It is currently 20 Mar 2018, 16:33

### 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

# M02-08

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

16 Sep 2014, 00:17
Expert's post
8
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:27) correct 31% (02:03) wrong based on 162 sessions

### HideShow timer Statistics

If $$x$$ and $$y$$ are consecutive integers ($$x \gt y$$) and $$x^2-1 \gt y^2-4y+x-1$$, then which of the following must be true?

A. $$y \le 0$$
B. $$y \gt 0$$
C. $$y \gt 1$$
D. $$y \gt 7$$
E. $$y \gt 8$$
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

16 Sep 2014, 00:17
Expert's post
4
This post was
BOOKMARKED
Official Solution:

If $$x$$ and $$y$$ are consecutive integers ($$x \gt y$$) and $$x^2-1 \gt y^2-4y+x-1$$, then which of the following must be true?

A. $$y \le 0$$
B. $$y \gt 0$$
C. $$y \gt 1$$
D. $$y \gt 7$$
E. $$y \gt 8$$

Since $$x$$ and $$y$$ are consecutive integers and $$x \gt y$$ then $$x=y+1$$. Substitute $$x$$ with $$y+1$$ in the given equation:

$$(y+1)^2-1 \gt y^2-4y+(y+1)-1$$;

$$5y \gt 0$$;

$$y \gt 0$$.

_________________
Intern
Joined: 09 Dec 2013
Posts: 8

### Show Tags

09 Oct 2014, 05:21
Bunuel wrote:

Since x and y are consecutive positive integers and x \gt y then x=y+1.

In the question stem is only written consecutive integers. How can we tell that x and y are positive?
Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

09 Oct 2014, 05:26
martinnotceoyet wrote:
Bunuel wrote:

Since x and y are consecutive positive integers and x \gt y then x=y+1.

In the question stem is only written consecutive integers. How can we tell that x and y are positive?

The word "positive" there was wrong. Edited. Check again.
_________________
Intern
Joined: 09 Dec 2013
Posts: 8

### Show Tags

09 Oct 2014, 05:39
Oh! Sweet thank you very much!
Current Student
Joined: 18 Sep 2014
Posts: 231

### Show Tags

24 Mar 2015, 03:30
Hi,
Lets make this a little complicated. Assume that, in the given problem, its is just mentioned that " x and y are positive integers". Then the approach will be a little different.

LHS : x^2 - 1 = (x+1)(x-1)
Since x is positive, we will only consider (x-1)........Eq1
RHS : y^2 -4y +x-1........Eq2

Equating both: (x-1)>y^2 -4y +x-1
We get y(y-4)> 0
Therefore y>0 as the best case and must be true.
_________________

Kindly press the Kudos to appreciate my post !!

Manager
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 129
Location: Peru
GPA: 3.98

### Show Tags

24 Mar 2015, 16:31
I agree that b must be true. However, i be is true, then A must also be true.
If y > 0, then it is also true that Y >= 0.
_________________

Clipper Ledgard
GMAT Coach

Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

25 Mar 2015, 03:36
cledgard wrote:
I agree that b must be true. However, i be is true, then A must also be true.
If y > 0, then it is also true that Y >= 0.

That's not true. If y=0 and x=y+1=1, then $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true.
_________________
Manager
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 129
Location: Peru
GPA: 3.98

### Show Tags

25 Mar 2015, 12:59
Bunuel wrote:
cledgard wrote:
I agree that b must be true. However, i be is true, then A must also be true.
If y > 0, then it is also true that Y >= 0.

That's not true. If y=0 and x=y+1=1, then $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true.

This is a problem of semantics. I agree that Y cannot be 0.
What I say is that if Y is more than 0, then it must also be true that Y is more than -1 , or -2, or it is equal or more than 0.

If you give me any valid number for Y , answers Y>0 and y>= 0 are always true.
_________________

Clipper Ledgard
GMAT Coach

Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

26 Mar 2015, 03:52
cledgard wrote:
Bunuel wrote:
cledgard wrote:
I agree that b must be true. However, i be is true, then A must also be true.
If y > 0, then it is also true that Y >= 0.

That's not true. If y=0 and x=y+1=1, then $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true.

This is a problem of semantics. I agree that Y cannot be 0.
What I say is that if Y is more than 0, then it must also be true that Y is more than -1 , or -2, or it is equal or more than 0.

If you give me any valid number for Y , answers Y>0 and y>= 0 are always true.

No, that's not correct.

The question asks: which of the following must be true?

A says $$y\geq{0}$$, so it allows y to be 0. But y cannot be 0 because in this case $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true. Thus A is not always true.
_________________
Manager
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 129
Location: Peru
GPA: 3.98

### Show Tags

26 Mar 2015, 07:39
I agree that b must be true. However, if b is true, then A must also be true.
If y > 0, then it is also true that Y >= 0.

Quote:
That's not true. If y=0 and x=y+1=1, then $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true.

This is a problem of semantics. I agree that Y cannot be 0.
What I say is that if Y is more than 0, then it must also be true that Y is more than -1 , or -2, or it is equal or more than 0.

If you give me any valid number for Y , answers Y>0 and y>= 0 are always true.[/quote]

Quote:
No, that's not correct.

The question asks: which of the following must be true?

A says $$y\geq{0}$$, so it allows y to be 0. But y cannot be 0 because in this case $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true. Thus A is not always true.

