GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Feb 2019, 19:45

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# Data Sufficiency Pack 1, Question 2) Is the sum...

Author Message
TAGS:

### Hide Tags

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13562
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

27 Oct 2015, 20:58
1
8
00:00

Difficulty:

65% (hard)

Question Stats:

46% (01:02) correct 54% (00:48) wrong based on 211 sessions

### HideShow timer Statistics

QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum...

Is the sum of 7x and 7y divisible by 14?

(1) x = y
(2) x and y are both even integers

48 Hour Window Answer & Explanation Window
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation

_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Manager Joined: 13 Mar 2013 Posts: 163 Location: United States Concentration: Leadership, Technology GPA: 3.5 WE: Engineering (Telecommunications) Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink] ### Show Tags 27 Oct 2015, 21:45 Is the sum of 7x and 7y divisible by 14? (1) x = y (2) x and y are both even integers (7x + 7y )/14 = 7(x + y)/14 = (x + y)/2 Effectively question becomes is x + y a multiple of 2 . 1 ) x =y --> 2y/2 or 2x/2 = both are multiple of 2 .hence sufficient 2) x,y are both even integer --> both will be divisible by 2 hence sufficient D ans _________________ Regards , Manager Status: One Last Shot !!! Joined: 04 May 2014 Posts: 237 Location: India Concentration: Marketing, Social Entrepreneurship GMAT 1: 630 Q44 V32 GMAT 2: 680 Q47 V35 Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink] ### Show Tags 27 Oct 2015, 21:54 1 1 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum... Is the sum of 7x and 7y divisible by 14? (1) x = y (2) x and y are both even integers 48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4-Pack series Scroll Down For Official Explanation Question stem: $$\frac{7x+7y}{14}$$ $$=> \frac{7(x+y)}{14}$$ $$=> \frac{x+y}{2}$$ So basically we need to find whether x+y is even S1: $$x = y$$ This will work if x and y are integers. And will not work otherwise. eg: if $$x=3, y=3$$ $$=> x+y = 3+3 = 6$$ Even But if $$x=0.75, y=0.75$$ $$=> x+y = 0.75+0.75 = 1.50$$ Not even Hence Insufficient. S2: $$x$$ and $$y$$ are both even integers This will always work. $$x+y$$ will always yield an even integer $$even+even = even$$ Hence Sufficient. Answer B _________________ One Kudos for an everlasting piece of knowledge is not a bad deal at all... ------------------------------------------------------------------------------------------------------------------------ Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. -Mark Twain CEO Joined: 20 Mar 2014 Posts: 2629 Concentration: Finance, Strategy Schools: Kellogg '18 (M) GMAT 1: 750 Q49 V44 GPA: 3.7 WE: Engineering (Aerospace and Defense) Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink] ### Show Tags 28 Oct 2015, 07:35 2 EMPOWERgmatRichC wrote: QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum... Is the sum of 7x and 7y divisible by 14? (1) x = y (2) x and y are both even integers 48 Hour Window Answer & Explanation Window Earn KUDOS! Post your answer and explanation. OA, and explanation will be posted after the 48 hour window closes. This question is part of the Quant 4-Pack series Scroll Down For Official Explanation The question asks whether 7x+7y=14p , p $$\in$$ non negative integer ---> x+y=2p = even integer? Per statement 1, x=y . "yes" to "x+y=2p = even integer" if x=y=1 but "no" for "x+y=2p = even integer" if x=y=1/3. Not sufficient. Per statement 2, x and y both are even integer ---> clearly sufficient. B is the correct answer. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13562 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink] ### Show Tags 29 Oct 2015, 23:00 2 Hi All, This DS question, like many DS questions on Test Day, is meant to test the 'thoroughness' of your thinking. It's important to think about what you KNOW about the variables and what you DON'T know... We're asked if the sum of 7X and 7Y is divisibly by 14. This is a YES/NO question. It's important to remember that we were NOT told anything about X and Y (maybe they're integers, but maybe they're not). TESTing VALUES will prove to be quite useful here. 1) X = Y This Fact tells us that the two variables are equal to one another, but we don't know what they actually are. IF... X = Y = 1/2 Then 7(1/2) + 7(1/2) = 7 and the answer to the question is NO. IF... X = Y = 1 Then 7(1) + 7(1) = 14 and the answer to the question is YES. Fact 1 is INSUFFICIENT 2) X and Y are both even integers This Fact gives us a very specific restriction - X and Y are BOTH EVEN integers. With this restriction, ANY possible values that you choose for X and Y will lead to a total that is divisible by 14. For example... IF... X = Y = 2 Then 7(2) + 7(2) = 28 and the answer to the question is YES. IF... X = 0 Y = 2 Then 7(0) + 7(2) = 14 and the answer to the question is YES. IF... X = -2 Y = -4 Then 7(-2) + 7(-4) = -42 and the answer to the question is YES. Fact 2 is SUFFICIENT. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Intern
Joined: 14 Nov 2015
Posts: 5
Schools: Wharton '18 (S)
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

