Last visit was: 03 Oct 2024, 19:25 It is currently 03 Oct 2024, 19:25
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Joined: 20 Feb 2012
Posts: 25
Own Kudos [?]: 2663 [342]
Given Kudos: 6
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 95922
Own Kudos [?]: 664877 [220]
Given Kudos: 87494
Send PM
avatar
Joined: 03 Apr 2015
Posts: 18
Own Kudos [?]: 22 [6]
Given Kudos: 6
Schools: ISB '16 (A)
Send PM
General Discussion
avatar
Joined: 02 Jul 2015
Posts: 16
Own Kudos [?]: 175 [0]
Given Kudos: 45
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
Can you please explain why the other number has to be even as p is odd?
When we take two odd numbers ie {(1,3),(3,5),(5,7)} etc.. the sum of squares are (10,34,74) and all those give a remainder of 2. Please do explain.
Current Student
Joined: 10 Mar 2013
Posts: 353
Own Kudos [?]: 2796 [4]
Given Kudos: 200
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.7
WE:Marketing (Telecommunications)
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
2
Kudos
2
Bookmarks
BANON
If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.

Got it wrong, was happy to see that Statement 1 is sufficient and rushed on Statement 2..)))

(1) p=8k+5: 5, 13, 21, 29 etc. we have a valid pattern here and each time a remainder of 1. Sufficient
(2) p is the sum of the squares of two positive integers -> the least possible number is \(1^2+2^2=5\) , 13, 17, 25, 29 and each time we have a remainder of 1 (actually almost the samt thing as above) Sufficient

Answer D

Also see the post from Ron(MGMAT) it's really good:
https://www.manhattanprep.com/gmat/foru ... t3557.html
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10129
Own Kudos [?]: 17430 [2]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.

In the original condition, there is 1 variables(p), which should match with the number of equation. So you need 1 equation. For 1) 1euquation, for 2) 1 equation, which is likely to make D the answer. In 1), the remainder from p=8m+5=4(2m+1)+1 is 1, which is unique and sufficient.
In 2), from p=odd=a^2+b^2, either a or b should be an even integer and the other should be an odd integer. In case of even^2+odd^2, even^2 is always divided by 4. For odd^2, from 1^2=1, 3^2=9, 5^2=25, 7^2=49, 9^2=81, all of them are divided by 4 and the remainder is 1, which is unique and sufficient. Therefore, the answer is D.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
Joined: 06 Nov 2014
Posts: 1789
Own Kudos [?]: 1391 [4]
Given Kudos: 23
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
4
Kudos
Expert Reply
BANON
If p is a positive odd integer, what is the remainder when p is divided by 4 ?

(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers.

GIven: P is a positive odd integer.
Required: Remainder of p/4

Statement 1:Remainder (p/8) = 5
Hence p = 8k + 5 = 8k + 4 + 1
Hence Remainder (p/5) = 1
SUFFICIENT

Statement 2: p = x^2 + y^2
We are given that p = odd
Hence p = (2k)^2 + (2n+1)^2
p = 4(k^2 + n^2) + 4n + 1
Remainder of (p/4) = 1
SUFFICIENT

Correct Option: D
Joined: 03 Aug 2018
Posts: 13
Own Kudos [?]: 4 [0]
Given Kudos: 46
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
Alternative way to solve the first statement is-
As 4 is the factor of 8, so if the number leaves a remainder of 5 when divided by 8, it will leave the remainder 5-4 =1, when divided by 4. For ex if n left a remainder of 3 (or any positive integer less than 4), then remainder 3 will remain same when n is divided by 4. Detailed theory below-


If a number leaves a remainder ‘r’ (the number is the divisor), all its factors will have the same remainder ‘r’ provided the value of ‘r’ is less than the value of the factor.
Eg. If remainder of a number when divided by 21 is 5, then the remainder of that same number when divided by 7 (which is a factor of 21) will also be 5.

If the value of ‘r’ is greater than the value of the factor, then we have to take the remainder of ‘r’ divided by the factor to get the remainder.
Eg. If remainder of a number when divided by 21 is 5, then the remainder of that same number when divided by 3 (which is a factor of 21) will be remainder of 5/3, which is 2.
Joined: 02 Jan 2016
Status:Studying 4Gmat
Posts: 363
Own Kudos [?]: 115 [0]
Given Kudos: 314
Location: India
Concentration: Strategy, Entrepreneurship
GMAT 1: 590 Q37 V33
GPA: 4
WE:Law (Manufacturing)
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
Question stem analysis:
From question stem we know that R is less than divisor i.e. R is less than 4, as the dividend is odd it can be either 3 or 1.

Statement I is pretty straightforward. Dividend can be 5, 5+8, 5+16....everytime we will get 1 as remainder.

Statement II the smallest non-negative will be "2", hence when we raise it to power of 2, we will always have 4*Someinteger form. Hence 2/4/6 raised to power of 2 will be divisible by 4. however for odd number from 1/3/5/ raised to power of two, we will always get remainder as 1.

Even^2/4 + Odd^2/4 has remainder as 1. sufficient.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 35105
Own Kudos [?]: 890 [0]
Given Kudos: 0
Send PM
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
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.
GMAT Club Bot
Re: If p is a positive odd integer, what is the remainder when p is divide [#permalink]
Moderator:
Math Expert
95922 posts