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How many twodigit numbers yield a remainder of 1 when divided by both
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23 Jul 2015, 23:53
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66% (01:35) correct 34% (01:48) wrong based on 192 sessions
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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24 Jul 2015, 01:21
Bunuel wrote: How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. Solution  In order to divide both 4 and 14 by a number, the number must be divisible by their least common multiple, which is 28. Twodigit multiple of 28 are 28, 56, and 84. The numbers that have remainder 1 when divided by 4 and 14 are 29, 57, or 85. ANS D.
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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24 Jul 2015, 02:54
Bunuel wrote: How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. Easier to start with numbers that are of the form 14p+1 > 15,29,43,57,71,85,99. Out of these 3 (29,57,85) are also of the form 4q+1. Thus 3 is the answer. D is the correct answer.



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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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24 Jul 2015, 04:16
2 digit numbers that are multiples of 14 are 14,28,42,56,70,84,98. So, there are 7 numbers, viz., 15, 29, 43, 57, 71, 85, 99 that would give a remainder of 1 when divided by 14. Multiples of 14 that are also multiples of 4 are 28, 56, 84. So, there are 3 such numbers, viz., 29, 57, and 85. Ans (D).
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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24 Jul 2015, 05:48
Bunuel wrote: How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. the correct method would be to find LCM and then add 1 to LCM, 2*LCM, and so on LCM of 4 &14=28.. first required number=29, next 2*28+1 and third 3*28+1... thereafter it will be a 3 digit number so ans 3 D
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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24 Jul 2015, 07:01
Bunuel wrote: How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. LCM of 4 & 14 is 28, hence 1st 2digit no. which yields rem. of 1 when divided by both 4 & 14 is 28+1 = 29 2nd no. would be 28*2 +1 = 57 this is of the form 28k+1, where k is an integer and k>0 hence, for k = 1, 28k+1 = 29 k = 2, = 57 k = 3, = 85 k = 4, = 113......we will stop here as this is now 3 digits, hence total 2digit nos. are 3 And. D
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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26 Jul 2015, 11:18
Bunuel wrote: How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. 800score Official Solution:Let’s use n to denote a twodigit number that fits the requirement in the question. Since we are looking for a remainder of 1 when n is divided by 4 or 14, then (n – 1) must be divisible by both 4 and 14. All numbers divisible by both 4 and 14 must be divisible by their least common multiple, which is 28. So n – 1 can equal any twodigit multiple of 28. These possible values are: n – 1 = 28, 56, or 84. Therefore, n = 29, 57, or 85 (3 different twodigit numbers). The correct answer is choice (D).
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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26 Jul 2015, 21:18
Bunuel wrote: Bunuel wrote: How many twodigit numbers yield a remainder of 1 when divided by both 4 and 14?
A. 0 B. 1 C. 2 D. 3 E. 4
Kudos for a correct solution. 800score Official Solution:Let’s use n to denote a twodigit number that fits the requirement in the question. Since we are looking for a remainder of 1 when n is divided by 4 or 14, then (n – 1) must be divisible by both 4 and 14. All numbers divisible by both 4 and 14 must be divisible by their least common multiple, which is 28. So n – 1 can equal any twodigit multiple of 28. These possible values are: n – 1 = 28, 56, or 84. Therefore, n = 29, 57, or 85 (3 different twodigit numbers). The correct answer is choice (D).Thanks Bunuel, this is more smarter way!
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Re: How many twodigit numbers yield a remainder of 1 when divided by both
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27 Jul 2015, 05:57
LCM (4, 14) =28 two digit multiple of 28 are 28, 56 and 84 two digits numbers that yield remainder of 1 when divisible by 4 and 14 are 28+1, 56+1 and 84+1 ans: D
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