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
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
m and n are integers. [#permalink]
07 Dec 2017, 03:16
Expert's post
00:00
Question Stats:
76% (00:54) correct
23% (00:23) wrong based on 17 sessions
m and n are integers.
Quantity A
Quantity B
\((\sqrt{10^{2m}})(\sqrt{10^{2n}})\)
\(10^{mn}\)
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: m and n are integers. [#permalink]
08 Dec 2017, 05:13
1
This post received KUDOS
Hello,
for this question it is best to try out different values.
For instance.
If m and n are both zero, both expressions will be equal to 1 (since anything exponent zero is one) => Answer C If m and n are both 3, Qty A becomes 10^6 and Qty B becomes 10^9 => Answer B,
since the square root and exponent 2 cancel each other out, Qty A becomes 10^m * 10^n => 10^(m+n)= 10^(3+3)<10^(3*3)
Re: m and n are integers. [#permalink]
08 Dec 2017, 10:59
2
This post received KUDOS
Expert's post
Carcass wrote:
m and n are integers.
Quantity A
Quantity B
\((\sqrt{10^{2m}})(\sqrt{10^{2n}})\)
\(10^{mn}\)
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.
RULE: √x = x^(1/2)
So, √[10^(2m)] = [10^(2m)]^(1/2) = 10^m [once we apply the Power of a Power rule]
Likewise, √[10^(2n)] = [10^(2n)]^(1/2) = 10^n [once we apply the Power of a Power rule]
We get:
QUANTITY A: (10^m)(10^n) QUANTITY B: 10^(mn)
Simplify to get: QUANTITY A: 10^(m+n) QUANTITY B: 10^(mn)
Let's test some values of m and n
m = 0 and n = 0 We get: QUANTITY A: 10^(0+0) = 10^0 = 1 QUANTITY B: 10^[(0)(0)] = 10^0 = 1 In this case the two quantities are equal
m = 1 and n = 1 We get: QUANTITY A: 10^(1+1) = 10^2 = 100 QUANTITY B: 10^[(1)(1)] = 10^1 = 10 In this case Quantity is greater
Answer: D
RELATED VIDEO
_________________
Brent Hanneson – Creator of greenlighttestprep.com Sign up for our free GRE Question of the Dayemails
greprepclubot
Re: m and n are integers.
[#permalink]
08 Dec 2017, 10:59
close
76% (00:54) correct
