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

 It is currently 14 Dec 2018, 10:15

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

December 14, 2018

December 14, 2018

10:00 PM PST

11:00 PM PST

Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# a, b, c, and d are positive integers. If (a + b) (c – d) = r

Author Message
TAGS:

### Hide Tags

Manager
Joined: 18 Oct 2011
Posts: 86
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

16 Jan 2013, 13:31
5
00:00

Difficulty:

55% (hard)

Question Stats:

62% (02:14) correct 38% (02:31) wrong based on 187 sessions

### HideShow timer Statistics

a, b, c, and d are positive integers. If (a + b) (c – d) = r, where r is an integer, is √(c + d) an integer?

(1) (a + b) (c + d) = r^2
(2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.

Thought I'd seen 'em all...then got stumped with this one! Give it a try.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

06 Jan 2014, 23:18
10
sambam wrote:
a, b, c, and d are positive integers. If (a + b) (c – d) = r, where r is an integer, is √(c + d) an integer?

(1) (a + b) (c + d) = r^2
(2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.

Thought I'd seen 'em all...then got stumped with this one! Give it a try.

All this question is trying to do is confuse you with a ton of variables. The concept being tested here is simple - the prime factors of a perfect square have even powers.

"is √(c + d) an integer?" is just another way of saying "is (c+d) a perfect square?"

(1) $$(a + b) (c + d) = r^2$$
$$(a + b) (c + d) = (a + b)^2 * (c - d)^2$$
$$(c+d) = (a+b)(c - d)^2$$
We know now that (c+d) is a product of (a+b) and a perfect square. If (a+b) is a perfect square too, then (c+d) is a perfect square. Else it is not. Not sufficient.

(2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.
This tells us that (a+b) is a perfect square. Though alone it is not sufficient since it doesn't tell us anything about (c+d), together with statement 1, it is sufficient.

_________________

Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4489
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

16 Jan 2013, 13:47
8
1
sambam wrote:
a, b, c, and d are positive integers. If (a + b) (c – d) = r, where r is an integer, is √(c + d) an integer?
(1) (a + b) (c + d) = r^2
(2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.

I'm happy to help with this.

Statement #1: (a + b) (c + d) = r^2
The prompt told us that (a + b) (c – d) = r. If we divide the statement #1 equation by the prompt equation, we get [(c + d)]/[(c - d)] = r, which is intriguing, but which doesn't, by itself, tell us anything about whether (c + d), the numerator, is a perfect square. This is insufficient.

Statement #2: (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers
This one definitively tells us that (a + b) is a perfect square, so we know a perfect square times (c - d) equals r, but we know nothing at all about (c + d). This one by itself, doesn't tell us anything. This is insufficient.

Now, consider the statements combined.
Statement #1: (a + b) (c + d) = r^2
Statement #2: (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers
Now, we know that (a + b) is a perfect square, because it has even powers of all prime factors. We also know that r^2 is a perfect square, so it must also have even powers of all prime factors. This can only mean that (c + d) has even powers of all prime factors, and therefore must be a perfect square.
Another way to say that --- we could re-arrange the statement #1 equation to (c + d) = [r^2]/[(a + b))], and we know this quotient is a positive integer. If the ratio of two squares is an integer, that integer must also be a perfect square.
Either way, the combination of statements is now sufficient to give a definitive answer to the prompt.

One thing that's a little unusual about this question --- with the information in both statements, we could answer the prompt question, but as it turned out, the equation given in the prompt was irrelevant. I don't know that this would happen on the GMAT.

Let me know if anyone reading this has any questions.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

SVP
Joined: 06 Sep 2013
Posts: 1721
Concentration: Finance
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

06 Jan 2014, 09:04
1
sambam wrote:
a, b, c, and d are positive integers. If (a + b) (c – d) = r, where r is an integer, is √(c + d) an integer?

(1) (a + b) (c + d) = r^2
(2) (a + b) = x^4 y^6 z^2, where x, y, and z are distinct prime numbers.

Thought I'd seen 'em all...then got stumped with this one! Give it a try.

OK I will give it a try

We are told that (a+b)(c-d) is an integer. We need to find if (c+d) is a perfect square

Statement 1

(a+b)(c+d) = Perfect square

We also have that (a+b)(c-d) is an integer. Let's say x = a+b

Then we have that x(c+d) perfect square and x(c-d) is an integer. What does this tell us?

That x = c+d or that a+b = c+d. But not enough to answer the question

Statement 2

(a+b) = x^4y^6z^2

Clearly insuff

Both together

If (a+b)(c+d) is a perfect square and then (a+b) = x^4y^6z^2 then it must follow that (c+d) is AT LEAST X^2*Z^4 to make it a perfect square

Is X^2*Z^4 a perfect square? Well we are told that x and z are integers so yes

Hope it helps

Kudos rain!!
Cheers!
J
SVP
Joined: 06 Sep 2013
Posts: 1721
Concentration: Finance
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

02 Apr 2014, 14:43
Thanks Karishma, that was precise.

Do you agree with Mike in that it is unlikely that information given in the prompt of a DS question will not be used? Honestly I've never seen a question in which information is given and then not used. Haven't even seen a case such as this one in which it could be used for one of the statements only

Thanks!
Cheers
J
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

02 Apr 2014, 20:53
jlgdr wrote:
Thanks Karishma, that was precise.

Do you agree with Mike in that it is unlikely that information given in the prompt of a DS question will not be used? Honestly I've never seen a question in which information is given and then not used. Haven't even seen a case such as this one in which it could be used for one of the statements only

Thanks!
Cheers
J

I agree that the question is not very well thought out. It has a lot of clutter as if the question maker had something else in mind but it didn't work out and he changed direction mid way. The prompt equation did not add value to analyzing even statement 1 alone though we figure that out after analyzing it using the prompt equation. It's still equivalent to knowing that r is an integer.

Though it is absolutely fine if the prompt info is useful only for one statement. e.g. often you are given in the prompt that xy is not 0 implying that neither x nor y is 0.
x and/or y might be in the denominator in only one statement. It would be fine.
_________________

Karishma
Veritas Prep GMAT Instructor

Non-Human User
Joined: 09 Sep 2013
Posts: 9158
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r  [#permalink]

### Show Tags

27 Feb 2018, 10:59
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: a, b, c, and d are positive integers. If (a + b) (c – d) = r &nbs [#permalink] 27 Feb 2018, 10:59
Display posts from previous: Sort by