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If a and b are the digits of the two-digit number X, what is

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by BTGmoderatorDC » Sun Sep 01, 2019 2:14 am

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Answers

A

B

C

D

E

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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

OA D

Source: Manhattan Prep
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by Jay@ManhattanReview » Sun Sep 01, 2019 10:00 pm
BTGmoderatorDC wrote: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

OA D

Source: Manhattan Prep
To know the remainder when X is divided by 9, divide the sum of digits of X by 9.

Let's take each statement one by one.

(1) a + b = 11

Thus, the sum of digits of X = 11. Dividing 11 by 9, we get 2 as remainder. Sufficient.

(2) X + 7 is divisible by 9.

=> [(X - 2) + 9] is divisible by 9.
=> (X - 2) is divisible by 9.

Thus, X divisible by 9 will leave 2 as remainder. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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