What is the two-digit number N?

What is the two-digit number N?

Any two-digit integer can be represented as 10a+b (wher a and b are singel digit integers), for example 37=3*10+7, 88=8*10+8, etc.So, let's say N=10a+b.

(1) The difference between N and the number formed by reversing its digits is 9 --> (10a+b)-(10b+a)=9 --> a-b=1 --> N can be: 21, 32, ... Not sufficient.

(2) The number N is divisible by 9 --> in order a number to b divisible by 9, the sum of its digit must b divisible by 9. Thus we are given that a+b=9 (in this case N can be 18, 27, 36, 45, 54, 63, 72, 81, or 90) or a+b=18 (in this case N can only be 99). Notice that a+b cannot be a multiple of 9 more than 18, since a and b are single digit integers. Not sufficient.

(1)+(2) N cannot be 99 (a+b=18), since 99-99=0 not 9 as (1) states. So, we have that a-b=1 and a+b=9 --> a=5 and b=4, thus N=54. Sufficient.

Answer: C.

Hope it's clear.
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Let the num N = 10x + Y

wher x and y are the unit and tens places

from statement 1 we get

10x + y - 10y - x =9

ie 9x - 9y = 9

x - y = 1

Not sufficient

Statement 2

n = 9p

not sufficient

Combining we get

N = 9p >>>>>>>>>> 9, 18, 27,36,45,54

as per statement 1 Tenth digit - unit digit = 1

i.e 54 = 5-4 =1

C is the answer.

Even when we combine both the statements, N can be 54 or 45, right? So isn't the answer E?

N cannot be 45, because 45-54=-9 not 9 as stated in (1).
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quick question: doesn't the difference between two numbers mean the absolute value? The difference between 54 and 45 is 9, does it the same as the difference between 45 and 54?

Agreed. In fact, I also chose E, because of this reason. Difference between 45 and 54 should always be 9, irrespective of the fact which comes earlier.

No answer has been provided yet why the difference is 'first value minus second value' and not '|first value minus second value|' or '|second value minus first value|'.

Can anyone explain this?

Difference should be absolute value. the qn is poorly worded.

Dear EMPOWERgmatRichC & GMATPrepNow

Each statements alone is insufficient.

Statement 1 states (the difference is 9) which does not mean 9 or -9.

So N could be 45 and its reversal is 54. Or

N could be 54 and its reversal is 45.

In both cases difference is 9.

Why answer is not E?

Hi Mo2men,

To start, there's an 'interpretational issue' with this question that you would NOT see on the Official GMAT. Fact 1 uses the phrase "difference between"; depending on how you interpret that phrase, it's unclear whether the original value of N must be greater than the 'reversed value' or not. If you interpret that information to mean that N must be the larger value, then you will end up with Answer C; if you don't, then you will end up with Answer E. The questions that you'll see on the Official GMAT are written in a far more rigorous fashion, so you won't be left to interpret the 'intent' of what the prompt states.

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Thanks a lot for your kind reply.

Statement 1 could be 87 - 78 = 9 or any other

98 - 89 etc.. so insufficient.

Statement 2

N could be 18,27,36,45,54,63,72,81,90 etc..

Insufficient.

Now combined

The only one that satisfies both is 54.

Answer choice C

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