation but I have not understood :lol: Might be your way is correct but P&C are my weaknesses :lol:

lnm87 wrote:
I tried one although i can't say that that is a definite one. ;)
See the combinations i did if you are okay with it.


A year ago i was in a similar position on P&C but Ron's 'Thursday's with Ron' videos helped.You might have seen them,if not, you must.

I used to run away the moment i saw P&C problem; today the difference is not much - I try to walk away :tongue_opt1 :lol: but not without giving a try.
The catch is, first, more important, the P&C problems are worded in that manner, second counting is involved. If counting is not correct there's no way they can be solved. Its still not that that i solve every &C problem.

In this one, let me know if i can he you.
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8296
Re: On writing first 252 positive integers in a straight line, how many ti  [#permalink]

Show Tags

New post 25 Feb 2020, 22:29
Bunuel wrote:

Competition Mode Question



On writing first 252 positive integers in a straight line, how many times digit 4 appears?

A. 50
B. 52
C. 54
D. 55
E. 56


Are You Up For the Challenge: 700 Level Questions


If you are looking for a method that does not entail looking for each number separately, we can use combination..
Now digit 4 can be at any of the places - tens, units but not hundred as we are counting till 252.

Tens place
Place 4 at tens place --- a4b
Now a or hundreds place can be taken by 0, 1 or 2, so 3 ways
b or units place can take any of the 0-9, so 10 ways
Total - 3*1*10=30 times

units place
Place 4 at units place --- ab4
Now a or hundreds place can be taken by 0, 1 or 2, so 3 ways
b or units place can take any of the 0-9, so 10 ways
Total - 3*1*10=30 times
BUT we have counted till 299 while we had to count only till 252, so minus 254, 264, 274, 284, 294 or 5 numbers, so 30-5=25

Total 30+25=55
_________________
GMAT Club Bot
Re: On writing first 252 positive integers in a straight line, how many ti   [#permalink] 25 Feb 2020, 22:29
Display posts from previous: Sort by

On writing first 252 positive integers in a straight line, how many ti

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





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