I was doing a practice test last night and this is the first problem that popped up. I have never seen another one like it. Any suggestions would be greatly appreciated. Thanks in advance.
(1/5)^m * (1/4)^18= 1/2(10)^35
then m=?
Is it just me or does this seem a little hard for a first question???
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AleksandrM
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Wow, durgesh, that is a pretty kool approach. I have seen people pick apart bases with unknown exponents, but I've never seen anyone carry out the reciprocal approach. I will have to put this one in my notes.
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netigen
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Another way to solve such problems is to understand that power of 5 can only come from 10 in this case. Since, there is no other source to get 5 but the 10, look at it's power and that will be the answer.
so power of 5 on LHS will be 35.
so power of 5 on LHS will be 35.
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stevennu
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What are the governing rules when simplifying by way of using the reciprocal? Can you just flip everything on both sides and call it a day?durgesh79 wrote:its actualy an easy problem, presented as a complicated one.
take the reciprocal of everything
5^m * 4^18 = 2 * 10^35
5^m * 2^36 = 2 *(2*5)^35
5^m * 2^36 = 5^35 * 2^36
m = 35
Why doesn't 10^35 become 1/10^35?
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Brent@GMATPrepNow
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Another approach is to focus solely on the 5's.If (1/5)^m * (1/4)^18 = 1/[2(10)^35] then m =
(1/5)^m * (1/4)^18 = 1/2(10)^35 [original equation]
(1/5)^m * (1/4)^18 = 1/2(2 * 5)^35 [rewrote 10 as 2 * 5]
(1/5)^m * (1/4)^18 = 1/[2(2^35) * (5^35)] [applied power of a product rule]
(1/5)^m * (1/4)^18 = 1/(2^36) * 1/(5^35) [rewrote right-hand side]
(1/5)^m * (1/4)^18 = 1/(2^36) * (1/5)^35 [rewrote 1/(5^35)]
(1/5)^m * (some stuff with 4's) = (some stuff with 2's) * (1/5)^35 [ignore non-5 stuff]
m = 35
Cheers,
Brent
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Hi AZ2hot,
The explanations/information provided by the people who commented in this post are correct (and exactly what you need to know).
In answer to your last question though...
No, this question is not too hard for the first question. This is a mid-level prompt, it has just 1 variable and the question itself is based on a few public-domain exponent rules that you were probably taught when you were 14 years old. If you're a little "rusty" on the rules, then that's understandable. Most people don't use exponent rules in their day-to-day lives, so this question might seem harder than it actually is. Once you know the rules though, it's straight-forward enough.
A big takeaway from this question is that you might need to brush up on the various math formulas and rules that the GMAT will present to you, so that you're ready the next time an exponent rule question shows up.
GMAT assassins aren't born, they're made,
Rich
The explanations/information provided by the people who commented in this post are correct (and exactly what you need to know).
In answer to your last question though...
No, this question is not too hard for the first question. This is a mid-level prompt, it has just 1 variable and the question itself is based on a few public-domain exponent rules that you were probably taught when you were 14 years old. If you're a little "rusty" on the rules, then that's understandable. Most people don't use exponent rules in their day-to-day lives, so this question might seem harder than it actually is. Once you know the rules though, it's straight-forward enough.
A big takeaway from this question is that you might need to brush up on the various math formulas and rules that the GMAT will present to you, so that you're ready the next time an exponent rule question shows up.
GMAT assassins aren't born, they're made,
Rich
