Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 24 May 2015, 15:21

### 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

# if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Intern
Joined: 06 Jun 2010
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18 [#permalink]  16 Jun 2010, 09:41
00:00

Difficulty:

(N/A)

Question Stats:

77% (02:33) correct 23% (01:12) wrong based on 52 sessions
can someone help with the below DS problems.

1st problem
-----------------
if xy=-6 what is xy(x+y)
1.x-y = 5
2.xy^2 = 18.

2nd problem
-----------
can the +ve integer "p" be expressed as the product of two integers, each of which is greater than 1?
1. 31<p<37
2. p is odd.
Math Expert
Joined: 02 Sep 2009
Posts: 27472
Followers: 4312

Kudos [?]: 42232 [1] , given: 5968

Re: NUMBERS !!!! [#permalink]  16 Jun 2010, 10:08
1
KUDOS
Expert's post
1. If xy=-6, what is xy(x+y)?

As given that $$xy=-6$$, then we should be able to determine only the value of $$x+y$$.

(1) $$x-y = 5$$ --> $$x=y+5$$ --> $$(y+5)y=-6$$ --> solving for $$y$$ gives $$y=-3$$ or $$y=-2$$ --> if $$y=-3$$, then $$x=2$$ and $$x+y=-1$$ but if $$y=-2$$, thren $$x=3$$ and $$x+y=1$$. Two values for $$x+y$$. Not sufficient.

(2) $$xy^2 = 18$$ --> $$(xy)*y=18$$ --> as $$xy=-6$$ --> $$-6y=18$$ --> $$y=-3$$ and $$x=2$$ --> $$x+y=-1$$. Sufficient.

2. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

If positive integer p cannot be expressed as the product of two integers >1 it would mean that p is a prime number. So, basically question asks is p prime?

(1) 31<p<37 --> between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient.

(2) p is odd --> odd numbers can be primes as well as non-primes. Not sufficient.

Hope it helps.

P.S. Pleas post one question per topic.
_________________
Intern
Joined: 06 Jun 2010
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: NUMBERS !!!! [#permalink]  16 Jun 2010, 10:37
Many thanks Bunuel !!!
Intern
Joined: 15 Oct 2011
Posts: 35
Followers: 0

Kudos [?]: 4 [0], given: 21

Re: NUMBERS !!!! [#permalink]  13 Oct 2012, 11:57
Thanks for the explanation!
Can this also be solved as:

xy=-6 => the question amounts to -6(x+y) = ?

a) x-y=5.. => x = y+5 => -6(2y+5) = ?

Y can take any value.. hence, insufficient.

b) sufficient because as y=-3 and x =2, -6(x+y) can be determined.

Hence B.

Is the reasoning for Statement 1 above being insufficient, correct?

Bunuel wrote:
1. If xy=-6, what is xy(x+y)?

As given that $$xy=-6$$, then we should be able to determine only the value of $$x+y$$.

(1) $$x-y = 5$$ --> $$x=y+5$$ --> $$(y+5)y=-6$$ --> solving for $$y$$ gives $$y=-3$$ or $$y=-2$$ --> if $$y=-3$$, then $$x=2$$ and $$x+y=-1$$ but if $$y=-2$$, thren $$x=3$$ and $$x+y=1$$. Two values for $$x+y$$. Not sufficient.

(2) $$xy^2 = 18$$ --> $$(xy)*y=18$$ --> as $$xy=-6$$ --> $$-6y=18$$ --> $$y=-3$$ and $$x=2$$ --> $$x+y=-1$$. Sufficient.

2. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

If positive integer p can not be expressed as the product of two integers >1 it would mean that p is a prime number. So, basically question asks is p prime?

(1) 31<p<37 --> between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient.

(2) p is odd --> odd numbers can be primes as well as non-primes. Not sufficient.

Hope it helps.

P.S. Pleas post one question per topic.
Math Expert
Joined: 02 Sep 2009
Posts: 27472
Followers: 4312

Kudos [?]: 42232 [0], given: 5968

if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18 [#permalink]  13 Oct 2012, 12:16
Expert's post
prep wrote:
Thanks for the explanation!
Can this also be solved as:

xy=-6 => the question amounts to -6(x+y) = ?

a) x-y=5.. => x = y+5 => -6(2y+5) = ?

Y can take any value.. hence, insufficient.

b) sufficient because as y=-3 and x =2, -6(x+y) can be determined.

Hence B.

Is the reasoning for Statement 1 above being insufficient, correct?

Bunuel wrote:
1. If xy=-6, what is xy(x+y)?

