Anindya Madhudor wrote:How many numbers that are not divisible by 6 divide evenly into 264,600?
a. 16
b. 36
c. 51
d. 63
e. 72
OA: D
264,600 = 2³ * 3³ * 5² * 7².
At its core, this is a COMBINATORICS question.
A factor of 264,600 can COMBINE up to three 2's, three 3's, two 5's, and two 7's.
Any FACTOR COMBINATION that does not include both 2 and 3 will not be a multiple of 6.
Case 1: Factor combinations that include NO 2's OR 3's
Number of options for 5 = 3. (No 5's, one 5, or two 5's.)
Number of options for 7 = 3. (No 7's, one 7, or two 7's.)
To combine these options, we multiply:
3*3 = 9.
Case 2: Factors combinations that include AT LEAST ONE 2
Number of options for 2 = 3. (One 2, two 2's, or three 2's.)
Number of options for 5 = 3. (No 5's, one 5, or two 5's.)
Number of options for 7 = 3. (No 7's, one 7, or two 7's.)
To combine these options, we multiply:
3*3*3 = 27.
Case 3: Factor combinations that include AT LEAST ONE 3
Number of options for 3 = 3. (One 3, two 3's, or three 3's.)
Number of options for 5 = 3. (No 5's, one 5, or two 5's.)
Number of options for 7 = 3. (No 7's, one 7, or two 7's.)
To combine these options, we multiply:
3*3*3 = 27.
Total options = 9+27+27 = 63.
The correct answer is
D.
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
