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How to Reduce sqrt(264) Mentally – GMAT Quick Math
Hi, I was looking at this GMAT problem on the Beat the Gmat, I don’t understand how they deduce 2*sqrt(66) from the sqrt of 264? How are we supposed to know to do this?GMATPill Response
When I see 264 I notice first thing that it’s an even number. If it’s an even number that is divisible by 4, then I can break it up easily since I can do something like sqrt(4) * sqrt(?) = sqrt(264)
The sqrt(4) = 2, that’s easy. So then I would be left with 2*sqrt(?) = sqrt(264)
Well, what’s the question mark?
sqrt(4) * sqrt(?) = sqrt(264)
We need to divide 264 by 4. Take the first two digits 26 and divide it by 4. You can do that 6 times and that would give you 24.Do your long division. 26-24 = 2
Now add on the 4 digit and you get 24Divide 24 by 4 and you get 6 agaain.
So the two 6′s give you 66.
So sqrt(4) * sqrt(?) = sqrt(264)
becomes
sqrt(4) * sqrt(66) = sqrt(264)
= 2*sqrt(66)So that’s how you get 2*sqrt(66)–hope that helps!
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GMAT Prep Question From Student
Number Properties – GMAT Prep Quant Question
“I can’t seem to figure out how the GMAT arrived at the answer to this question on a GMATPrep test . Can you assist?”
Q: The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number, then f(p) =
A) p – 1
B) p – 2
C) (p+1)/2
D) (p-1)/2
E) 2The answer is p-1. Why is the answer not 2?
Thanks,
GMAT Pill Response
Just pick any prime number like 7 or 11.
Say 7. f(7) = # of positive integers less than 7. Well, there are 6 positive numbers less than 7: 1, 2, 3, 4, 5, and 6.
But it also has to have no positive factor in common with 7 other than 1.
So just go through the list: 1, 2, 3, 4, 5, and 6—–compare them each with 7 and 1 like so:7 and 6: Do they share no positive factor other than 1? Yes.
7 and 5: Do they share no positive factor other than 1? Yes.
7 and 4: Do they share no positive factor other than 1? Yes.
7 and 3: Do they share no positive factor other than 1? Yes.
7 and 2: Do they share no positive factor other than 1? Yes.
7 and 1: Do they share no positive factor other than 1? Yes. The only factor that 7 and 1 have in common is 1. So yes, this counts as one also.And the above up and basically all the numbers work between 1-6 so since 6 is one less than 7, then the answer is 1 less than n.
So answer is p-1. Hope that helps!
Zeke
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GMAT Prep Question From Student – Don’t Confuse Idioms With Real Grammar Errors
Why don’t you use “to shape” in this case. I remember from the frameworks – you say that with linking verbs you need “to” between the verbs.Here are some examples of linking verbs where the first verb leads into the second verb. These are preferred–though they do not necessarily other forms are incorrect:
I want her to study.
The law requires you to make…
She recommends I vote.
She recommends me to vote.These examples are a bit different from the one in the question. These are in the form of A wants something out of B. She wants me to vote. The law requires you to make. etc..
In the above question, both forms (With or without the “to”) are acceptable. “She helped me grow the business” and “she helped me to grow the business”–both are ok.
So the question here is not testing which one is right or wrong.
She helped grow the business. —ok
She helped to grow the business. —ok
She helped shape public opinion. —ok
She helped to shape public opinion. —okThere are always preferred and non-preferred ways of wording things on the GMAT. Your job is to figure out what ELSE is being tested. If there are other problems in the questions–focus on those.
Notice in an example where both forms are acceptable, you will never be in a situation where you need to choose one or the other because there will be other errors in the sentence.
In (C), the problem is the word “like” since you should be using the form of “such…as..” rather than “such….like…”
In (A), the problem is also the word “like”—”like” should not be used when giving an example. “Like” should be used in comparing two things.
Here you are providing examples of “fundamentally important areas”—for this you use “as.”So this question is not testing “shape vs to shape”–it is testing “such as vs like.”
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