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How many twodigit whole numbers yield a remainder of 3 when divided
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04 Dec 2014, 07:40
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Tough and Tricky questions: Geometry. How many twodigit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4? A) One B) Two C) Three D) Four E) Five Kudos for a correct solution.Source: Chili Hot GMAT
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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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04 Dec 2014, 10:54
A whole number is essentially an integer and a two digit whole number is 1099, inclusive. I'm not sure whether we consider positive and negative or just positive. Let's stick to just positives for now.
All positive twodigit integers that leave a remainder of 3 when divided by 10 are: 13, 23, 33, 43, 53, 63, 73, 83 and 93. Of these only the numbers with an even tens digit leave a remainder of 3 when divided by 423, 43, 63 and 83. Answer is 4. I guess that means we don't consider negatives.
Choice D



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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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Updated on: 05 Dec 2014, 00:28
Numbers yield a remainder of 3 when divided by 10. Let x be the number. x= 10m+3 ......... 1
Numbers yield a remainder of 3 when divided by 4. x= 4n+3 .......... 2
combining 1 and 2, x= 20p+3 ....... (20 is the LCM of 10 and 4 and 3 is the first term in the series that satisfies both equations) p can take value of 1,2,3 and 4 to keep x a two digit number. so total numbers = 4
Ans  D



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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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05 Dec 2014, 00:26
Answer = D) Four Numbers giving remainder 3 when divided by 10 = 13, 23, 33, 43, 53, 63, 73, 83, 93 Numbers giving remainder 3 when divided by 4 = Alternate numbers (coloured in red) = 4
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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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05 Dec 2014, 00:27
desaichinmay22 wrote: Numbers yield a remainder of 3 when divided by 10. Let x be the number. x= 10m+3 ......... 1
Numbers yield a remainder of 3 when divided by 4. x= 4n+3 .......... 2
combining 1 and 2, x= 20p+3 ....... (20 is the LCM of 10 and 4 and 3 is the first term in the series that satisfies both equations) p can take value of 0,1,2,3 and 4 to keep x a two digit number. so total numbers = 5
Ans  E If we place p = 0, it will return x = 3 (Single digit number)
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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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05 Dec 2014, 00:29
PareshGmat wrote: desaichinmay22 wrote: Numbers yield a remainder of 3 when divided by 10. Let x be the number. x= 10m+3 ......... 1
Numbers yield a remainder of 3 when divided by 4. x= 4n+3 .......... 2
combining 1 and 2, x= 20p+3 ....... (20 is the LCM of 10 and 4 and 3 is the first term in the series that satisfies both equations) p can take value of 0,1,2,3 and 4 to keep x a two digit number. so total numbers = 5
Ans  E If we place p = 0, it will return x = 3 (Single digit number) Yes.. missed on that... I have corrected the solution



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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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05 Dec 2014, 07:22
Bunuel wrote: Tough and Tricky questions: Geometry. How many twodigit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4? A) One B) Two C) Three D) Four E) Five Kudos for a correct solution.Source: Chili Hot GMAT The correct answer is D.
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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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02 Jan 2015, 01:18
First Of all we could arrange every 2 digit number when we divide by 10 give us reminder 3 . It Is obvious that the number will have 3 in its unit digit so we will have the list of numbers as follows : 13 , 23, 33, 43, 53, 63, 73, 83, and 93...... in this stage we should divide each number by 4 and see which of them yields reminder 3 after dividing by 4 we see here the first number (13) gives us reminder 1 so it is out the second number( 23) gives us reminder 3 so it is OK the third number gives reminder 1 so out and if we continue this action we see the pattern will be repeat again one by one so the even members will give us reminder 3 if we count the even number we see here we have 23 , 43, 63, and 83 so we have 4 number and Option D is fit ...



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How many twodigit whole numbers yield a remainder of 3 when divided
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06 Mar 2017, 14:57
How many twodigit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4?
A) One B) Two C) Three D) Four E) Five
lowest value of n=3 interval between possible values of n=lcm of divisors=20 let x=number of twodigit values of n 3+20x<100 20x<97 x<4.9 x=4 D



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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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07 Mar 2017, 17:18
Bunuel wrote: Tough and Tricky questions: Geometry. How many twodigit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4? A) One B) Two C) Three D) Four E) Five We need to determine how many twodigit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4. Let’s list out the numbers that have a remainder of 3 when divided by 10. Remainder of 3 when divided by 10: 13, 23, 33, 43, 53, 63, 73, 83, 93 Of those numbers, only 23, 43, 63, and 83 leave a remainder of 3 when divided by 4. Alternate Solution: Note that for a number to yield a remainder of 3 when divided by 10, the unit digit must be 3. Note also that for a number to yield a remainder of 3 when divided by 4, three less than that number must be divisible by 4. Combining these two pieces of information, we need to look for twodigit numbers that are divisible by 4 and that have a units digit of zero. These numbers are 20, 40, 60, and 80. Therefore, 23, 43, 63, and 83 are the only twodigit numbers that yield a remainder of 3 when divided by 4 and by 10. Answer: D
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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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15 Mar 2017, 22:51
LCM of 10 and 4 is 20. The only 2digit multiples of 20 are 20,40,60,80. The 2 digit numbers which when divided by 4 and 10 have remainder 3 are thus: 23, 43, 63, 83.
4 in all.
Answer is D.



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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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13 May 2017, 06:43
take the lcm of 4 and 10. which is 20.
now take the first common number from both the patters 10k+3 and 4q+3, which is 3.
now common series is 20n+3 and we will get 0,23,43,63 and 83.
since we have been asked only 2 digit numbers, the answer is 4.
option D is the correct asnwer.



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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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Re: How many twodigit whole numbers yield a remainder of 3 when divided
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