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

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N is a 2-digit integer. When the digits of N are reversed, [#permalink] New post 19 Jun 2018, 05:52
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N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. If the sum of N’s digits is 15, and -1 < N - M < 15, what is the value of N?

[Reveal] Spoiler:
87

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Brent Hanneson – Creator of greenlighttestprep.com
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Re: N is a 2-digit integer. When the digits of N are reversed, [#permalink] New post 21 Jun 2018, 06:52
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GreenlightTestPrep wrote:
N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. If the sum of N’s digits is 15, and -1 < N - M < 15, what is the value of N?

[Reveal] Spoiler:
87


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

GIVEN: 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

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

Answer: 78

Cheers,
Brent
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Re: N is a 2-digit integer. When the digits of N are reversed, [#permalink] New post 12 Jul 2018, 12:39
The provided answer is wrong. It should be 87.
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Re: N is a 2-digit integer. When the digits of N are reversed, [#permalink] New post 18 Jul 2018, 18:39
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GreenlightTestPrep wrote:
N is a 2-digit integer. When the digits of N are reversed, the resulting number is M. If the sum of N’s digits is 15, and -1 < N - M < 15, what is the value of N?

[Reveal] Spoiler:
87


So we know that n = ab where ab are integers representing a two digit integer. We also know that the sum of the digits for n equal 15 so that mean that a + b = 15. We need to find a value of n that when n - m is between -1 and 15.

Lets try \(a=9\) and \(b=6\) in which case \(n = 96\) and \(m = 69\):
\(96 - 69 = 27\) which is greater than 15 so no go

Lets try \(a=8\) and \(b=7\) in which case \(n = 87\) and \(m = 78\):
\(87 - 78 = 9\) which is greater than -1 and less than 15.

The answer is \(n = 87\)
Re: N is a 2-digit integer. When the digits of N are reversed,   [#permalink] 18 Jul 2018, 18:39
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N is a 2-digit integer. When the digits of N are reversed,

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