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# If N is a two-digit positive integer, what is the value of

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Intern
Joined: 14 Sep 2010
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If N is a two-digit positive integer, what is the value of [#permalink]

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18 Jan 2011, 00:02
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If N is a two-digit positive integer, what is the value of its tens digit?
1. 2N is a two-digit integer whose tens digit is 7
2. The tens digit of (N-9) is 2

I already have seen the solution and I know that this can be solved by testing numbers to get the correct answer. However, I have been trying to solve it via pure ALGEBRA and I am not sure how to do approach it in that way.

My approach has been to say N = 10x + y , therefore 2N = 20x + 2y ,Also 2N = 10* (7) + b
To make both equations equal and then solve for x .... Should I use another variable (for example b) , or should I stick with y ...

Can someone help me as I am doing something wrong....

P.S. this problem is actually very easy if you test numbers ...

Thanks, I appreciate it !!

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Knewton GMAT Instructor
Joined: 04 Jan 2011
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Location: NY, NY
Schools: BA New School, PhD Candidate CUNY
Re: GMAT CLUB TEST question [#permalink]

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20 Jan 2011, 12:06
I don't know if there's a straightforward algebraic solution to this one. One thing I tried was setting up Statement (1) as follows:

2n = 70 + b (following your setup)
n = 35 + b/2

Then, I realized that, implicit in Statement (1) is that 0<b<10, so, when we divide by 2, we also must realize that 0<b/2<5. Since n must be an integer, b must be even, so b/2 must be 3 or 4, making n = 37 or 39, Sufficient.

However, this isn't pure algebra, I know. I guess what I'd like to ask you is: Why do you want to find a way to do this problem with pure algebra? Let me give you an example question:

If p is even and q is odd, is p^2*q odd?

The answer, of course, is no. But we can also do algebra:

p = 2n and q = 2m+1, where n and m are integers
(2n)^2 * (2m+1) = 4n^2 * (2m+1) = 8mn^2 + 4n^2 = 2*(4mn^2 + 2n^2), which is even because the term in parentheses is an integer and 2 times an integer is even.

Seriously? Seriously? Let's not do this anymore. To all who seek algebraic answers to easy questions: Don't do this anymore. The goal of this, remember, is to get a high GMAT score, get into business school, and then succeed with your MBA. That is the only point. Also remember that a good businessperson doesn't look for the most complex-but-interesting solution to a problem: he or she looks for the best, most efficient, most situation-appropriate solution to the problem. The GMAT tests this skill, and well it should.

Not that I mind posting these questions here, after all, it's fun, and I am eager to see if someone DOES have a purely algebraic solution here ... but let's all remember that, in terms of studying for the GMAT, trying to find a longer, more awkward way of doing an otherwise-easy problem is somewhat counterproductive.
_________________

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Re: If N is a two-digit positive integer, what is the value of [#permalink]

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12 Jul 2013, 01:38
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Hi guys, just to have all answers, here is the more simplistic approach:
N= AB, where A is the 10th digit and B is the units digit.
1) 2N is a two-digit integer whose tens digit is 7
2N = CD, where C =7.
This means CD could generally be: 70,71,72,73,74,75,76,78,79.
However, CD must be divisible by 2 in order that N is AB --> thus CD must be even, leaving us with 70, 72,74,76,78 for possible values of CD.
Any of these 5 numbers (70, 72, 74, 76, 78) divided by 2 will result in N. So N(N=CD) can only be: 35, 36, 37, 38, 39. SO the 10th digit of N (N=CD) is one way or the other always 3.
--> Sufficient
2) The tens digit of (N-9) is 2
N= CD. So: CD – 9 = AB, where A =2.
Two-digit numbers with 10th digit of 2 can only be: 20, 21, 22, 23, 24, 25, 26, 27, 28, and 29.
CD – 9 = one of the numbers: 20, 21, 22, 23, 24, 25, 26, 27, 28, and 29.
So adding 9 to any of the numbers will give us CD:
20+9 = 29
21+9 = 30
22+9 = 31, and so on until 29+9=38.
Thus, it is not clear whether CD is 29 or any integer between 30 and 38.
--> Not sufficient.

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Re: If N is a two-digit positive integer, what is the value of   [#permalink] 12 Jul 2013, 01:38
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# If N is a two-digit positive integer, what is the value of

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