If x, y and k are integers, is xy divisible by 3?
1. y = 2¹� - 1
2. The sum of the digits of x = 6^k
Information every test-taker should know:
1) a² - b² = (a+b)(a-b).
2) The powers of 2 up to 2¹�.
3) If the sum of the digits of an integer is a multiple of 3, then the integer itself is a multiple of 3.
Statement 1: 1. y = 2¹� - 1
y = 2¹� - 1 = (2� + 1)(2� - 1) = (256 + 1)(256 - 1) = (257)(255)
Since 2+5+5 = 12, 255 is a multiple of 3.
Thus, y is multiple of 3, implying that xy is divisible by 3.
SUFFICIENT.
Statement 2: The sum of the digits of x = 6^k
If k=0, then the sum of the digits of x = 6� = 1.
It's possible that x=1 and y=3, in which case xy is divisible by 3.
It's possible that x=1 and y=2, in which case xy is NOT divisible by 3.
INSUFFICIENT.
The correct answer is
A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
