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Math Expert V
Joined: 02 Sep 2009
Posts: 58320
If a and b are the digits of the two-digit number X, what is the remai  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 69% (01:38) correct 31% (01:45) wrong based on 198 sessions

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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.

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Intern  Joined: 01 Nov 2014
Posts: 2
Re: If a and b are the digits of the two-digit number X, what is the remai  [#permalink]

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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.
Intern  Joined: 04 Jul 2014
Posts: 45
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Re: If a and b are the digits of the two-digit number X, what is the remai  [#permalink]

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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.

Manager  Joined: 22 Sep 2012
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Re: If a and b are the digits of the two-digit number X, what is the remai  [#permalink]

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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

D) is the answer
Manager  B
Joined: 17 Jun 2015
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GMAT 1: 540 Q39 V26 GMAT 2: 680 Q46 V37 Re: If a and b are the digits of the two-digit number X, what is the remai  [#permalink]

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Statement 1

This speaks of the numbers 29,38,47,56,65,74,83,92. ALl of them when divided by 9 give the remainder 2,
Hence, Sufficient

Statement 2

X+7 is divisible by 9
This implies X is of the from 9n + 2. Hence remainder 2. Sufficient.

Each statement alone is sufficient. D
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Manager  Joined: 18 Sep 2014
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Re: If a and b are the digits of the two-digit positive integer X, what is  [#permalink]

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If a and b are the digits of the two-digit positive integer X, what is the remainder when X is divided by 9?

(1) a + b = 11

(2) X + 7 is divisible by 9

a+b=11
Say 29,92,38,83,47,74,56,65...Every case has 2 as a remainder when divided by 9...

X+7 is divisible by 9 itself shows that it leaves a remainder...

D is the answer...

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Re: If a and b are the digits of the two-digit positive integer X, what is  [#permalink]

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_________________ Re: If a and b are the digits of the two-digit positive integer X, what is   [#permalink] 24 Feb 2019, 10:49
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