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:

When a positive integer n is divided by 5, the remainder is 2. What is
[#permalink]

Show Tags

13 Apr 2018, 07:48

1

Top Contributor

MathRevolution wrote:

[GMAT math practice question]

When a positive integer \(n\) is divided by \(5\), the remainder is \(2\). What is the remainder when \(n\) is divided by \(3\)?

1) \(n\) is divisible by \(2\) 2) When \(n\) is divided by \(15\), the remainder is \(2\).

Target question:What is the remainder when n is divided by 3?

Given: When positive integer n is divided by 5, the remainder is 2 ----ASIDE---------------------- When it comes to remainders, we have a nice rule that says: If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. ----------------------------------- So, from the given information, we can conclude that some possible values of n are: 2, 7, 12, 17, 22, 27, 32, 37, etc

Statement 1: n is divisible by 2 When we examine our list of possible n-values (2, 7, 12, 17, 22, 27, 32, 37, ... ), we see that n could equal 2, 12, 22, 32, 42, etc Let's test two of these possible n-values: Case a: n = 2. In this case, 2 divided by 3 equals 0 with remainder 2. So, the answer to the target question is the remainder is 2 Case b: n = 12. In this case, 12 divided by 3 equals 4 with remainder 0. So, the answer to the target question is the remainder is 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 15, the remainder is 2 In other words, n is 2 greater than some multiple of 15 We can write: n = 15k + 2, where k is some integer. IMPORTANT: notice we can take n = 15k + 2 and rewrite it as n = 3(5k) + 2 Notice that 3(5k) is a multiple of 3, which means 3(5k) + 2 is 2 MORE than some multiple of 3 This means that, when we divide n by 3, the remainder is 2 So, the answer to the target question is the remainder is 2 Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Re: When a positive integer n is divided by 5, the remainder is 2. What is
[#permalink]

Show Tags

15 Apr 2018, 18:43

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

We have 1 variable (n) and 1 equation. So, D is most likely to be the answer, and we should consider each of the conditions on its own first.

Plugging-in numbers is the suggested approach to remainder questions.

Condition 1) The possible values of n are \(n = 2, 4, 6, 8, …\) When these are divided by \(3\), the remainders are \(0, 1\) and \(2\). Since the answer is not unique, condition 1) is not sufficient.

Condition 2) The possible values of n are \(n = 17, 32, 47, 62, …\) When these are divided by \(3\), the remainder is always \(2\). Since the answer is unique, condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________