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How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 05:50
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How many positive integers less than 500 begin with a 3, end with a 3, or both? A) 149 B) 150 C) 159 D) 199 E) 200 *kudos for all correct solutions
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How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 09:16
GMATPrepNow wrote: How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149 B) 150 C) 159 D) 199 E) 200
*kudos for all correct solutions Let's see how many start with 3.... Single digit...3 1 2digits ...3039  10 3digits.....300399 100 Total 1+19+100=111 Let's see how many end with 3.... Every tens has one 3.. 3,13,23,33...,9310 Number of tens ... 500/10=50 Numbers repeated above .. those starting and ending with 3 10 in 300s  303,313,...393 33 in 2digits 3 in single digit So total 12 Ans 111+5012=16112=149 A
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Re: How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 11:35
chetan2u Thanks a lot for the easy explanation. I just have a quick question, the no of digits between 30 and 39 that start with 3 would be 10 right? which makes the total 111? Also, there would be one more redundant value in the single digit group which is 3? Is that correct or am I missing something?



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Re: How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 12:03
GMATPrepNow wrote: How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149 B) 150 C) 159 D) 199 E) 200
*kudos for all correct solutions Lets start with single digit numbers, we have only 1 number 3 Now 2 digit numbers we have of the form 3_ & _3 3_ are 10 numbers (30,31,32,33....39) _3 are 9 numbers (13,23,33,.....93) we get 33 in both sets, hence we remove 1 from total of 2 digit numbers, Hence total 2 digit numbers is 18 Now 3 digit numbers, we have of the form 3 _ _ & _ _ 3 3 _ _ are 100 numbers (300,301,302,303,.....399) _ _ 3 are 40 numbers (103,113,....203,213,....303,313,....413,423,...493) we also have numbers of the form 3 _ 3 (303,313,...393) common to both sets, these are 10 such numbers. Hence total 3 digit numbers is 100 + 40 10 = 130 Hence the total numbers of the required form = 1 + 18 + 130 = 149. Answer A. Thanks, GyM Ps. You can also use combinatorics to count the numbers, for e.g. 3 _ _ can be 1*10C1*10C1 = 100 & _ _ 3 can be 4C1*10C1*1 = 40
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How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 12:31
The total number of 3 digit numbers that begin with 3 = 100. The total number of numbers that end with 3 = From 0 to 100  10 From 100 to 200  10 From 200 to 300  10, Excluding all numbers ending with 3 in 300s as already counted. From 400 to 500  10 The total number of numbers beginning with 3 but are 2 digit numbers = 9 (30, 31, 32, 34, 35, 36, 37, 38, 39)  Excluding 33 as was already counted in the ending with 3 section. Total = 100 + 40 + 9 = 149.



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How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 14:31
GMATPrepNow wrote: How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149 B) 150 C) 159 D) 199 E) 200
*kudos for all correct solutions We need to include one digit, twodigit, and threedigit numbers less than 500. 1993 is the only one digit number 3039 are the two digit numbers starting with 3. (Total of 10 numbers) 13,23,43,53,63,73,83,93 are the twodigit numbers ending with 3. (Total of 8 numbers) \(100199\) 113,123,133,143,153,163,173,183,and 193 are the twodigit numbers ending with 3 in this range Similarly, both the ranges 200299 and 400499 have 10 numbers each which end with 3. The range \(300399\) has all the hundred numbers starting with 3(we needn't include those numbers in this range which end with 3 because that would lead to double counting) Therefore, there are a total of \(1 + 8 + 10*4 + 100 = 149\) (Option A) such numbers less than 500.
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How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 14:58
rishabhmail125 wrote: chetan2u Thanks a lot for the easy explanation. I just have a quick question, the no of digits between 30 and 39 that start with 3 would be 10 right? which makes the total 111? Also, there would be one more redundant value in the single digit group which is 3? Is that correct or am I missing something? Yes, rishabhmail125  Your observation is correct. The numbers starting with 3 will include 33 in the list. The total numbers starting with 3 is 111. Also, 3 is part of both the lists. The total numbers which are part of both lists are 12 in number. Therefore, the total numbers(starting with 3, ending with 3, or both) less than 500 are 149(111+5012)
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Re: How many positive integers less than 500 begin with a 3, end with a 3,
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20 Jun 2018, 15:57
rishabhmail125 wrote: chetan2u Thanks a lot for the easy explanation. I just have a quick question, the no of digits between 30 and 39 that start with 3 would be 10 right? which makes the total 111? Also, there would be one more redundant value in the single digit group which is 3? Is that correct or am I missing something? Rishabh, you are absolutely correct.. There was a typo in the post, edited now. There will be 111 positive integers starting with 3 and 50 ending with 3 but 12 common to both so 111+5012=149
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Re: How many positive integers less than 500 begin with a 3, end with a 3,
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22 Jun 2018, 06:15
GMATPrepNow wrote: How many positive integers less than 500 begin with a 3, end with a 3, or both?
A) 149 B) 150 C) 159 D) 199 E) 200
There are 499 integers from 1 to 499 inclusive. Let's determine how many of those 499 integers DO NOT meet the condition of beginning with a 3, ending with a 3, or both 1digit integers that DO NOT begin with a 3, end with a 3, or both1, 2, 4, 5, 6, 7, 8, and 9 TOTAL = 82digit integers that DO NOT begin with a 3, end with a 3, or bothIn the tens position, we can have 1, 2, 4, 5, 6, 7, 8, or 9 ( 8 possibilities) In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 ( 9 possibilities) TOTAL number of 2digit integers that DO NOT begin with a 3, end with a 3, or both = ( 8)( 9) = 723digit integers that DO NOT begin with a 3, end with a 3, or bothIn the hundreds position, we can have 1, 2, or 4 ( 3 possibilities) In the tens position, we can have 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 ( 10 possibilities) In the units position, we can have 0, 1, 2, 4, 5, 6, 7, 8, or 9 ( 9 possibilities) TOTAL number of 3digit integers that DO NOT begin with a 3, end with a 3, or both = ( 3)( 10)( 9) = 270So, the TOTAL number of integers that DO NOT meet the given condition = 8 + 72 + 270 = 350TOTAL number of integers that MEET the given condition So, the = 499  350 = 149 Answer: A Cheers, Brent
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Re: How many positive integers less than 500 begin with a 3, end with a 3,
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