mikepamlyla wrote:If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?
(1) b = (a/100)^(-1)
(2) c = 100^b
Does (a/100) * (b/100) * c = integer?
Test integer values such that a < b < c.
Statement 1: b = (a/100)¯¹
Thus, b = 100/a.
Test the smallest possible value for a.
Case 1: a=1
Here, b =100/1 = 100.
In this case, (a/100) * (b/100) * c = 1/100 * 100/100 * c = c/100.
If c = 200, then c/100 = 2, which is an integer.
If c = 201, then c/100 = 201/100, which is not an integer.
INSUFFICIENT.
Statement 2: c = 100^b
Test the smallest possible value for b.
Case 2: b=2
Here, a=1 and c = 100² = 10000.
In this case, (a/100) * (b/100) * c = 1/100 * 2/100 * 10000 = 2, which is an integer.
Test an extreme value for b.
Case 3: b=100
Here, c = 100¹��.
In this case, (a/100) * (b/100) * c = a/100 * 10/100 * 100¹�� = 10a * 100��, which is an integer.
Cases 2 and 3 illustrate that -- given that c = 100^b -- (a/100) * (b/100) * c will always be equal to an integer value.
SUFFICIENT.
The correct answer is
B.
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
