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

 It is currently 05 Dec 2019, 17:09

### 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

# For how many unique coordinate points (P, Q), such that P and Q are in

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: You have to have the darkness for the dawn to come
Joined: 09 Nov 2012
Posts: 277
Daboo: Sonu
GMAT 1: 590 Q49 V20
GMAT 2: 730 Q50 V38
For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

### Show Tags

Updated on: 30 Mar 2017, 09:34
3
17
00:00

Difficulty:

95% (hard)

Question Stats:

36% (02:12) correct 64% (02:31) wrong based on 86 sessions

### HideShow timer Statistics

For how many unique coordinate points (P, Q), such that P and Q are integers, is it true that P^2 - Q^2 = 1155?

a) 16
b) 24
c) 32
d) 48
e) 64

Originally posted by daboo343 on 30 Mar 2017, 09:30.
Last edited by Bunuel on 30 Mar 2017, 09:34, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 59561
For how many unique coordinate  [#permalink]

### Show Tags

30 Mar 2017, 09:34
daboo343 wrote:
For how many unique coordinate points (P, Q), such that P and Q are integers, is it true that P2 - Q2 = 1155?

a) 16
b) 24
c) 32
d) 48
e) 64

This is a copy of the following MGMAT question: https://gmatclub.com/forum/for-how-many ... 97167.html
Intern
Joined: 17 Jun 2018
Posts: 6
Re: For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

### Show Tags

05 Jul 2018, 08:10
1
P^2-Q^2=(P+Q)(P-Q)=1155=3*5*7*11
We can think of this as two numbers multiply with each other, and we need to find out the different combination to make the multiple of these two numbers equal to 1155.
3,5,7,11 these 4 numbers can have 8 different combination to get 1155.
(1，3*5*7*11)；(3，5*7*11)；(5，3*7*11)；(7，3*5*11)；(11，3*5*7)；(3*5，7*11)；(5*7，3*11)；(3*7，5*11）
These 4 numbers can also be negative, so we have another 8 different combination to get 1155.
So we totally have (8+8)*2 = 32 different unique combination.
Why we need to multiple by 2?
IF A*B=1155, the value is assigned to A can also be assigned to B. For example, 15*77 and 77*15, both equal to 1155, but they are different points on coordinate.
Intern
Joined: 06 Mar 2018
Posts: 1
Location: India
For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

### Show Tags

Updated on: 08 Jul 2019, 21:27
Can I do this question by using the number of distinct factors formula?
Which says if A x B = N where N = a^p . b^q . c^r . d^s , where a,b,c,d are prime factors,
then the number of distinct factors of A x B = (p+1)(q+1)(r+1)(s+1)
which turns out to be 2.2.2.2 = 16.
Now P and Q both can take these distinct values, therefore the total number of possible values= 16 . 2 =32
The number of distinct factors will give us how many different values can A and B take.

Originally posted by baljitbagga on 08 Jul 2019, 17:05.
Last edited by baljitbagga on 08 Jul 2019, 21:27, edited 1 time in total.
Manager
Joined: 23 Jan 2018
Posts: 222
Location: India
WE: Information Technology (Computer Software)
Re: For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

### Show Tags

08 Jul 2019, 20:20
baljitbagga wrote:
Can I do this question by using the number of distinct factors formula?
Which says if A x B = N where N = a^p . b^q . c^r . d^s , where a,b,c,d are prime factors,
then the number of distinct factors of A x B = (p+1)(q+1)(r+1)(s+1)
which turns out to be 2.2.2.2 = 32.
Number of distinct factors will give us how many different values can A and B take.

This multiplication equals to 16.

Quote:
which turns out to be 2.2.2.2 = 32.

I think you need to add 1 also as a factor. So the factors are 1,3,5,7 and 11.

Now it will be 32.

Intern
Joined: 22 Oct 2019
Posts: 13
Location: India
Schools: HEC Montreal '21
Re: For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

### Show Tags

15 Nov 2019, 05:11
How can we consider combinations od (P+Q) and (P-Q) as the possible answer choices for (P,Q)?
It is quite possible that P and Q turn out to be fractions while they add up to the possibilities. And it is clearly mentioned that P and Q are integers.
Re: For how many unique coordinate points (P, Q), such that P and Q are in   [#permalink] 15 Nov 2019, 05:11
Display posts from previous: Sort by