Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
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:
1) When divided equal part of 10 meter each, a piece of 5 meter is left.
2) When divided equal of 6 meter each, a piece of 1 meter is left.
What is the value of length n<100 meter of wire?
(1) When divided equal part of 10 meter each, a piece of 5 meter is left --> \(n=10q+5\): 5, 15, 25, ..., 95. Not sufficient.
(2) When divided equal of 6 meter each, a piece of 1 meter is left --> \(n=6p+1\): 1, 7, 13, 19, 25, ..., 97. Not sufficient.
(1)+(2) General formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\) would be \(n=30m+25\) --> \(n\) can be: 25, 55 or 85. Not sufficient.
Answer: E.
To elaborate more. How to derive general formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\): divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, \(n\) must be of a type \(n=30m+25\): 25, 55 or 85.
1) When divided equal part of 10 meter each, a piece of 5 meter is left.
2) When divided equal of 6 meter each, a piece of 1 meter is left.
What is the value of length n<100 meter of wire?
(1) When divided equal part of 10 meter each, a piece of 5 meter is left --> \(n=10q+5\): 5, 15, 25, ..., 95. Not sufficient.
(2) When divided equal of 6 meter each, a piece of 1 meter is left --> \(n=6p+1\): 1, 7, 13, 19, 25, ..., 97. Not sufficient.
(1)+(2) General formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\) would be \(n=30m+25\) --> \(n\) can be: 25, 55 or 85. Not sufficient.
Answer: E.
To elaborate more. How to derive general formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\): divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, \(n\) must be of a type \(n=30m+25\): 25, 55 or 85.
To elaborate more. How to derive general formula of \(n\) based on \(n=10q+5\) and \(n=6p+1\): divisor will be the least common multiple of above two divisors 6 and 10, hence 30. Remainder will be the first common integer in above two patterns, hence 25. So, to satisfy both conditions, \(n\) must be of a type \(n=30m+25\): 25, 55 or 85.
Thanks very much. Above would have been very difficult to figure out in the real exam.
Re: What is the value of length n<100 meter of wire?
[#permalink]
Show Tags
30 Jul 2014, 03:14
Actually, this problem you can solve at most in 10 seconds:)
The main point here is that all numbers with exact remainder form arithmetic progression with difference=divisor.
For example, all x such that "when x is divided by 5 the remainder is 1" form arithmetic progression with first element 1 and difference 5: 1, 6, 11, 16, 21.....
If 50<x<100 for example, I can definitely say that there are several such x, because the distance between all such numbers is 5.
To solve this problem you need just to check if the divisor=(distance between numbers) large enough to have only 1 number inside interval.
So, I need to find exact number less than 100. (1) The difference=divisor=10 is quite small for 100. Insufficient. (2) The difference=divisor=6 is quite small for 100. Insufficient.
(1)+(2) The new difference=least common multiple of 10 and 6=30 is small for 100. Insufficient.
The correct answer is E
You don't really need here to write formula for x and first several values for each statement. _________________
I'm happy, if I make math for you slightly clearer And yes, I like kudos:)
Re: What is the value of length n<100 meter of wire?
[#permalink]
Show Tags
10 Mar 2015, 11:59
smyarga wrote:
Actually, this problem you can solve at most in 10 seconds:)
The main point here is that all numbers with exact remainder form arithmetic progression with difference=divisor.
For example, all x such that "when x is divided by 5 the remainder is 1" form arithmetic progression with first element 1 and difference 5: 1, 6, 11, 16, 21.....
If 50<x<100 for example, I can definitely say that there are several such x, because the distance between all such numbers is 5.
To solve this problem you need just to check if the divisor=(distance between numbers) large enough to have only 1 number inside interval.
So, I need to find exact number less than 100. (1) The difference=divisor=10 is quite small for 100. Insufficient. (2) The difference=divisor=6 is quite small for 100. Insufficient.
(1)+(2) The new difference=least common multiple of 10 and 6=30 is small for 100. Insufficient.
The correct answer is E
You don't really need here to write formula for x and first several values for each statement.
For (1)+(2), we need to know that the first number is 25. Only then we could say that this is insufficient. If the first number was >70, (1)+(2), could've been sufficient.
Re: What is the value of length n<100 meter of wire?
[#permalink]
Show Tags
25 Sep 2017, 23:35
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
close
69% (01:56) correct 