Of course 0 is not true. You must not test O (zero) because it is not a valid answer. What I said is that for any valid integer of Y , y>0 is true, but also Y>=0 is true. This is what the the question asks for.
Let' see it as a sets problem. B is the set of all positive integers, and A is the set of all non-negative integers. This way A has the same elements of B, as well as the 0; therefore, any element that is in B is also in A.
B says that y>0, and that is true. A says that Y is equal or more than 0. If Y is more than 0 -excluding 0- it means that Y>= 0 (more or equal, one or the other). We can even say that Y must be more than -10, and it will be true. Y does not have to be 0 in order to be equal or more than 0.

Study the question carefully.
The question did not ask for all possible values of Y;

The question is: Is A true for all values of Y? The answer is YES
The question is not: : Is Y true for all values of A? The answer is NOT
_________________

Clipper Ledgard
GMAT Coach

Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

26 Mar 2015, 08:43
cledgard wrote:
I agree that b must be true. However, if b is true, then A must also be true.
If y > 0, then it is also true that Y >= 0.

Quote:
That's not true. If y=0 and x=y+1=1, then $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true.

This is a problem of semantics. I agree that Y cannot be 0.
What I say is that if Y is more than 0, then it must also be true that Y is more than -1 , or -2, or it is equal or more than 0.

If you give me any valid number for Y , answers Y>0 and y>= 0 are always true.

Quote:
No, that's not correct.

The question asks: which of the following must be true?

A says $$y\geq{0}$$, so it allows y to be 0. But y cannot be 0 because in this case $$x^2-1 \gt y^2-4y+x-1$$ does NOT hold true. Thus A is not always true.

Of course 0 is not true. You must not test O (zero) because it is not a valid answer. What I said is that for any valid integer of Y , y>0 is true, but also Y>=0 is true. This is what the the question asks for.
Let' see it as a sets problem. B is the set of all positive integers, and A is the set of all non-negative integers. This way A has the same elements of B, as well as the 0; therefore, any element that is in B is also in A.
B says that y>0, and that is true. A says that Y is equal or more than 0. If Y is more than 0 -excluding 0- it means that Y>= 0 (more or equal, one or the other). We can even say that Y must be more than -10, and it will be true. Y does not have to be 0 in order to be equal or more than 0.

Study the question carefully.
The question did not ask for all possible values of Y;

The question is: Is A true for all values of Y? The answer is YES
The question is not: : Is Y true for all values of A? The answer is NOT[/quote]

Edited option A to avoid ambiguity. Thank you.
_________________
Manager
Joined: 05 Jul 2015
Posts: 106
GMAT 1: 600 Q33 V40
GPA: 3.3

### Show Tags

10 Jan 2016, 19:36
I went about it with a mix of algebra and number plugging:
Since X= Y+1

The inequality turns out to be:

Y^2+2Y > Y^2-4y+y
2y>-3y

You might notice right here that Y will increase by 2 on the left and decrease by -3 on the right with any number greater than 0 keeping the statement true. I didn't realize it right away so I just tried a few numbers: 0,1, and finally -1 (made it not true)

Also, you could further reduce the inequality like Bunuel did just to double prove it:
2y > -3y
5y>0
y>0
Intern
Joined: 06 May 2016
Posts: 14

### Show Tags

28 Aug 2016, 06:13
I got the answer as y>0 but it is a must be true question.

So i chose y>8, which wil also be true.

Why not E?
Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

28 Aug 2016, 06:17
gmatravi wrote:
I got the answer as y>0 but it is a must be true question.

So i chose y>8, which wil also be true.

Why not E?

How y > 8 will be true if y > 0? What if y = 1, is 1 greater than 8?
_________________
SVP
Joined: 26 Mar 2013
Posts: 1515

### Show Tags

29 Aug 2016, 07:26
Bunuel wrote:
If $$x$$ and $$y$$ are consecutive integers ($$x \gt y$$) and $$x^2-1 \gt y^2-4y+x-1$$, then which of the following must be true?

A. $$y \le 0$$
B. $$y \gt 0$$
C. $$y \gt 1$$
D. $$y \gt 7$$
E. $$y \gt 8$$

Rearranging the inequality: x(x-1) > y (y-4) & x>y

Another way is to plug in values depending on answer choices

A. $$y \le 0$$ ........Put y= 0 and x =1...........then 0>0 eliminate A

B. y>0 ........................Put y=1 and x = 2...........then 2>-3 .....Keep

To cover choice C,D &E ..put y=9 & x=10..... then 90> 45....Keep

Then for any y>0, the inequality hold true.

Manager
Joined: 23 Jun 2016
Posts: 137

### Show Tags

14 Nov 2017, 21:05
4 of the answer choices are:

2. y>0
3. y>1
4. y>7
5. y > 8

now since it is a "must be true" question, doesn't 3,4,5 reduce to 2? That is, if y > 8, it MUST be true that y > 0.
What am I missing here?
Math Expert
Joined: 02 Sep 2009
Posts: 44351

### Show Tags

14 Nov 2017, 21:29
sevenplusplus wrote:
4 of the answer choices are:

2. y>0
3. y>1
4. y>7
5. y > 8

now since it is a "must be true" question, doesn't 3,4,5 reduce to 2? That is, if y > 8, it MUST be true that y > 0.
What am I missing here?

Yes, if y > 8, then y > 0 too. But the correct answer is y > 0 (y must be greater than 0) and this does not mean that y must necessarily be greater than 8.
_________________
Re: M02-08   [#permalink] 14 Nov 2017, 21:29
Display posts from previous: Sort by

# M02-08

Moderators: chetan2u, Bunuel

 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®.