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11 Nov 2014, 06:02
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:45) correct
31%
(01:52)
wrong
based on 394
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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
(1) a + b = 11
(2) X + 7 is divisible by 9
11 Nov 2014, 06:29
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Answer should be Option D: Either Statement is enough.
It can be determined by using a simple rule - the digits of a number divisible by nine add up to 9.
Statement 1: a + b = 11. It means that X - 2 would be divisible by 9. And remainder for X divided by 9 should be 2.
Statement 2: X + 7 is divisible by 9. It means that X - 2 is also divisible by 9 => Remainder for x divided by 9 is 2.
So, both statement 1 alone and statement 2 alone is sufficient to answer the question.
It can be determined by using a simple rule - the digits of a number divisible by nine add up to 9.
Statement 1: a + b = 11. It means that X - 2 would be divisible by 9. And remainder for X divided by 9 should be 2.
Statement 2: X + 7 is divisible by 9. It means that X - 2 is also divisible by 9 => Remainder for x divided by 9 is 2.
So, both statement 1 alone and statement 2 alone is sufficient to answer the question.
General Discussion
14 Nov 2014, 00:58
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Bunuel
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.
Hence Answer D.
