Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
May 1408:30 AM PDT
-09:30 AM PDT
Most GMAT test-takers are intimidated by the hardest GMAT Verbal questions. In this session, Target Test Prep GMAT instructor Erika Tyler-John, a 100th percentile GMAT scorer, will show you how top scorers break down challenging Verbal questions..
May 1212:00 PM EDT
-11:59 PM EDT
Make the most of your break with the most realistic GMAT™ prep. Take up to $700 off select products.- Jun 10
06:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..
24 Jan 2017, 00:10
Kudos
Bookmarks
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
61% (01:50) correct
39%
(02:07)
wrong
based on 240
sessions
History
Date
Time
Result
Not Attempted Yet
Find the number of divisors 544 which are greater than 3.
(A) 15
(B) 10
(C) 12
(D) 8
(E) 14
(A) 15
(B) 10
(C) 12
(D) 8
(E) 14
24 Jan 2017, 01:08
Kudos
Bookmarks
saswata4s
Finding the Number of Factors of an Integer
First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors.
Check for more here: math-number-theory-88376.html
BACK TO THE QUESTION:
544 = 2^5*17, thus the number of factors is (5 + 1)(1 + 1) = 12, out of which all but 1 and 2 are greater than 3.
Answer: B.
27 Jan 2017, 11:02
Kudos
Bookmarks
saswata4s
We can start by breaking 544 into prime factors.
544 = 4 x 136 = 4 x 4 x 34 = 2^2 x 2^2 x 2 x 17 = 2^5 x 17^1
The factors that are greater than 3 are as follows:
2^2, 2^3, 2^4, 2^5, 17, 2 x 17, 2^2 x 17, 2^3 x 17, 2^4 x 17, and 2^5 x 17.
Thus, there are 10 divisors of 544 greater than 3.
Alternate solution:
We can start by breaking 544 into prime factors.
544 = 4 x 136 = 4 x 4 x 34 = 2^2 x 2^2 x 2 x 17 = 2^5 x 17^1
The complete factorization (as opposed to prime factorization) requires that the number 1 (which is not prime) also be included in the complete factorization: 1 x 2^5 x 17^1
Recall that the number of divisors of a number can be found by using the following method:
1) Add 1 to each of the exponents (of the prime factors) in the number’s complete factorization.
2) Multiply the resulting numbers.
Thus, the number of divisors of 544 is (5 + 1) x (1 + 1) = 6 x 2 = 12. Of the 12 divisors of 544, only 1 and 2 are not greater than 3, so 10 of them will be greater than 3.
Answer: B
