gmatwarroom wrote:thanks Anurag, Brent and GMATGuruNY.
GMATGuruNY - thanks for getting to reasoning, as that's what exactly I was looking for. But, somehow, I am still not able to get step #2 Add 1 to each exponent. When I did this, I considered only 4 choices from 2 and 4 from 3 and so 4*4 = 16 and so couldnt find any matching answer and so just went with 8 (guess
)
Is it because 1 is ALWAYS a factor or every number? But 1 is not a prime factor --
may be I am missing something basic...
72 = 2³ * 3².
The prime-factorization here implies the following:
To create a factor of 72, we can choose from TWO BUCKETS.
The first bucket (2³) contains three 2's.
The second bucket (3²) contains two 3's.
From the 2³ bucket we can choose no 2's, one 2, two 2's, or three 2's, for A TOTAL OF 4 OPTIONS -- ONE MORE than 2's exponent.
From the 3² bucket, we can choose no 3's, one 3, or two 3's, for A TOTAL OF 3 OPTIONS -- ONE MORE than 3's exponent.
In each case, the number of options from each bucket is ONE MORE than the value of the exponent.
It is for this reason that we ADD ONE to each exponent in the prime-factorization and multiply:
Total number of factors of 72 = (3+1)(2+1) = 12.
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
