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Senior Manager  G
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]

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3
17 00:00

Difficulty:   95% (hard)

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

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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 V
Joined: 02 Sep 2009
Posts: 59561
For how many unique coordinate  [#permalink]

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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  B
Joined: 17 Jun 2018
Posts: 6
Re: For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

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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  B
Joined: 06 Mar 2018
Posts: 1
Location: India
For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

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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  G
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Re: For how many unique coordinate points (P, Q), such that P and Q are in  [#permalink]

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

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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
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