Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
If N is a two-digit positive integer, what is the value of [#permalink]
18 Jan 2011, 00:02
This post was BOOKMARKED
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 ...
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. _________________
Re: If N is a two-digit positive integer, what is the value of [#permalink]
12 Jul 2013, 01:38
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.
Re: If N is a two-digit positive integer, what is the value of
12 Jul 2013, 01:38