BTGmoderatorDC wrote: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.
OA D
Source: GMAT Prep
Let's take each statement one by one.
(1) When p is divided by 8, the remainder is 5.
=> p = 8q + 5; where q is a quotient
Thus, p/4 = (8q + 5)/4 = (8q + 4 + 1)/4 = 4(2q + 1)/4 + 1/4 = (2q + 1) + 1/4
Remainder when p is divided by 4 is 1. Sufficient.
(2) p is the sum of the squares of two positive integers.
Since p is an odd integer and is equal to the sum of the squares of two positive integers, one of the two positive integers must be even and the other must be odd.
So, we have p = E^2 + O^2; where E = Even integer and O = Odd integer
Note that E^2 is always a multiple of 4, thus divisible by 4; thus, the remainder when p is divided by 4 would be determined by O^2/4.
So, O is one among 1, 3, 5, 7, 9, ...
Case 1: Say O = 1, thus, O^2 = 1^2 = 1 => 1/4 => remainder = 1;
Case 2: Say O = 3, thus, O^2 = 3^2 = 1 => 9/4 => remainder = 1;
Case 3: Say O = 5, thus, O^2 = 5^2 = 1 => 25/4 => remainder = 1
In each case, the remainder = 1. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
_________________
Manhattan Review GMAT Prep
Locations:
Lausanne GMAT Prep |
Free TOEFL Practice Questions |
LSAT Prep Courses Montreal |
Hong Kong SAT Prep Courses | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor!
Click here.
