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Re: If a and b are the digits of the two-digit number X, what is the remai
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14 Nov 2014, 00:58
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Bunuel wrote:
Tough and Tricky questions: Remainders.
If a and b are the digits of the two-digit number X, what is the remainder when X is divided by 9?
(1) a + b = 11
(2) X + 7 is divisible by 9
Kudos for a correct solution.
The digits of the two digit number is a & b. But we are not given the info about which digit is unit's digit & which digit is ten's digit. Hence the number can be of the form 'ab' or 'ba'.
Now moving on to the statements...
S1 : a+b = 11. Since both a & b can only be single digit numbers [ab/ ba is a two digit no.] ..the combinations possible are (2,9); (3,8); (4,7); (5,6); (6,5); .....(9,2). We could see that in all these cases the reminder is '2' [i.e. 29/9 -> rem 2 ; 38/9 -> rem 2 ; 92/9 -> rem 2 etc]. Hence S1 sufficient.
S2 : X+7 is divisible by 9 ....if x+7=63 , X=56 which when divided by 9 gives reminder 2 ; If x+7=27 , x=20...again reminder 2...therefore for value X takes reminder is 2. Hence S2 is sufficient.
Re: If a and b are the digits of the two-digit number X, what is the remai
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15 Nov 2014, 21:49
Statement 1: a + b = 11 The number can be represented by = 10*a +b or, 9*a +(a+b) 9*a is a multiple of 9, therefore the remainder of a+b divided by 9 gives the remainder of the number ab, which is 2 . Sufficient
Statement 2: X + 7 is divisible by 9 X can be represented as = 9*a + r [Where r is the remainder when X is divided by 9] Since X + 7 is divisible by 9, we can say that r+7 is also divisible by 9, for which r has to be 2. Sufficient
Re: If a and b are the digits of the two-digit positive integer X, what is
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24 Feb 2019, 10:49
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