As given that $$xy=-6$$, then we should be able to determine only the value of $$x+y$$.

(1) $$x-y = 5$$ --> $$x=y+5$$ --> $$(y+5)y=-6$$ --> solving for $$y$$ gives $$y=-3$$ or $$y=-2$$ --> if $$y=-3$$, then $$x=2$$ and $$x+y=-1$$ but if $$y=-2$$, thren $$x=3$$ and $$x+y=1$$. Two values for $$x+y$$. Not sufficient.

(2) $$xy^2 = 18$$ --> $$(xy)*y=18$$ --> as $$xy=-6$$ --> $$-6y=18$$ --> $$y=-3$$ and $$x=2$$ --> $$x+y=-1$$. Sufficient.

2. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

If positive integer p can not be expressed as the product of two integers >1 it would mean that p is a prime number. So, basically question asks is p prime?

(1) 31<p<37 --> between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient.

(2) p is odd --> odd numbers can be primes as well as non-primes. Not sufficient.

Hope it helps.

P.S. Pleas post one question per topic.

Not quite. As you can see from my post: xy=-6 and x-y=5 has two sets of solutions: x=2 and y=-3 OR x=3 and y=-2. So, saying that we cannot determine the value of -6(2y+5) because y can take ANY value is not correct.

Hope it's clear.
_________________
Intern
Joined: 15 Oct 2011
Posts: 35
Followers: 0

Kudos [?]: 4 [0], given: 21

Re: if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18 [#permalink]  14 Oct 2012, 10:07
Bunuel wrote:
Not quite. As you can see from my post: xy=-6 and x-y=5 has two sets of solutions: x=2 and y=-3 OR x=3 and y=-2. So, saying that we cannot determine the value of -6(2y+5) because y can take ANY value is not correct.

Hope it's clear.

Thanks! I totally understand your solution and the fact that a quadratic gets two roots and hence two solutions.
But for a moment consider y takes 0. (the question has no restriction on y)
thus -6(5) = -30
Now, if y takes 2, then -6(9) = -54... and so on.
Hence, there isn't a distinct value the equation xy(x+y) is arriving at, given the conditions. Thus, insufficient. Not sure if this is the way to approach it though!

Another way could be: -6(x+y) = z (some constant) and then solve x-y=5 , simultaneously. So, three unknowns and two equations. Hence no solutions.
Please let me know your thoughts on this.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5539
Location: Pune, India
Followers: 1370

Kudos [?]: 6969 [0], given: 178

Re: NUMBERS !!!! [#permalink]  14 Oct 2012, 20:51
Expert's post
prep wrote:
Thanks for the explanation!
Can this also be solved as:

xy=-6 => the question amounts to -6(x+y) = ?

a) x-y=5.. => x = y+5 => -6(2y+5) = ?

Y can take any value.. hence, insufficient.

Is the reasoning for Statement 1 above being insufficient, correct?

Responding to a pm:

"xy=-6 => the question amounts to -6(x+y) = ?"
This is fine. You have replaced one part fo the question but don't forget that we still have some info on the other part i.e. on x and y. We know that xy = -6 so x = -6/y

Statement 1 tells us x-y=5.. => x = y+5. Fine.

The questions becomes: -6(2y+5) = ?

What are the restrictions on y?
-6/y = y + 5
-6 = y^2 + 5y
y = -2 or -3

Mind you, y cannot be 0 because xy must be -6 and x-y must be 5.
y can take NO value other than -2 or -3.

Hence, it is incorrect to say that y can take any value and hence not sufficient.

Say, statement 2 were different and it gave you 2 values for y: -2 or 5
If you use your logic, you would say that the answers is E since you cannot get a unique value for y. But in that case, the answer would have been C since -2 would be the common value out of the two statements.

