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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

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:

number properties discrepancy [#permalink]
03 Nov 2010, 08:52

00:00

A

B

C

D

E

Difficulty:

(N/A)

Question Stats:

50% (02:17) correct
50% (00:59) wrong based on 21 sessions

Hi everybody! I am stuck with a solution method for two similar questions from the area of number properties.

Here is the first: The sum of three consecutive even integers is always divisible by which of the following?

I. 2 II. 3 III. 4 IV. 8

A) I and II only B) I and IV only C) II and IV only D) I, II and III only E) I, II and IV only

OA: D

The solution method is the following: Sum of three integers = n+n+2+n+4= 3n+6 3n+6 is divisible by 2, 3, 4, but not by 8 for all n=(2,4,6,8...)

(the Source: Winners' Guide to GMAT Math - Part II)

Here is the second question:

Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is

a) 12 b) 6 c) 8 d) 10 e) 14

OA: e

The solution method is the following: Let the three even numbers be (x-2), x, (x+2) Then 3(x-2)-2(x+2)=2 3x-6-2x-4=2, x=2 The third number= 12+2=14 Hence: e

(the Source: Math Question Bank for GMAT Winners)

But there is there is one point I cannot understand:

The starting point of both questions is the same because they both deal with three consecutive even integers. This is why both solution methods can presumably be applied alternatively to each other.

In other words, both questions must be soluable regardless whether we take three consecitive even integers as n, n+2, n+3 or as (x-2), x, (x+2). However, it does not work if we take (x-2), x, (x+2) as a starting point for the first question or if we take n, n+2, n+3 as a starting point for the second question.

Pls., can someone disprove my remark and give better explanation?

Re: number properties discrepancy [#permalink]
03 Nov 2010, 09:12

1

This post received KUDOS

Expert's post

feruz77 wrote:

Hi everybody! I am stuck with a solution method for two similar questions from the area of number properties.

Here is the first: The sum of three consecutive even integers is always divisible by which of the following?

I. 2 II. 3 III. 4 IV. 8

A) I and II only B) I and IV only C) II and IV only D) I, II and III only E) I, II and IV only

OA: D

The solution method is the following: Sum of three integers = n+n+2+n+4= 3n+6 3n+6 is divisible by 2, 3, 4, but not by 8 for all n=(2,4,6,8...)

(the Source: Winners' Guide to GMAT Math - Part II)

Here is the second question:

Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is

a) 12 b) 6 c) 8 d) 10 e) 14

OA: e

The solution method is the following: Let the three even numbers be (x-2), x, (x+2) Then 3(x-2)-2(x+2)=2 3x-6-2x-4=2, x=2 The third number= 12+2=14 Hence: e

(the Source: Math Question Bank for GMAT Winners)

But there is there is one point I cannot understand:

The starting point of both questions is the same because they both deal with three consecutive even integers. This is why both solution methods can presumably be applied alternatively to each other.

In other words, both questions must be soluable regardless whether we take three consecitive even integers as n, n+2, n+3 or as (x-2), x, (x+2). However, it does not work if we take (x-2), x, (x+2) as a starting point for the first question or if we take n, n+2, n+3 as a starting point for the second question.

Pls., can someone disprove my remark and give better explanation?

You should get the same answer whether you choose \(x\) or \(x-2\) for the first even number.

1. The sum of three consecutive even integers is always divisible by which of the following? I. 2 II. 3 III. 4 IV. 8

A. I and II only B. I and IV only C. II and IV only D. I, II and III only E. I, II and IV only

Let the first even # be \(x\). Note that as \(x\) is even then \(x=2k\), for some integer \(k\): \(x+(x+2)+(x+4)=3x+6=3*2k+6=6(k+1)\) --> so the sum of 3 consecutive even integers is divisible by 2, 3 and 6.

Now, if take the first integer to be \(x-2\) then: \((x-2)+x+(x+2)=3x=3*2k=6k\) --> so the sum of 3 consecutive even integers is divisible by 2, 3 and 6.

Answer: A.

2. Three consecutive even numbers are such that thrice the first number exceeds double the third by two, the third number is A. 12 B. 6 C. 8 D. 10 E. 14

Let the first even # be \(x\) (so the 3 consecutive integers are \(x\), \(x+2\), and \(x+4\)), then: \(3x=2(x+4)+2\) --> \(x=10\) --> third # is \(x+4=10+4=14\).

