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

 It is currently 19 Sep 2018, 17:40

### 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

# What is the value of x^2 – y^2?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Dec 2015
Posts: 3
What is the value of x^2 – y^2?  [#permalink]

### Show Tags

Updated on: 18 Dec 2015, 01:01
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:13) correct 37% (00:51) wrong based on 182 sessions

### HideShow timer Statistics

What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

Originally posted by porvakanti on 18 Dec 2015, 00:23.
Last edited by Bunuel on 18 Dec 2015, 01:01, edited 2 times in total.
Renamed the topic, edited the question and moved to DS forum.
Math Expert
Joined: 02 Aug 2009
Posts: 6787
What is the value of x^2 – y^2?  [#permalink]

### Show Tags

18 Dec 2015, 00:35
1
porvakanti wrote:
Hi,
I'm new here. I'd like to know how to solve the below problem:

What is the value of x2 – y2?
I) x+ y= 66
II) xy = 9
A] I alone is sufficient while II alone is not sufficient
B] II alone is sufficient while I alone is not sufficient
C] Neither I nor II is sufficient
D] Both I and II together are sufficient

A brief approach to solve would be very helful.

Hi,
firstlwhat is DS..
you have a statement,.."What is the value of x2 – y2?..
can this be answered by any of the statement?" is what you have to look for..
what is x^2-y^2? (x-y)(x+y)...
so either we know the values of the difference and sum of two numbers or the values of x and y..
lets see the statements.
1)x+ y= 66.... we are yet to know x-y.. insuff
2)xy=9.. again nothing what we are looking for..

combined it gives an imaginary number.. different values of x and y, which will not give you a unique answer..
E
you may search for DS and you will get a way to move around these type of Qs..best of luck
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 18 Dec 2015
Posts: 3
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

18 Dec 2015, 00:54
Thanks Chetan.
So the answer is C - Neither 1 or 2 is sufficient ?
Math Expert
Joined: 02 Sep 2009
Posts: 49251
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

18 Dec 2015, 01:02
1
chetan2u wrote:
porvakanti wrote:
Hi,
I'm new here. I'd like to know how to solve the below problem:

What is the value of x2 – y2?
I) x+ y= 66
II) xy = 9
A] I alone is sufficient while II alone is not sufficient
B] II alone is sufficient while I alone is not sufficient
C] Neither I nor II is sufficient
D] Both I and II together are sufficient

A brief approach to solve would be very helful.

Hi,
firstly the Q does not seem to be a correct one..
what is DS..
you have a statement,.."What is the value of x2 – y2?..
can this be answered by any of the statement?" is what you have to look for..
what is x^2-y^2? (x-y)(x+y)...
so elther we know teh values of the difference and sum of two numbers or thevalues of x and y..
lets see the statements.
1)x+ y= 66.... we rae yet to know x-y.. insuff
2)xy=9.. again nothing what we are looking for..

combined it gives an imaginary number..

you may search for DS and you will get a way to move around these type of Qs..best of luck

According to my calculation the system of equation does not give imaginary numbers. Can you please check again?
_________________
Math Expert
Joined: 02 Aug 2009
Posts: 6787
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

18 Dec 2015, 01:14
Bunuel wrote:
chetan2u wrote:
porvakanti wrote:
Hi,
I'm new here. I'd like to know how to solve the below problem:

What is the value of x2 – y2?
I) x+ y= 66
II) xy = 9

According to my calculation the system of equation does not give imaginary numbers. Can you please check again?

hi Bunuel,
I have the two statements which give me teh sum of the roots and product of the roots..
with these info , I can make the Quad eq as.
x^2-66x+9=0...
Also by substituting the value of y obtained from stat II, I would get the same eq..
in the eq above, if I find the Discriminant..
D=$$\sqrt{(b^2-4ac)}$$....
which is $$\sqrt{(66^2-4*9)}$$, which is going to besquare root of a negat....,
after writing till here, i realize ofcourse it will be positive,... an oversight
thanks
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Math Expert
Joined: 02 Aug 2009
Posts: 6787
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

18 Dec 2015, 01:17
porvakanti wrote:
Thanks Chetan.
So the answer is C - Neither 1 or 2 is sufficient ?

Hi since none are sufficient and combined too they are not suff,
answer will be C, when you get a certain answer after you have combine the info provided by the two statement
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 22 Nov 2015
Posts: 20
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

