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

 It is currently 22 Sep 2018, 10:01

### 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

# Is x > y? (1) x= y+2 (2) x/2 = y-1

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49303
Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

02 Jul 2012, 02:39
1
16
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:02) correct 31% (01:00) wrong based on 1242 sessions

### HideShow timer Statistics

The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Is x > y?

(1) x = y+2
(2) x/2 = y-1

Diagnostic Test
Question: 37
Page: 25
Difficulty: 550

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49303
Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

02 Jul 2012, 02:39
SOLUTION

Is x > y?

(1) x = y+2. $$x$$ is 2 more than $$y$$, so $$x>y$$. Sufficient.

(2) x/2 = y-1 --> $$x=2y-2$$. If $$y=0$$ then $$x=-2$$ and the answer is NO but if $$y=3$$ then $$x=4$$ and the answer is YES. Not sufficient.

_________________
Current Student
Joined: 29 Mar 2012
Posts: 317
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

02 Jul 2012, 02:44
Hi,

Difficulty level: 600

Using (1),
x = y + 2, so for any value of y, x > y. Sufficient.

Using (2),
x/2 = y - 1
for x = 0, y = 1 or x < y
for x = 2, y = 2 or x = y
for x = 4, y = 3 or x > y, Thus the relationship depends on value of x & y. Insufficient.

Regards,
Intern
Joined: 25 Apr 2012
Posts: 1
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

02 Jul 2012, 12:28
1) Sufficient . X is always 2 greater than Y. (+,-ve and fraction).
2) Insufficient. For y=5, x = 8 so x> y but for y=-5, x= -12 so y> x..

A)
Senior Manager
Joined: 23 Oct 2010
Posts: 358
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

03 Jul 2012, 09:53
(1) x = y+2 sufficient .try zero, negative, positive integers and non-integers, and u will get answer YES, x>y.
(2) x/2 = y-1 means x=2(y-1) if y=1 x =0 so, the answ is No, but if y=3 x=4 the answer is Yes
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Manager
Joined: 07 Sep 2011
Posts: 68
GMAT 1: 660 Q41 V40
GMAT 2: 720 Q49 V39
WE: Analyst (Mutual Funds and Brokerage)
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

03 Jul 2012, 13:42
1
Is x > y?

(1) x = y+2
Regardless of whether y is a positive or negative, if x=y+2, then y is greater than x. SUFFICIENT.
(2) x/2 = y-1
This kind of logic pops up frequently from the GMAT probelms I have done.
x=2(y-1)
x=2y-2
Whenever you see mult/div AND sub/add on the other side of x, you won't be able to tell whether whether one integer is greater than the other. It could be either of the case.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6227
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

21 Nov 2015, 10:18
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.

Is x > y?

(1) x = y+2
(2) x/2 = y-1

We get x-y>0? when we modify the questions.
For condition 1, x-y=2>0 This is a 'yes', and sufficient.
For condition 2, x=2y-2, x-y=y-2. We cannot determine the sign of x-y, so this is insufficient.

For (C), x=y+2, x=2y-2 --> y=2, x=4. This is insufficient as it is too trivial.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________

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.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12425 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Is x > y? (1) x= y+2 (2) x/2 = y-1 [#permalink] ### Show Tags 13 Dec 2017, 21:25 Hi All, We're asked if X is greater than Y. This is a YES/NO question. We can solve it by TESTing VALUES. 1) X = Y +2 With this Fact, we can see that X is "2 greater" than Y, so the answer to the question is ALWAYS YES. You can see this pattern with a few TESTs: IF.... Y = 0, X = 2 Y = 5, X = 7 Y = -3, X = -1 Etc. Fact 1 is SUFFICIENT 2) X/2 = Y - 1 IF.... Y = 1, X = 0 and the answer to the question is NO Y = 3, X = 4 and the answer to the question is YES Fact 2 is INSUFFICIENT 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!***********************

Manager
Joined: 23 Oct 2017
Posts: 64
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

13 Dec 2017, 21:48
stmt 1: x= y +2 => x-y = 2 => x-y >0 => x > y (sufficient)
stmt 2: x/2 = y-1 => x = 2y -2 => x- 2y <0 => x< 2y (not sufficient)
Manager
Joined: 21 Jul 2015
Posts: 177
GMAT 1: 710 Q49 V38
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

26 Jan 2018, 14:54
Bunuel VeritasPrepKarishma

Could you please provide graphical approach to solve Statement 2? I am able to draw the line on the graph. The line meets the x axis and y axis at points (-2,0) and (0,1) respectively. From this point, how do we determine if there would be a case when y < x. Number plugging approach doesn't come very easily to me, so trying out other ways to solve.

_________________

Please take a moment to hit Kudos if my post helps.

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1343
Location: India
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

29 Jan 2018, 01:42
1
sdlife wrote:
Bunuel VeritasPrepKarishma

Could you please provide graphical approach to solve Statement 2? I am able to draw the line on the graph. The line meets the x axis and y axis at points (-2,0) and (0,1) respectively. From this point, how do we determine if there would be a case when y < x. Number plugging approach doesn't come very easily to me, so trying out other ways to solve.

Hi

They can provide better explanation but I will try. So you have drawn a line of x/2 = y - 1. The other line you should also draw is x = y (or y = x). Why you may ask? Because the question asks you whether x is > y or not? Once you have the line y = x on the graph (it will be a line with positive slope of 1 passing through origin inclined at 45 degrees with x axis), you can see that:- the area on graph below this line y=x will be the area where x > y and the area on the graph above this line y=x will be the area where x < y.

