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Math Expert V
Joined: 02 Sep 2009
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How many two-digit numbers are there whose remainder when divided by 1  [#permalink]

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Question Stats: 88% (02:00) correct 12% (02:00) wrong based on 103 sessions

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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

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Re: How many two-digit numbers are there whose remainder when divided by 1  [#permalink]

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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

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GMAT Club Legend  V
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Re: How many two-digit numbers are there whose remainder when divided by 1  [#permalink]

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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.

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Re: How many two-digit numbers are there whose remainder when divided by 1  [#permalink]

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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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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: How many two-digit numbers are there whose remainder when divided by 1   [#permalink] 09 Oct 2019, 20:05
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