19 Dec 2015, 07:37
According to Question: value of x^2-y^2 ?

Statement 1: x+y=66
x^2-y^2=(x+y)(x-y)==>(66)(x-y)==> No value . NOT SUFF

Statement 2: xy=9
x^2-y^2=(x+y)(x-y)==> no meaning of xy=9. No value . NOT SUFF

Combining (1)+(2) , no ans, no value. NOT SUFF

ANS: E
Intern
Joined: 24 Mar 2015
Posts: 6
WE: Design (Manufacturing)
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

21 Dec 2015, 06:45
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

x^2-y^2 = (x+y)(x-y)

Using (1) and (2) this question can be solved by using the following formula:
(x+y)^2 = (x-y)^2 + 4xy.

By (1) we have the value of (x+y) and by (2) we have the value of xy.
Putting them both in the above equation will help us get (x-y).
So we have the values of (x+y) as well as (x-y).

Thus C.
Math Expert
Joined: 02 Aug 2009
Posts: 6787
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

21 Dec 2015, 07:35
1
umodi wrote:
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

x^2-y^2 = (x+y)(x-y)

Using (1) and (2) this question can be solved by using the following formula:
(x+y)^2 = (x-y)^2 + 4xy.

By (1) we have the value of (x+y) and by (2) we have the value of xy.
Putting them both in the above equation will help us get (x-y).
So we have the values of (x+y) as well as (x-y).

Thus C.

Hi,
a good approach to the Q but the last step is not correct..
what you finally get is the value of (x-y)^2...
and this will give you two answers for x-y, one positive and one negative..
here (x+y)^2 = (x-y)^2 + 4xy...
(66)^2 = (x-y)^2 + 4*9..
so .(x-y)^2=66^2-36..
so x-y= $$\sqrt{66^2-36}$$ or -$$\sqrt{66^2-36}$$..
so insuff..hope it helped
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 05 Nov 2014
Posts: 112
Location: India
Concentration: Strategy, Operations
GMAT 1: 580 Q49 V21
GPA: 3.75
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

27 Feb 2018, 05:43
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

Can you provide a solution pushpitkc
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3131
Location: India
GPA: 3.12
Re: What is the value of x^2 – y^2?  [#permalink]

### Show Tags

27 Feb 2018, 06:32
harikrish wrote:
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

Can you provide a solution pushpitkc

The individual statements are not enough. But when we combine the
information in both the statements, we know that the quadratic equation
will be x^2 - (sum of roots)x + product of roots = 0 -> x^2 -66x + 9=0

The roots of this equation are
$$\frac{66 + \sqrt4320}{2} = 33 + 32.86 = 65.86$$ (approximately)
$$\frac{66 - \sqrt4320}{2} = 33 - 32.86 = 0.14$$ (approximately)

If there are two roots, the value of x^2 - y^2 will not be unique. (Insufficient - Option E)
_________________

You've got what it takes, but it will take everything you've got

Manager
Joined: 18 Jun 2018
Posts: 154
What is the value of x^2 – y^2?  [#permalink]

### Show Tags

24 Aug 2018, 09:46
porvakanti wrote:
What is the value of x^2 – y^2?

(1) x + y = 66
(2) xy = 9

OA:E
What is the value of $$x^2 – y^2$$ or $$(x-y)(x+y)$$?

(1) $$x + y = 66$$
We are given the value of $$x + y$$, and not given the value of $$x-y$$
So Statement 1 alone is not sufficient.

(2) $$xy = 9$$
The product of $$xy$$ is given but we cannot find either individual value of $$x$$ and $$y$$ or value of expression of $$x^2 – y^2$$ or $$(x-y)(x+y)$$
So Statement 2 alone is not sufficient.

Combining 1 and 2, we get

$$x + y = 66$$
$$(x-y)^2 =(x + y)^2-4xy$$
$$(x-y)^2=(66)^2-4*9=(66)^2-(6)^2 =(66+6)(66-6)=72*60=2^1*3^1*5^1*12^2$$
$$x-y = ±12\sqrt{30}$$
So Expression $$x^2 – y^2$$ can have 2 values : $$12*66*\sqrt{30}$$ or $$-12*66*\sqrt{30}$$
Combining (1) and (2) will also not give unique value of expression $$x^2 – y^2$$
What is the value of x^2 – y^2? &nbs [#permalink] 24 Aug 2018, 09:46
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®.