So on one hand, you have this line y=x and on the other hand you have the line x/2 = y-1. You will see that some part of line x/2 = y-1 will fall below the y=x line and some part of line x/2 = y-1 will be above the y=x line. So what does this tell us? This tells us that with the data x/2 = y-1, we CANNOT be sure whether x > y or not.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

30 Jan 2018, 03:00
1
sdlife wrote:
Bunuel VeritasPrepKarishma

Could you please provide graphical approach to solve Statement 2? I am able to draw the line on the graph. The line meets the x axis and y axis at points (-2,0) and (0,1) respectively. From this point, how do we determine if there would be a case when y < x. Number plugging approach doesn't come very easily to me, so trying out other ways to solve.

Yes, you have the line which depicts x/2 = y-1. You see that this represents a line with slope 1/2. So y increases by 1/2 for every 1 unit increase in x.
It passes through (-2, 0) and (0, 1). So if x increases by 2, y increases by 1 so (2, 2) lies on this line. If x increases by another 2, y increases just by 1 so (4, 3) lies on this line too.
In case of some points x > y and in other cases x < y. So this statement alone is not sufficient.
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Joined: 21 Jul 2015
Posts: 177
GMAT 1: 710 Q49 V38
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

30 Jan 2018, 14:29
VeritasPrepKarishma wrote:

Yes, you have the line which depicts x/2 = y-1. You see that this represents a line with slope 1/2. So y increases by 1/2 for every 1 unit increase in x.
It passes through (-2, 0) and (0, 1). So if x increases by 2, y increases by 1 so (2, 2) lies on this line. If x increases by another 2, y increases just by 1 so (4, 3) lies on this line too.
In case of some points x > y and in other cases x < y. So this statement alone is not sufficient.

Hi Karishma,

Thank you very much for your response. Could you please explain the highlighted part?

SD
_________________

Please take a moment to hit Kudos if my post helps.

Manager
Joined: 21 Jul 2015
Posts: 177
GMAT 1: 710 Q49 V38
Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

30 Jan 2018, 19:43
amanvermagmat wrote:
They can provide better explanation but I will try. So you have drawn a line of x/2 = y - 1. The other line you should also draw is x = y (or y = x). Why you may ask? Because the question asks you whether x is > y or not? Once you have the line y = x on the graph (it will be a line with positive slope of 1 passing through origin inclined at 45 degrees with x axis), you can see that:- the area on graph below this line y=x will be the area where x > y and the area on the graph above this line y=x will be the area where x y or not.

amanvermagmat

Thanks a ton for your response. I do understand the solution now. A couple questions if you don't mind answering:

1) How did you think of drawing a line x=y for this question? One clue maybe since it was asked if x>y? But I couldn't even think of it. Any tips on how to solve these type of problems?

2) Probably a dumb question. How do decide that the side above the line y=x will have y>x, while below is x<y?

Thank you very much for your help!
_________________

Please take a moment to hit Kudos if my post helps.

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

30 Jan 2018, 21:57
1
sdlife wrote:
VeritasPrepKarishma wrote:

Yes, you have the line which depicts x/2 = y-1. You see that this represents a line with slope 1/2. So y increases by 1/2 for every 1 unit increase in x.
It passes through (-2, 0) and (0, 1). So if x increases by 2, y increases by 1 so (2, 2) lies on this line. If x increases by another 2, y increases just by 1 so (4, 3) lies on this line too.
In case of some points x > y and in other cases x < y. So this statement alone is not sufficient.

Hi Karishma,

Thank you very much for your response. Could you please explain the highlighted part?

SD

Check this post. It explains you the slope concept of the line.

http://www.veritasprep.com/blog/2010/12 ... he-graphs/
_________________

Karishma
Veritas Prep GMAT Instructor

GMAT self-study has never been more personalized or more fun. Try ORION Free!

DS Forum Moderator
Joined: 22 Aug 2013
Posts: 1343
Location: India
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1  [#permalink]

### Show Tags

30 Jan 2018, 22:08
1
sdlife wrote:
amanvermagmat wrote:
They can provide better explanation but I will try. So you have drawn a line of x/2 = y - 1. The other line you should also draw is x = y (or y = x). Why you may ask? Because the question asks you whether x is > y or not? Once you have the line y = x on the graph (it will be a line with positive slope of 1 passing through origin inclined at 45 degrees with x axis), you can see that:- the area on graph below this line y=x will be the area where x > y and the area on the graph above this line y=x will be the area where x y or not.

amanvermagmat

Thanks a ton for your response. I do understand the solution now. A couple questions if you don't mind answering:

1) How did you think of drawing a line x=y for this question? One clue maybe since it was asked if x>y? But I couldn't even think of it. Any tips on how to solve these type of problems?

2) Probably a dumb question. How do decide that the side above the line y=x will have y>x, while below is x<y?

Thank you very much for your help!

Hi

I dont mind answering any questions, as far as I know their answers

1) Yes, you are right. I thought of drawing x=y because I got the clue from x > y (which the question was asking). As you understand more about graphs, I am sure you will get better in these.

2) Once you plot the line y=x, I am sure you would agree that on one side of it, x > y and on another side of it x < y. How to check which is which? Just take any one point from any one side of the line, and see whether it fits in x > y or x < y. Eg., here you have the line y=x with you. Now on the right side of this line (or below) lets choose a point (3,-1). The x-coordinate of the point is 3, and y coordinate is -1, and its clear that here x > y. So no need to check further, we can be sure that on the right side of the line x=y, all points will have x > y. This means automatically on the left side of the line (or you can say above the line), all points will have x < y (or you could check with any point above the line x=y, and you will find that x < y.
Re: Is x > y? (1) x= y+2 (2) x/2 = y-1 &nbs [#permalink] 30 Jan 2018, 22:08
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.