GRE Prep 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.
The integer y is positive. If 6y is a factor of
[#permalink]
10 Mar 2019, 10:37
10 Mar 2019, 10:37
Expert Reply
00:00
Question Stats:
95% (00:37) correct
4% (01:59) wrong based on 43 sessions
Hide Show timer Statistics
The integer \(y\) is positive. If \(6^y\) is a factor of \((2^{14})( 3^{24})\), then what is the greatest possible value of \(y\)?
A. 7
B. 8
C. 14
D. 18
E. 36
A. 7
B. 8
C. 14
D. 18
E. 36
Re: The integer y is positive. If 6y is a factor of
[#permalink]
13 Mar 2019, 13:08
13 Mar 2019, 13:08
Can you explain how got this? I though i would simplify the expression to (2*3)^(14+24) which would equal 6^38
Re: The integer y is positive. If 6y is a factor of
[#permalink]
14 Mar 2019, 01:24
14 Mar 2019, 01:24
Expert Reply
1
Bookmarks
Actually, this question is hard unless you master very well the properties of exponents/roots
First off, you can NOT add two different exponent bases as you did. You can add up only when the base is the same. E.G \(3^2*3^5 = 3^7\)
In this case, manipulate the denominator splitting it into two factors
\(\frac{2^{14} 3^{24}}{(2*3)^y} = \frac{2^{14} 3^{24}}{2^y3^y}\)
As you can see for being divisible our fraction our y must contain at most 14 factors of two. Of course, the rule says that you are limited by the smallest number of factors to have a perfect division.
Hope this helps
First off, you can NOT add two different exponent bases as you did. You can add up only when the base is the same. E.G \(3^2*3^5 = 3^7\)
In this case, manipulate the denominator splitting it into two factors
\(\frac{2^{14} 3^{24}}{(2*3)^y} = \frac{2^{14} 3^{24}}{2^y3^y}\)
As you can see for being divisible our fraction our y must contain at most 14 factors of two. Of course, the rule says that you are limited by the smallest number of factors to have a perfect division.
Hope this helps