Hence, it is important to understand and utilize all the constraints given.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 15 Oct 2011 Posts: 35 Followers: 0 Kudos [?]: 4 [0], given: 21 Re: NUMBERS !!!! [#permalink] 14 Oct 2012, 20:54 Thanks a lot! That makes it clear VeritasPrepKarishma wrote: prep wrote: Thanks for the explanation! Can this also be solved as: xy=-6 => the question amounts to -6(x+y) = ? a) x-y=5.. => x = y+5 => -6(2y+5) = ? Y can take any value.. hence, insufficient. Is the reasoning for Statement 1 above being insufficient, correct? Responding to a pm: "xy=-6 => the question amounts to -6(x+y) = ?" This is fine. You have replaced one part fo the question but don't forget that we still have some info on the other part i.e. on x and y. We know that xy = -6 so x = -6/y Statement 1 tells us x-y=5.. => x = y+5. Fine. The questions becomes: -6(2y+5) = ? What are the restrictions on y? -6/y = y + 5 -6 = y^2 + 5y y = 2 or 3 Mind you, y cannot be 0 because xy must be -6 and x-y must be 5. y can take NO value other than 2 or 3. Hence, it is incorrect to say that y can take any value and hence not sufficient. Say, statement 2 were different and it gave you 2 values for y: 2 or 5 If you use your logic, you would say that the answers is E since you cannot get a unique value for y. But in that case, the answer would have been C since 2 would be the common value out of the two statements. Hence, it is important to understand and utilize all the constraints given. Intern Joined: 15 Oct 2011 Posts: 35 Followers: 0 Kudos [?]: 4 [0], given: 21 Re: if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18 [#permalink] 14 Oct 2012, 20:55 Thanks a lot for the explanations!! Bunuel wrote: prep wrote: Thanks for the explanation! Can this also be solved as: xy=-6 => the question amounts to -6(x+y) = ? a) x-y=5.. => x = y+5 => -6(2y+5) = ? Y can take any value.. hence, insufficient. b) sufficient because as y=-3 and x =2, -6(x+y) can be determined. Hence B. Is the reasoning for Statement 1 above being insufficient, correct? Bunuel wrote: 1. If xy=-6, what is xy(x+y)? As given that $$xy=-6$$, then we should be able to determine only the value of $$x+y$$. (1) $$x-y = 5$$ --> $$x=y+5$$ --> $$(y+5)y=-6$$ --> solving for $$y$$ gives $$y=-3$$ or $$y=-2$$ --> if $$y=-3$$, then $$x=2$$ and $$x+y=-1$$ but if $$y=-2$$, thren $$x=3$$ and $$x+y=1$$. Two values for $$x+y$$. Not sufficient. (2) $$xy^2 = 18$$ --> $$(xy)*y=18$$ --> as $$xy=-6$$ --> $$-6y=18$$ --> $$y=-3$$ and $$x=2$$ --> $$x+y=-1$$. Sufficient. Answer: B. 2. Can the positive integer p be expressed as the product of two integers, each of which is greater than 1? If positive integer p can not be expressed as the product of two integers >1 it would mean that p is a prime number. So, basically question asks is p prime? (1) 31<p<37 --> between these numbers there is no prime. Hence ANY integer from these range CAN be expresses as the product of two numbers. Sufficient. (2) p is odd --> odd numbers can be primes as well as non-primes. Not sufficient. Answer: A. Hope it helps. P.S. Pleas post one question per topic. Not quite. As you can see from my post: xy=-6 and x-y=5 has two sets of solutions: x=2 and y=-3 OR x=3 and y=-2. So, saying that we cannot determine the value of -6(2y+5) because y can take ANY value is not correct. Hope it's clear. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5539 Location: Pune, India Followers: 1370 Kudos [?]: 6969 [0], given: 178 Re: if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18 [#permalink] 14 Oct 2012, 21:27 Expert's post warya75 wrote: can someone help with the below DS problems. 1st problem ----------------- if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18. You can use some identities of algebra to solve it too. 1. x-y = 5 (x + y)^2 = (x - y)^2 + 4xy = 5^2 + 4(-6) = 1 So (x+y) can be 1 or -1. Not sufficient. 2. xy^2 = 18 (-6)y = 18 So y = -3 which gives x = 2 Now you have a unique value for xy(x+y) so sufficient. Answer (B) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 12 Oct 2012
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18 [#permalink]  14 Oct 2012, 22:28
Thanks a lot nice sharing of data sufficiency questions.
Re: if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18   [#permalink] 14 Oct 2012, 22:28
Similar topics Replies Last post
Similar
Topics:
11 If xy = - 6, what is the value of xy(x+y)? 9 18 Feb 2014, 02:52
2 If xy = -6 , what is the value of xy(x+y ) ? 3 07 Oct 2010, 05:46
If xy=-6, what is xy(x + y)? 1) x - y = 5 2) x(y^2) = 18 7 29 Jan 2008, 17:12
If XY=-6, what is the value of XY(X+Y)? 1) X-Y=5 2) XY^2=18 4 21 Aug 2007, 21:50
If xy = -6 , what is the value of xy(x+y ) ? (1) x y = 5 (2) 6 18 Apr 2007, 10:00
Display posts from previous: Sort by

# if xy=-6 what is xy(x+y) 1.x-y = 5 2.xy^2 = 18

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.