Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 11:07

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If k is an integer such that 56 < k < 66, what is the value

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 6

Kudos [?]: 2694 [0], given: 0

If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

06 Dec 2012, 07:56
21
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

58% (02:26) correct 42% (01:23) wrong based on 1472 sessions

### HideShow timer Statistics

If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 38856
Followers: 7725

Kudos [?]: 106024 [2] , given: 11602

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

06 Dec 2012, 07:59
2
KUDOS
Expert's post
3
This post was
BOOKMARKED
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.

(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.

(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.

_________________
Intern
Joined: 02 Oct 2013
Posts: 12
Followers: 0

Kudos [?]: 4 [0], given: 1

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

21 Oct 2013, 19:53
Bunuel wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.

(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.

(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.

Hi Bunuel

Could you please explain the last part , I am still not able to figure out how E is the answer

Regards
Math Expert
Joined: 02 Sep 2009
Posts: 38856
Followers: 7725

Kudos [?]: 106024 [1] , given: 11602

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

21 Oct 2013, 21:56
1
KUDOS
Expert's post
DivyanshuRohatgi wrote:
Bunuel wrote:
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1 --> k is an odd number, thus it could be 57, 59, 61, 63, or 65. Not sufficient.

(2) If k + 1 were divided by 3, the remainder would be 0 --> k is 1 less than a multiple of 3, thus it could be 59, 62, or 65. Not sufficient.

(1)+(2) k could still take more than one value: 59 or 65. Not sufficient.

Hi Bunuel

Could you please explain the last part , I am still not able to figure out how E is the answer

Regards

From (1) k can be: 57, 59, 61, 63, or 65.
From (2) k can be: 59, 62, or 65.

Thus k can be 59, or 65. Two different answers. Hence not sufficient.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15428
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

19 Dec 2014, 13:43
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15428
Followers: 649

Kudos [?]: 207 [0], given: 0

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

20 Jan 2016, 08:11
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.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 3288
GPA: 3.82
Followers: 239

Kudos [?]: 2021 [0], given: 0

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

20 Jan 2016, 22:23
Expert's post
1
This post was
BOOKMARKED
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.

In the original condition, there is 1 variable(k), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), k=2t+1=57,59,61...., which is not unique and not sufficient.
For 2), k+1=3m, k=3m-1=59, 62, 65, which is not unique and not sufficient.
When 1) & 2), n=59,65, which is not unique and not sufficient. Therefore, the answer is E.

 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Intern
Joined: 28 Dec 2015
Posts: 22
Schools: Olin '19, Price
Followers: 3

Kudos [?]: 14 [1] , given: 82

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

21 Jan 2016, 00:55
1
KUDOS
k is an integer such that 56 < k < 66 which means k=(57,58,59,60,61,62,63,64,65)
Now
Statement 1
If k were divided by 2, the remainder would be 1. which means k is odd so possible values of k=(57,59,61,63,65), not sufficient

Statement 2
If k + 1 were divided by 3, the remainder would be 0 so the possible values of k+1 are 60,63,66 so possible values of k=(59,62,65), insufficient

Combining 1 and 2
we still get 2 values 59 and 65 so insufficient

Please consider a kudos if you get the explanation
Intern
Joined: 11 Nov 2014
Posts: 42
Concentration: Marketing, Finance
WE: Programming (Computer Software)
Followers: 0

Kudos [?]: 10 [0], given: 102

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

11 May 2016, 02:53
the most common mistake while solving this question is -

frm stat 1 and stat 2
people will compare the values of k = 57 59 61 63 65 (from stat 1 )
to the values of k+1 = 60 63 66 (from stat 2 )

and will end up choosing 63 as the value of K which is WRONG
but from stat 2
the values of k will be 59 62 and 65.

so from 1 and 2 the values will be 59 and 65...not sufficient.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 895
Followers: 34

Kudos [?]: 506 [0], given: 2

If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

14 May 2016, 05:59
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.

Solution:

We are given that k is between 56 and 66. We must determine the value of k.

Statement One Alone:

If k were divided by 2, the remainder would be 1.

This means k must be an odd number. However, since 56 < k < 66, k can be any odd integer between 56 and 66, which means that k could be 57, 59, 61, 63, or 65. Statement one is not sufficient to determine a value of k. We can eliminate answer choices A and D.

Statement Two Alone:

If k + 1 were divided by 3 the remainder would be 0.

This means k + 1 is a multiple of 3. However, since 56 < k < 66, there is more than one value between 56 and 66 that, when increased by 1, will be a multiple of 3. For example, since 60, 63 and 66 are all multiples of 3, we see that k could be 59, 62 or 65. Since we have three possible values for k, statement two is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

From statement one we know that k can be 57, 59, 61, 63, or 65, and from statement two we know that k could be 59, 62 or 65. From the combined statements, then, k could be either 59 or 65; thus, we can’t determine a unique value for k. Statements one and two together are not sufficient to answer the question.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Joined: 02 Sep 2016
Posts: 419
Followers: 3

Kudos [?]: 25 [0], given: 60

Re: If k is an integer such that 56 < k < 66, what is the value [#permalink]

### Show Tags

01 Apr 2017, 10:50
If k is an integer such that 56 < k < 66, what is the value of k ?

(1) If k were divided by 2, the remainder would be 1.
(2) If k + 1 were divided by 3, the remainder would be 0.

k can be 57, 58,...........65

(1) K is odd because on division with 2, the remainder is 1.
So k is of the form 2n+1.

K can be 57, 59, 61, 63, or 65

Not sufficient

BCE

(2) That means k is not divisible by 3.
k can be 59, 62, or 65

Not sufficient

Both statement together:

Statement 1: k=57, 59, 61, 63, or 65
Statement 2: k= 59,62, or 65

No unique value for k.

E
Re: If k is an integer such that 56 < k < 66, what is the value   [#permalink] 01 Apr 2017, 10:50
Similar topics Replies Last post
Similar
Topics:
If m, j, and k are integers, is k < mj? 2 11 Jan 2017, 07:55
4 If k is an integer, what is the value of k? 8 24 Dec 2015, 15:11
4 If k is an integer and 2 < k < 8, what is the value of k ? 4 21 Apr 2017, 07:42
22 If k is an integer, what is the value of k? 13 29 Sep 2016, 11:26
12 What is the value of the integer k? 12 18 Jul 2016, 01:55
Display posts from previous: Sort by