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

 It is currently 23 Oct 2019, 16:23

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

xy and yx are a pair of reversed two digit positive integers. If x^2-y

Author Message
TAGS:

Hide Tags

VP
Joined: 07 Dec 2014
Posts: 1224
xy and yx are a pair of reversed two digit positive integers. If x^2-y  [#permalink]

Show Tags

26 Aug 2018, 15:03
4
00:00

Difficulty:

85% (hard)

Question Stats:

51% (02:42) correct 49% (02:04) wrong based on 68 sessions

HideShow timer Statistics

xy and yx are a pair of reversed two digit positive integers. If x^2-y^2=45, how many such pairs are there?

A. 0
B. 1
C. 2
D. 3
E. 4
Senior SC Moderator
Joined: 22 May 2016
Posts: 3581
xy and yx are a pair of reversed two digit positive integers. If x^2-y  [#permalink]

Show Tags

26 Aug 2018, 18:44
gracie wrote:
xy and yx are a pair of reversed two digit positive integers. If x^2-y^2=45, how many such pairs are there?

A. 0
B. 1
C. 2
D. 3
E. 4

If $$x^2-y^2=45$$, then
$$(x+y)(x-y)=45$$

$$(x+y)=a$$: one factor of 45
$$(x-y)=b$$: another factor of 45

Factors of 45
$$(a)*(b)=45$$
$$1*45=45$$
$$3*15=45$$
$$5*9=45$$

The first set of factors will not work
$$x+y=45$$
$$x-y=1$$ Add
$$2x=46$$
$$x=23$$

Second set of factors
$$x+y=15$$
$$x-y=3$$ Add
$$2x=18$$
$$x=9$$

$$x-y=3$$
$$9-y=3$$
$$y=6$$

One pair, xy and yx: 96 and 69
$$(x^2-y^2)=(9^2-6^2)=(81-36)=45$$

Third set of factors
$$x+y=9$$
$$x-y=5$$ Add
$$2x=14$$
$$x=7$$

$$x-y=5$$
$$7-y=5$$
$$y=2$$

Another pair: 72 and 27
$$(x^2-y^2)=(7^2-2^2)=(49-4)=45$$

There are no more factor sets.

xy and yx are
96 and 69
72 and 27

Number of pairs: 2

_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.

Instructions for living a life. Pay attention. Be astonished. Tell about it. -- Mary Oliver
Director
Joined: 24 Nov 2016
Posts: 643
Location: United States
xy and yx are a pair of reversed two digit positive integers. If x^2-y  [#permalink]

Show Tags

19 Oct 2019, 08:10
gracie wrote:
xy and yx are a pair of reversed two digit positive integers. If x^2-y^2=45, how many such pairs are there?

A. 0
B. 1
C. 2
D. 3
E. 4

$$1≤(x,y)≤9…2≤(x+y)≤18$$
$$x^2-y^2=45…(x+y)(x-y)=45…factor.pairs(45)=(45,1);(15,3);(9,5)$$
$$(x+y)(x-y)=(45)(1)…(x+y)=45=invalid…(x+y≤18)$$
$$(x+y)(x-y)=(15)(3)…(x+y)=15…(x-y)=3…2x=18…x=9…y=6$$
$$(x+y)(x-y)=(9)(5)…(x+y)=9…(x-y)=5…2x=14…x=7…y=2$$
$$(xy,yx)=(96,69);(72,72)=2.pairs$$

SVP
Joined: 03 Jun 2019
Posts: 1756
Location: India
Re: xy and yx are a pair of reversed two digit positive integers. If x^2-y  [#permalink]

Show Tags

19 Oct 2019, 08:15
gracie wrote:
xy and yx are a pair of reversed two digit positive integers. If x^2-y^2=45, how many such pairs are there?

A. 0
B. 1
C. 2
D. 3
E. 4

Given: xy and yx are a pair of reversed two digit positive integers.

Asked: If x^2-y^2=45, how many such pairs are there?

(x-y)(x+y) = 45 = 9*5 = 15*3

Case 1:
x-y = 5
x+y =9
(x,y) = (7,2)

Case 2:
x-y = 3
x+y = 15
(x,y) = (9,6)

xy = {72,27,96,69}
Pairs = 2

IMO C
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Re: xy and yx are a pair of reversed two digit positive integers. If x^2-y   [#permalink] 19 Oct 2019, 08:15
Display posts from previous: Sort by