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

It is currently 16 Oct 2019, 10:44

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

If x and y are consecutive integers and x < y, then y^2 - x^2 must be

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior RC Moderator
User avatar
V
Joined: 02 Nov 2016
Posts: 4106
GPA: 3.39
If x and y are consecutive integers and x < y, then y^2 - x^2 must be  [#permalink]

Show Tags

New post 04 Mar 2019, 14:13
1
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (01:16) correct 20% (01:21) wrong based on 40 sessions

HideShow timer Statistics

If x and y are consecutive integers and \(x < y\), then \(y^2 - x^2\) must be

A. a prime number.
B. an odd number.
C. an even number.
D. the square of an integer.
E. \((y-x)^2\).

_________________
Most Helpful Expert Reply
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3074
Re: If x and y are consecutive integers and x < y, then y^2 - x^2 must be  [#permalink]

Show Tags

New post 04 Mar 2019, 22:55

Solution



Given:
    • The numbers x and y are consecutive integers
    • Also x < y

To find:
    • Which of the given options is always true, regarding the value of \(y^2 – x^2\)

Approach and Working:
As x < y and x, y are consecutive integers, we can say that
    • If x = n, then y = n + 1
    • Therefore, \(y^2 – x^2 = (n + 1)^2 – n^2 = n^2 + 2n + 1 – n^2 = 2n + 1\), which is always an odd integer.

Alternatively, we can assume values also to determine the answer.
    • If x = 2 and y = 3, then \(y^2 – x^2 = 9 – 4 = 5\)
      o Therefore, \(y^2 – x^2\) can be either a prime or an odd number, we can rule out the other possibilities.

    • If x = 7 and y = 8, then \(y^2 – x^2 = 64 – 49 = 15\), which is odd but not a prime number.

Hence, the correct answer is option B.

Answer: B

Image

_________________
General Discussion
VP
VP
User avatar
D
Joined: 31 Oct 2013
Posts: 1469
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
CAT Tests
Re: If x and y are consecutive integers and x < y, then y^2 - x^2 must be  [#permalink]

Show Tags

New post 04 Mar 2019, 14:23
SajjadAhmad wrote:
If x and y are consecutive integers and \(x < y\), then \(y^2 - x^2\) must be

A. a prime number.
B. an odd number.
C. an even number.
D. the square of an integer.
E. \((y-x)^2\).



x and y are consecutive integers. Thus, one of them must be odd and one of them must be even.

even - odd = odd.

Result must be an odd integer.

B is the correct answer.
Manager
Manager
User avatar
G
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Premium Member
Re: If x and y are consecutive integers and x < y, then y^2 - x^2 must be  [#permalink]

Show Tags

New post 04 Mar 2019, 17:05
1
\(x < y\) and \(x\) and \(y\) are consecutive.

Hence we can rewrite \(y\) as: \(y = x +1\)

Thus: \(y^2 - x^2 = (y - x) (y + x) = (x + 1 - x) (x + 1 + x) = 2x + 1\),

which is an odd number.

_________________
If you like my post, Kudos are appreciated! Thank you.


MEMENTO AUDERE SEMPER
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If x and y are consecutive integers and x < y, then y^2 - x^2 must be  [#permalink]

Show Tags

New post 06 Mar 2019, 02:19
difference of square of two consective no will always result in an odd no
IMO B

SajjadAhmad wrote:
If x and y are consecutive integers and \(x < y\), then \(y^2 - x^2\) must be

A. a prime number.
B. an odd number.
C. an even number.
D. the square of an integer.
E. \((y-x)^2\).
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8069
Location: United States (CA)
Re: If x and y are consecutive integers and x < y, then y^2 - x^2 must be  [#permalink]

Show Tags

New post 08 Mar 2019, 08:00
SajjadAhmad wrote:
If x and y are consecutive integers and \(x < y\), then \(y^2 - x^2\) must be

A. a prime number.
B. an odd number.
C. an even number.
D. the square of an integer.
E. \((y-x)^2\).


Since x and y are consecutive integers and x < y, then y = x + 1. Thus, y^2 - x^2 = (x + 1)^2 - x^2 = x^2 + 2x + 1 - x^2 = 2x + 1, which is always an odd number, regardless of what integer x is.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Bot
Re: If x and y are consecutive integers and x < y, then y^2 - x^2 must be   [#permalink] 08 Mar 2019, 08:00
Display posts from previous: Sort by

If x and y are consecutive integers and x < y, then y^2 - x^2 must be

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne