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Re: How many two-digit numbers are there whose remainder when divided by 1
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31 Jan 2016, 12:46
2 digit numbers whose remainder when divided by 10 is 1 are 11 , 21 , 31 , 41 , 51 , 61 , 71 , 81 , 91 Out of above , numbers whose remainder when divided by 6 is 5 are 11 , 41 and 71
Answer A
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Re: How many two-digit numbers are there whose remainder when divided by 1
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28 Aug 2018, 13:42
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Bunuel wrote:
How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5?
A. 3 B. 4 C. 5 D. 6 E. 7
IMPORTANT: When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
Let's start with the second piece of information... The remainder is 5 when the number is divided by 6 So, the possible values are: 5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95,... (we'll stop here, since the questions specifies that the number is a 2-digit number)
The remainder is 1 when the number is divided by 10 So, the possible values are: 1, 11, 21, 31,... Notice this this basically tells us that the number has a UNITS DIGIT of 1
So, go back to examine the first set of possible values: {5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89, 95} 3 values have a UNITS DIGIT of 1
So, there are 3 values that satisfy both conditions. Answer: A
Re: How many two-digit numbers are there whose remainder when divided by 1
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09 Oct 2019, 20:05
1
Bunuel wrote:
How many two-digit numbers are there whose remainder when divided by 10 is 1, and whose remainder when divided by 6 is 5?
A. 3 B. 4 C. 5 D. 6 E. 7
Of all the 2-digit numbers that have a remainder of 1 when divided by 10, only 11, 11 + GCF(6, 10) = 11 + 30 = 41, and 41 + 30 = 71, when divided by 6, yield a remainder of 5.
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88% (02:00) correct 
