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.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
16 Jun 2018, 02:46
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:03) correct
50%
(02:07)
wrong
based on 470
sessions
History
Date
Time
Result
Not Attempted Yet
How many factors of 1500 are not divisible by 15?
A) 24
B) 12
C) 11
D) 9
E) 15
A) 24
B) 12
C) 11
D) 9
E) 15
Updated on: 01 Jul 2018, 00:35
Originally posted by CAMANISHPARMAR on 16 Jun 2018, 02:59.
Last edited by CAMANISHPARMAR on 01 Jul 2018, 00:35, edited 1 time in total.
Last edited by CAMANISHPARMAR on 01 Jul 2018, 00:35, edited 1 time in total.
Kudos
Bookmarks
Let's write 1500 in prime factorization form, \(1500=2^2*3^1*5^3\)
To find the number of factors of 1500 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]
Hence the no of factors of 1500 without any restriction = (2+1)(1+1)(3+1) = 3*2*4 = 24
The no factors of 1500 not divisible by 15 = Total of no factors of 1500 without any restriction - Total no of factors of 1500 which are divisible by 15
Therefore first we must find Total no of factors of 1500 which are divisible by 15:-
Now we can write, 1500 = 15 * 100 = 15 * \(5^2*2^2\)
Since 15 * \(5^2*2^2\) is multiple of 15, and every factor of \(5^2*2^2\) is also a factor of 1500 and is divisible by 15 if we are multiplying each factor of \(5^2*2^2\) by 15.
Hence the no of factors which are divisible by 15 are all the factors of \(5^2*2^2\); that is (2+1)(2+1) = 3*3 = 9
Therefore, the no factors of 1500 not divisible by 15 = 24 - 9 = 15
Correct Answer is option (E)
To find the number of factors of 1500 is a straightforward application of number of factors formula:-
(p+1)(q+1)(r+1)... [where p,q,r are exponents of each prime factor]
Hence the no of factors of 1500 without any restriction = (2+1)(1+1)(3+1) = 3*2*4 = 24
The no factors of 1500 not divisible by 15 = Total of no factors of 1500 without any restriction - Total no of factors of 1500 which are divisible by 15
Therefore first we must find Total no of factors of 1500 which are divisible by 15:-
Now we can write, 1500 = 15 * 100 = 15 * \(5^2*2^2\)
Since 15 * \(5^2*2^2\) is multiple of 15, and every factor of \(5^2*2^2\) is also a factor of 1500 and is divisible by 15 if we are multiplying each factor of \(5^2*2^2\) by 15.
Hence the no of factors which are divisible by 15 are all the factors of \(5^2*2^2\); that is (2+1)(2+1) = 3*3 = 9
Therefore, the no factors of 1500 not divisible by 15 = 24 - 9 = 15
Correct Answer is option (E)
16 Jun 2018, 04:00
Kudos
Bookmarks
CAMANISHPARMAR
To count the factors of a positive integer:
1. Prime-factorize the integer
2. Write the prime-factorization in the form (a^p)(b^q)(c^r)...
3. The number of factors = (p+1)(q+1)(r+1)...
\(1500 = 2^2 * 3^1 * 5^3\)
For a factor of 1500 not to be divisible by 15, its prime-factorization must not include both 3 and 5.
Number of factors that can be formed from \(2^2 * 3^1\):
(2+1)(1+1) = 6.
Number of factors that can be formed from \(2^2 * 5^3\):
(2+1)(3+1) = 12.
Total = 6+12 = 18.
In the blue total above, the factors that can be formed only from \(2^2\) have been double-counted, so they must be SUBTRACTED.
Number of factors that can be formed from \(2^2\):
2+1 = 3.
Subtracting 3 from the blue total above, we get:
18-3 = 15.
