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.
Apr 24Get an Extra 30% Off Target Test Prep Plans
08:00 PM EDT
-11:59 PM EDT
Grab 30% off any Target Test Prep GRE plan during our Flash Sale and join Brian and many other students who have used Target Test Prep to score high on the GRE. Just enter the coupon code FLASH30 at checkout to save big.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If 2^x = 5 and 4^y = 20, what is the value
[#permalink]
Updated on: 02 Jun 2018, 01:55
Updated on: 02 Jun 2018, 01:55
1
00:00
Question Stats:
86% (01:26) correct
13% (01:31) wrong based on 52 sessions
Hide Show timer Statistics
If \(2^x = 5\) and \(4^y = 20\), what is the value of x in terms of y?
A) \(y - 2\)
B) \(\frac{(y + 1)}{2}\)
C) \(2y - 2\)
D) \(\frac{y}{2} - 2\)
E) \(2y + 2\)
*kudos for all correct solutions
A) \(y - 2\)
B) \(\frac{(y + 1)}{2}\)
C) \(2y - 2\)
D) \(\frac{y}{2} - 2\)
E) \(2y + 2\)
*kudos for all correct solutions
Originally posted by GreenlightTestPrep on 01 Jun 2018, 07:03.
Last edited by Carcass on 02 Jun 2018, 01:55, edited 2 times in total.
Last edited by Carcass on 02 Jun 2018, 01:55, edited 2 times in total.
Edited by Carcass
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 2^x = 5 and 4^y = 20, what is the value
[#permalink]
02 Jun 2018, 05:17
02 Jun 2018, 05:17
GreenlightTestPrep wrote:
If \(2^x = 5\) and \(4^y = 20\), what is the value of x in terms of y?
A) \(y - 2\)
B) \(\frac{(y + 1)}{2}\)
C) \(2y - 2\)
D) \(\frac{y}{2} - 2\)
E) \(2y + 2\)
A) \(y - 2\)
B) \(\frac{(y + 1)}{2}\)
C) \(2y - 2\)
D) \(\frac{y}{2} - 2\)
E) \(2y + 2\)
There are several approaches we can take. Here's an algebraic approach
Given: 2^x = 5 and 4^y = 20
Take second equation and rewrite 4 as 2² to get: (2²)^y = 20
Simplify to get: 2^(2y) = 20
We now have:
2^(2y) = 20
2^x = 5
This means we can write: 2^(2y)/2^x = 20/5
Simplify: 2^(2y - x) = 4
Rewrite as: 2^(2y - x) = 2^2
So, it must be the case that 2y - x = 2
Add x to both sides: 2y = x + 2
Subtract 2 from both sides: 2y - 2 = x
Answer: C
RELATED VIDEO
Cheers,
Brent
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 2^x = 5 and 4^y = 20, what is the value
[#permalink]
02 Jun 2018, 05:31
02 Jun 2018, 05:31
GreenlightTestPrep wrote:
If \(2^x = 5\) and \(4^y = 20\), what is the value of x in terms of y?
A) \(y - 2\)
B) \(\frac{(y + 1)}{2}\)
C) \(2y - 2\)
D) \(\frac{y}{2} - 2\)
E) \(2y + 2\)
*kudos for all correct solutions
A) \(y - 2\)
B) \(\frac{(y + 1)}{2}\)
C) \(2y - 2\)
D) \(\frac{y}{2} - 2\)
E) \(2y + 2\)
*kudos for all correct solutions
Here's a totally different approach:
GIVEN: 2^x = 5
2^2 = 4 and 2^3 = 8
Since 5 is BETWEEN 4 and 8, we know that x is BETWEEN 2 and 3.
From here, we can estimate.
Since 5 is closer to 4 than it is to 8, we know that x will be closer to 2 than it is to 3.
Let's say that x ≈ 2.3
GIVEN: 4^y = 20
4^2 = 16 and 4^3 = 64
Since 20 is BETWEEN 16 and 64, we know that y is BETWEEN 2 and 3.
From here, we can estimate.
Since 20 is closer to 16 than it is to 64, we know that y will be closer to 2 than it is to 3.
Let's say that y ≈ 2.1
ASIDE: As we'll see, it doesn't matter if our estimates are a little off
Now that we know that x ≈ 2.3 and y ≈ 2.1, we check the answers to see which one works.
That is, when we replace y with 2.1, which one yields an x-value that's close to 2.3
A) y - 2 = 2.1 - 2 = 0.1
This suggests that, when y = 2.1, x = 0.1. We want x = 2.3. ELIMINATE A.
B) y - 1/2 = 2.1 - 0.5 = 1.6
This suggests that, when y = 2.1, x = 1.6. We want x = 2.3. ELIMINATE B.
C) 2y - 2 = 2(2.1) - 2 = 4.2 - 2.1 = 2.1
This is VERY CLOSE to 2.3. KEEP C.
D) y/2 - 2 = 2.1/2 - 2 = some negative number
We want x = 2.3. ELIMINATE D.
E) 2y - 1/2 = 2(2.1) - 0.5 = 3.7
This suggests that, when y = 2.1, x = 3.7. We want x = 2.3. ELIMINATE E
By the process of elimination, the correct answer must be C
Cheers,
Brent