25 Nov 2015, 18:22
Hi Rich,

I'm also a member of your website so I follow your posts quite frequently. One question I had was why we can't use the scenario for statement 2 with x=0 and y=0. There's nothing in statement two which says that we can't set both integers equal to 0. In that case 7(0) + 7(0) equals 0 which is not divisible by 14. Therefore, my thought is that B would not be sufficient and hence the correct choice would be (E).

I would love to hear your feedback when you have a moment.

--BH
Math Expert
Joined: 02 Sep 2009
Posts: 53020
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

26 Nov 2015, 04:15
Hi Rich,

I'm also a member of your website so I follow your posts quite frequently. One question I had was why we can't use the scenario for statement 2 with x=0 and y=0. There's nothing in statement two which says that we can't set both integers equal to 0. In that case 7(0) + 7(0) equals 0 which is not divisible by 14. Therefore, my thought is that B would not be sufficient and hence the correct choice would be (E).

I would love to hear your feedback when you have a moment.

--BH

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

Check more here: number-properties-tips-and-hints-174996.html
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13562
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

26 Nov 2015, 15:14

You CAN use X=0 and Y=0 for Fact 1, Fact 2 or both. 0 IS divisible by 14, so the answer to the question would be YES.

As a broader Number Property worth knowing, 0 is divisible by EVERY number (barring 0/0, which is a concept that you won't see on the GMAT).

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Director Joined: 06 Jan 2015 Posts: 587 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink] ### Show Tags 07 Dec 2015, 06:32 Hi Rich, Why Can't we try with 2 and -2 ? Thanks And Regards NSS _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13562 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Data Sufficiency Pack 1, Question 2) Is the sum... [#permalink] ### Show Tags 07 Dec 2015, 10:46 Hi NandishSS, For Fact 2, you CAN use 2 and -2. When you TEST those two values, the answer to the question is still YES. GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Joined: 22 Jan 2014
Posts: 174
WE: Project Management (Computer Hardware)
Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

08 Dec 2015, 06:15
EMPOWERgmatRichC wrote:
QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 2 Is the sum...

Is the sum of 7x and 7y divisible by 14?

(1) x = y
(2) x and y are both even integers

48 Hour Window Answer & Explanation Window
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation

7(x+y) mod 14 = 0
x+y mod 2 = 0

1) x=y
x=y=1 ; ans = yes
x=y=1/2 ; ans = no

2) x and y are even so 2 can is a common divisor of both, hence can be taken out of the brackets making the entity outside brackets as 14. Hence, sufficient.
_________________

Illegitimi non carborundum.

Board of Directors
Joined: 17 Jul 2014
Posts: 2587
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

18 Feb 2016, 19:11
1
ha! tricky one..you got me here...
never assume that you deal with integers on DS...never!!!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13562
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

19 Feb 2016, 12:21
2
Hi mvictor,

When working through DS questions, before jumping to the two Facts, I always write down whatever information I've been given and the specific question that I'm attempting to answer. In addition, if I have not been given ANY information about the variables in the prompt, then I will physically write down that information.... "X, Y can be ANYTHING." In that way, when I'm dealing with each of the Facts and doing whatever work is required, I have a constant reminder (on the PAD) that I need to consider more than just the obvious possibilities (re: positive integers).

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Board of Directors
Joined: 17 Jul 2014
Posts: 2587
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

21 Feb 2016, 11:15
EMPOWERgmatRichC wrote:
Hi mvictor,

When working through DS questions, before jumping to the two Facts, I always write down whatever information I've been given and the specific question that I'm attempting to answer. In addition, if I have not been given ANY information about the variables in the prompt, then I will physically write down that information.... "X, Y can be ANYTHING." In that way, when I'm dealing with each of the Facts and doing whatever work is required, I have a constant reminder (on the PAD) that I need to consider more than just the obvious possibilities (re: positive integers).

GMAT assassins aren't born, they're made,
Rich

thanks..i sometimes forget about this one..will definitely write on my scratch paper just the way you do.
Non-Human User
Joined: 09 Sep 2013
Posts: 9871
Re: Data Sufficiency Pack 1, Question 2) Is the sum...  [#permalink]

### Show Tags

22 Dec 2017, 12:50
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.
_________________
Re: Data Sufficiency Pack 1, Question 2) Is the sum...   [#permalink] 22 Dec 2017, 12:50
Display posts from previous: Sort by