N is a 2-digit integer. When the digits of N are reversed

Question

N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. If -1 < N – M < 15, what is the value of N?

(1) The sum of N’s digits is 15.
(2) The tens digit of N is 1 greater its units digit

*kudos for all correct solutions

gmatzpractice · Answer

(1) N = 87; M = 78
Sufficient

(1) N = 21; M = 12 
N = 32; M = 23
Not Sufficient

IMO Answer A. Statement (1) by itself is sufficient.

chetan2u · Answer

Let N be 10x+y, so M is 10y+X...
N-M = 10x+y-10y-x=9(x-y)...
So N-M has to be a multiple of 9...
Between -1 and 15, there are two multiples of 9 --> 0 and 9

1) sum of N's digits is 15... 
So both digits can not be same and N-M cannot be 0, it is 9..
Only possibility 87 and 78
Sufficient

2) the tens digit of N is 1 greater than units digit..
Various possiblities 32 &23, 43&34,87&78
Insufficient

A

tejyr · Answer

1.N=69,78
only 69 is satisfying N-m in (-1,15)
2.N=67,78,56,....
hence insufficient

BrentGMATPrepNow · Answer

Be careful, N = 69 does not satisfy the given conditions.

Cheers,
Brent

pushpitkc · Answer

N = 10x + y | M = 10y + x | N - M = 9(x - y) 
 -1 < 9(x - y) < 15

1. x + y = 15 -> x = 15 - y
9(15 - y - y) is 9(15 - 2y) and is in the range, only when y = 7.
There is only one possibility for such a 2-digit number, which is 87  (Sufficient)

2. x = y + 1 
There are various options for N such that this statement is true.
The numbers possible are 43,54,87  (Insufficient)   (Option A)

SSM700plus · Answer

I think we can do this without assuming any number. Let's try it.

Let's assume  N = 10x + y  and  M = 10y + x

so  N - M = 9(x - y) .

Given equation becomes 
 -1 < 9(x - y) < 15 .

Think for a moment. For what value of (x-y) the above inequality would be true. Surely it should be 1 and 0.

For any other number inequality will not hold true.

So here we have  x-y = 1  or  x-y = 0

A) The sum of N’s digits is 15.

This implies  x + y = 15.

We already have one equation:  x -y =1 .
and here statement A provides another equation. We will get to one value of N.

So it is sufficient.

We also understand that x-y =0 can't be used to get the value of x & y, because it will not give x & y as integer.

B) The tens digit of N is 1 greater its units digit.

tens digit is x and unit digit is y. So  x-y =1.

Notice that this statement doesn't provide any additional detail to help us find the the number.

Hence Not Sufficient.

Ans - A.

BrentGMATPrepNow · Answer

Target question :    What is the value of N?

Given : N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. -1 < N – M < 15  
Let x = the tens digit of N
Let y = the units digit of N
So, the VALUE of N = 10x + y

When we reverse the digits, we get M = yx
So, the VALUE of M = 10y + x

So, N - M = (10x + y) - (10y + x)
= 9x - 9y
= 9(x - y)
In other words, N - M =  some multiple of 9 
We're told that -1 < N – M < 15
There are exactly two multiples of 9 between -1 and 15. They are 0 and 9.
So EITHER   N – M = 0   OR   N – M = 9

Let's examine each case: 
CASE A: If  N - M = 0 , then 9(x - y) = 0, which means x - y = 0, which means   x = y   
CASE B: If  N - M = 9 , then 9(x - y) = 9, which means x - y = 1, which means   x = y + 1

Statement 1 : The sum of N’s digits is 15  
In other words, x + y = 15
If x and y are INTEGERS, and if x + y = 15, then   x cannot equal y  
This rules out CASE A, which means CASE B must be true. That is,   x = y + 1   
We now have two equations: 
x + y = 15
  x = y + 1

Since we COULD solve this system for x and y, we COULD determine the  value of N  
Since we COULD answer the  target question  with certainty, statement 1 is SUFFICIENT

Aside: If we solve the system, we get: x = 7 and y = 8
So,  N = 78

Statement 2 : The tens digit of N is 1 greater its units digit 
In other words, x = y + 1
This means CASE B is true (i.e.,   x = y + 1   )
Given this, there are many values of N that statement 2. 
For example, it could be the case that  N = 21  or  N = 32  or  N = 43  or  N = 54  etc. 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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N is a 2-digit integer. When the digits of N are reversed

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