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On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 00:24
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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
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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 01:50
I do not know the trick for this solution but I counted like this: From 0100 > 9 (leaving 4049) 100120 > 9 (leaving 140149) 200252 > 4 (leaving 240249) From (4049), (140149) and (240249)  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
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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 02:14
count the digit 4 values from 110 ; 1 1039 ; 3 4049;11 5099; 5 total ; 20 same for 100199 ; 20 now from 200252 ; 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



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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 02:37
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)
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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 05:03
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



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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 06:03
4,14,24,34,4049,54,64,74,84,94 There is an extra 4 in 44
So total 20 in (1100), Similarly 20 in (101200) and 15 in 201252 => 55
Answer  D



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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 09:11
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.
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Re: On writing first 252 positive integers in a straight line, how many ti
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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



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On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 17:13
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)



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Re: On writing first 252 positive integers in a straight line, how many ti
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20 Feb 2020, 23:28
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
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Re: On writing first 252 positive integers in a straight line, how many ti
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21 Feb 2020, 00:27
Leadership wrote: I do not know the trick for this solution but I counted like this: From 0100 > 9 (leaving 4049) 100120 > 9 (leaving 140149) 200252 > 4 (leaving 240249) From (4049), (140149) and (240249)  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.
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Re: On writing first 252 positive integers in a straight line, how many ti
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21 Feb 2020, 01:05
Thank you lnm87 for explanation but I have not understood Might be your way is correct but P&C are my weaknesses 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.
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Re: On writing first 252 positive integers in a straight line, how many ti
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21 Feb 2020, 01:39
Leadership wrote: Thank you lnm87 for explanation but I have not understood Might be your way is correct but P&C are my weaknesses 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 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.
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Re: On writing first 252 positive integers in a straight line, how many ti
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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 QuestionsIf 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 placePlace 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 09, so 10 ways Total  3*1*10=30 times units placePlace 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 09, 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 305=25 Total 30+25=55
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Re: On writing first 252 positive integers in a straight line, how many ti
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