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# 2 quant questions (functions and geometry) - please assist!

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2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 10:53
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Difficulty:

5% (low)

Question Stats:

83% (03:16) correct 16% (01:42) wrong based on 6 sessions
Can someone please assist with the following question (and perhaps provide a good guide to function q's in general)

The function of 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 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) 2

ALSO, PLEASE REVIEW ATTACHED FILE FOR A QUESTION ON GEOMETRY

Thanks,
Attachments

File comment: geometry question

geometry.png [ 50.24 KiB | Viewed 1594 times ]

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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 11:08
The diagram is not very clear, but i remember the problem. if it is asking for value of x, it has to be 70.

the two trangles based on sides of the central trangle are right angled triangles, by pythagorus theorum, the sides' length is 5, making the central triangle an isosceles. since both base angles have to be congruent, x = 180 - 2(55), i.e. 70.

About the first problem, i am not quite certain, but i would go with option E, i.e 2. Let me revert to u, in case i find the solution.
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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 11:13
thanks for the response!

1) with respect to the geometry problem, I understand you logic, but if you were looking at this from a different angle, does the larger triangle on the right not look like one that follows the '30,60.90' rule with each side equal to x, 2x,x^3?

2) the answer to the function question was a) p-1

thanks again
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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 11:22
Expert's post
The diagram is not very clear, but i remember the problem. if it is asking for value of x, it has to be 70.

Have you tried clicking the image? It should open up a larger version.
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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 11:35
Dont ever rely on the digrams blindly.. the hypoteneous is 13, one of the side is 12, the other has to be 5 irrespective of what the angles suggest. and 30-60-90 rule is 1, \sqrt{3}, 2 not x, 2x and x^3.

b.t.w. I did try clicking on the image, it did not look clear to me, especially the question bit. but anyways, i guess that suffice.

I am still not able to understand the first one. lets wait for others to explain their logic as well. it really helps!
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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 12:08
thanks,

just realized, with the geometry question (blond moment) the smaller triangle on the left following the 3,4,5 rule (that was easy) but on the triangle on the right, it was just a matter of 'a squared' + 'b squared' = 'c squared' ((13x13 = 169) - (12x12 = 145) = 25) sqrt of 25 obviously 5. Thus, isoceles triangle.

Also looking fwd to explanation on function f(n) question and some guideance on these types of questions in general.
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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 16:59
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The function of 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 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) 2

The confusing moment in this question is its wording. Basically question is: how many positive integers are less than given prime number p which has no common factor with p except 1.

Well as p is a prime, all positive numbers less than p have no common factors with p (except common factor 1). So there would be p-1 such numbers (as we are looking number of integers less than p).

If we consider p=7 how many numbers are less than 7 having no common factors with 7: 1, 2, 3, 4, 5, 6 --> 7-1=6.

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Re: 2 quant questions (functions and geometry) - please assist! [#permalink]  01 Nov 2009, 17:19
the part "with n other than 1" is placed in a such a CONFUSING way in the question that I can easily think the answer as p-2 also, even if I understood the question properly....
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Re: 2 quant questions (functions and geometry) - please assist!   [#permalink] 01 Nov 2009, 17:19
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