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What is the two-digit number N?

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What is the two-digit number N? [#permalink] New post 03 Nov 2012, 07:48
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What is the two-digit number N?

(1) The difference between N and the number formed by reversing its digits is 9.
(2) The number N is divisible by 9.
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Re: What is the two-digit number N? [#permalink] New post 03 Nov 2012, 09:07
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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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Re: What is the two-digit number N? [#permalink] New post 03 Nov 2012, 16:43
monikaleoster wrote:
What is the two-digit number N?

(1) The difference between N and the number formed by reversing its digits is 9.
(2) The number N is divisible by 9.


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.
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Re: What is the two-digit number N? [#permalink] New post 04 Nov 2012, 11:32
Bunuel wrote:
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.


Even when we combine both the statements, N can be 54 or 45, right? So isn't the answer E?
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Re: What is the two-digit number N? [#permalink] New post 04 Nov 2012, 13:50
Expert's post
Argon wrote:
Bunuel wrote:
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.


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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What is the two-digit number N? [#permalink] New post 30 May 2013, 01:35
What is the two-digit number N?

(1) The difference between N and the number formed by reversing its digits is 9.
(2) The number N is divisible by 9.
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Re: What is the two-digit number N? [#permalink] New post 30 May 2013, 01:37
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Re: What is the two-digit number N? [#permalink] New post 01 Jun 2013, 08:39
Bunuel wrote:
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.


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?
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Re: What is the two-digit number N? [#permalink] New post 11 Aug 2013, 06:37
kevinfa wrote:
Bunuel wrote:
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.


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.
Re: What is the two-digit number N?   [#permalink] 11 Aug 2013, 06:37
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