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.
x and y are positive integers such that x^25^y = 10,125
[#permalink]
14 Sep 2017, 06:52
14 Sep 2017, 06:52
4
Expert Reply
41
Bookmarks
00:00
Question Stats:
28% (01:44) correct
71% (01:41) wrong based on 382 sessions
Hide Show timer Statistics
x and y are positive integers such that \(x^25^y = 10,125\)
Quantity A |
Quantity B |
\(x^2\) |
\(5^y\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: x and y are positive integers such that x^25^y = 10,125
[#permalink]
28 Sep 2017, 08:37
28 Sep 2017, 08:37
9
1
Bookmarks
This is a tricky one.
If 10,125 is reduced to prime factors it is equal to \(5^2*3^4 = 5^2*9^2\) thus, one could be tempted of stating x = 9, y = 3 so that column B is greater. This is actually true. The problem is that this is not the only way to write 10,125 as x^2*5^y. Indeed, if we take x = 45 and y = 1, we get 10,125 too but in this case column A is greater.
Thus, our answer is D!
If 10,125 is reduced to prime factors it is equal to \(5^2*3^4 = 5^2*9^2\) thus, one could be tempted of stating x = 9, y = 3 so that column B is greater. This is actually true. The problem is that this is not the only way to write 10,125 as x^2*5^y. Indeed, if we take x = 45 and y = 1, we get 10,125 too but in this case column A is greater.
Thus, our answer is D!
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: x and y are positive integers such that x^25^y = 10,125
[#permalink]
28 Sep 2017, 12:12
28 Sep 2017, 12:12
8
2
Bookmarks
Carcass wrote:
x and y are positive integers such that \(x^25^y = 10,125\)
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
\(x^2\) |
\(5^y\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
This question begs for some prime factorization
10,125 = (5)(5)(5)(3)(3)(3)(3)
From this, we can see a few options for x² and 5^y
Here are two possible cases:
case 1: x = 45 and y = 1.
So, (x²)(5^y) = (45²)(5^1)
= [(3)(3)(5)]²(5)
= (3)(3)(3)(3)(5)(5)(5)
= 10,125
For this case, we get:
Quantity A: 45²
Quantity B: 5
Quantity A is clearly greater
case 2: x = 9 and y = 3.
So, (x²)(5^y) = (9²)(5^3)
= [(3)(3)]²(5)(5)(5)
= (3)(3)(3)(3)(5)(5)(5)
= 10,125
For this case, we get:
Quantity A: 81
Quantity B: 125
Quantity B is clearly greater
Answer:
Show: ::
D
Cheers,
Brent
