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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
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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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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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Hello from the GMAT Club BumpBot!

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