Now, if we take the first integer to be \(x-2\) (so the 3 consecutive integers are \(x-2\), \(x\), and \(x+2\)) then: \(3(x-2)=2(x+2)+2\) --> \(x=12\) --> third # is \(x+2=12+2=14\)

Re: number properties discrepancy [#permalink]
03 Nov 2010, 09:42

1

This post received KUDOS

Expert's post

feruz77 wrote:

Here is the first: The sum of three consecutive even integers is always divisible by which of the following?

I. 2 II. 3 III. 4 IV. 8

A) I and II only B) I and IV only C) II and IV only D) I, II and III only E) I, II and IV only

OA: D

The solution method is the following: Sum of three integers = n+n+2+n+4= 3n+6 3n+6 is divisible by 2, 3, 4, but not by 8 for all n=(2,4,6,8...)

(the Source: Winners' Guide to GMAT Math - Part II)

I'm not sure if there's a typo in the question above, or an error in the original source, but the sum of three consecutive even integers is certainly not always divisible by 4. Take 0+2+4, or 4+6+8 for example. Bunuel's solution above is perfect except that he must have thought they were asking about divisibility by 6, not by 4; as the question is written, the answer is A, not D. [edit - I guess Bunuel fixed that now]

The second question you've asked is not worded in a way at all similar to what you'll see on the test (you won't see the word 'thrice' on the GMAT, and the question contains a comma splice). _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: number properties discrepancy [#permalink]
03 Nov 2010, 09:50

Expert's post

IanStewart wrote:

feruz77 wrote:

Here is the first: The sum of three consecutive even integers is always divisible by which of the following?

I. 2 II. 3 III. 4 IV. 8

A) I and II only B) I and IV only C) II and IV only D) I, II and III only E) I, II and IV only

OA: D

The solution method is the following: Sum of three integers = n+n+2+n+4= 3n+6 3n+6 is divisible by 2, 3, 4, but not by 8 for all n=(2,4,6,8...)

(the Source: Winners' Guide to GMAT Math - Part II)

I'm not sure if there's a typo in the question above, or an error in the original source, but the sum of three consecutive even integers is certainly not always divisible by 4. Take 0+2+4, or 4+6+8 for example. Bunuel's solution above is perfect except that he must have thought they were asking about divisibility by 6, not by 4; as the question is written, the answer is A, not D.

The second question you've asked is not worded in a way at all similar to what you'll see on the test (you won't see the word 'thrice' on the GMAT, and the question contains a comma splice).

Sure, they are not asking about 6. _________________

Re: number properties discrepancy [#permalink]
04 Nov 2010, 06:54

To: Ian Stewart

You are right because there is not excluded a case with a sum of 0, 2, 4. Then the answer is A. OK.

It seems to me that the first question must be written more pricisely, otherwise one cannot determine whether it is meant only positive consecutive even integers. Without precision word "positive" I have assumed in my first trial of this question that three consecutive even numbers may be in the order -2, 0, 2. In such a case only 0 can satisfy the question, but there is no answer with zero.

Do you agree with my remark?

Do you think that there may such misrepresentation or trick in the official GMAT Test?

Re: number properties discrepancy [#permalink]
04 Nov 2010, 07:03

1

This post received KUDOS

Expert's post

feruz77 wrote:

To: Ian Stewart

You are right because there is not excluded a case with a sum of 0, 2, 4. Then the answer is A. OK.

It seems to me that the first question must be written more pricisely, otherwise one cannot determine whether it is meant only positive consecutive even integers. Without precision word "positive" I have assumed in my first trial of this question that three consecutive even numbers may be in the order -2, 0, 2. In such a case only 0 can satisfy the question, but there is no answer with zero.

Do you agree with my remark?

Do you think that there may such misrepresentation or trick in the official GMAT Test?

Everybody, pls. give your explanations?!

I'm not sure understood the red part above.

Anyway, the sum of ANY 3 consecutive even integers is ALWAYS divisible by 2, 3, and 6. If 3 consecutive even integers are -2, 0, and 2 then their sum is 0 and zero is divisible by every integer but zero itself, so it's divisible by 2, 3 and 6 too. So the answer is still A. _________________

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

After I was accepted to Oxford I had an amazing opportunity to visit and meet a few fellow admitted students. We sat through a mock lecture, toured the business...