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# Three questions from the gmat prep

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Intern
Joined: 26 May 2009
Posts: 6
Three questions from the gmat prep [#permalink]

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28 May 2009, 22:42
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Hi guys,

I need help with the following three questions as i really have no clue on how to derive the answers. I greatly appreciate your help.

1. What is the greatest prime factor of 4^17 - 2^28?

A. 2
B. 3
C. 5
D. 7
E. 11

2. attached
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1.gif [ 11.39 KiB | Viewed 1741 times ]

3. attached
Attachment:

Untitled-2.gif [ 1.18 KiB | Viewed 1743 times ]

Last edited by steliossb on 29 May 2009, 10:01, edited 2 times in total.
Director
Joined: 23 May 2008
Posts: 806
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 00:00
1
KUDOS
the first question has been recently discussed here. You can do a search for that one.

I'll take a crack at the other two

problem 2.

let q and m=quotients

given:

n=3q+2, t=5m+3

what is the remainder when nt/15?

nt/15= (3q+2)(5m+3)/15=

(15qm+9q+10m+6)/15

1) (n-2)/5 is an integer

n=3q+2 so 3q/5 is an integer

since 3 and 5 are prime q must be a multiple of 5

plugging into our equation 15qm+9q+10m+6)/15, we see that the first and second terms are multiples of 15, but we dont no about the third term

so insufficient

2) t/3 is an integer so t is a multiple of 3

t=5m+3 so m must be a multiple of 3 as well

plugging into our equation 15qm+9q+10m+6)/15 we find that the first and third terms are multiples of 15 but we dont know about the second term

so insufficient

togther we know all terms are multiples of 15 and the remainder is 6
sufficient

C

problem 3.

if x is -tive then whats the sqrt of -xlxl ?

if x is -tive then -x is x and lxl is also x so the sqrt of x^2 is x

so D
Intern
Joined: 12 May 2009
Posts: 47
Location: Mumbai
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 02:51
1
KUDOS
(1) Prime factor is 2.

4^17 - 2^28 = 2^34 - 2^28 = 2^6 = 64
So 2 is the only prime factor for 64

(2) Answer is C, we can derive the conclusion only with both the statements

(3) Since X < 0, it has to be a -ve number.
If X = -2
So, substitute -2 in the equation
Sqrt (-(-2)|-2|) = Sqrt (2*2) = 2

We took X = -2 and got an answer as 2, so the value will be -X
So I would go for -X, Option A

Thanks,
Manager
Joined: 12 Apr 2006
Posts: 215
Location: India
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 06:37
2
KUDOS
vesam wrote:
(1) Prime factor is 2.

4^17 - 2^28 = 2^34 - 2^28 = 2^6 = 64
So 2 is the only prime factor for 64

You can't add or subtract exponential power in addition and subtraction of bases.

Powers would be added or subtracted in case of multiplication and division only.

4^17 - 2^28 = 4^17 - 4^14 = 4^14 ( 4^3 - 1) = 4^14*63 = 4^14*7*9.

Greatest prime factor = 7

Last edited by humans on 29 May 2009, 10:58, edited 1 time in total.
Intern
Joined: 12 May 2009
Posts: 47
Location: Mumbai
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 07:59
Intern
Joined: 26 May 2009
Posts: 6
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 08:29
thanks a lot for the help guys, it was extremely useful.

last question i have for these forums:

Attachment:

4.gif [ 5.41 KiB | Viewed 1663 times ]
Manager
Joined: 12 Apr 2006
Posts: 215
Location: India
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 11:18
steliossb wrote:
thanks a lot for the help guys, it was extremely useful.

last question i have for these forums:

Manager
Joined: 08 Feb 2009
Posts: 145
Schools: Anderson
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 13:11
humans wrote:
steliossb wrote:
thanks a lot for the help guys, it was extremely useful.

last question i have for these forums:

There is an easier approach/formula for such problems rather than working out all the possible combinations.

If the probability of success in each trial is p, then the probability of r successes in n trials is $$^nC_r$$ $$p^r$$ $$q^{n-r}$$

Since, the question asks us to find out probability for at least 4 heads, it gives rise to two scenarios. r = 4 heads exactly or r = 5 heads exactly. And ADD the scenarios finally.

We can infer from the question that probability of heads = p = 0.6, r = 4 or 5, n=5 . Obviously probability for tails = q = 0.4.

Substituting
$$^5C_4$$ $$(0.6)^4$$ $$(0.4)^{5-4}$$ + $$^5C_5$$ $$(0.6)^5$$ $$(0.4)^{5-5}$$

= $$5 (0.6)^4 (0.4) + (0.6)^5$$

Solving the above we get the answer E
Director
Joined: 23 May 2008
Posts: 806
Re: Three questions from the gmat prep [#permalink]

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29 May 2009, 15:43
vesam wrote:
(1) Prime factor is 2.

4^17 - 2^28 = 2^34 - 2^28 = 2^6 = 64
So 2 is the only prime factor for 64

(2) Answer is C, we can derive the conclusion only with both the statements

(3) Since X < 0, it has to be a -ve number.
If X = -2
So, substitute -2 in the equation
Sqrt (-(-2)|-2|) = Sqrt (2*2) = 2

We took X = -2 and got an answer as 2, so the value will be -X
So I would go for -X, Option A

Thanks,

oops, you're right, should be -x, my bad
Manager
Joined: 13 Jul 2010
Posts: 167
Re: Three questions from the gmat prep [#permalink]

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19 Dec 2010, 16:45
On question 3, I got answer as D as well. sqrt(x*-x) or sqrt(-x^2)=x right? Please advise. thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 39708
Re: Three questions from the gmat prep [#permalink]

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19 Dec 2010, 17:06
gettinit wrote:
On question 3, I got answer as D as well. sqrt(x*-x) or sqrt(-x^2)=x right? Please advise. thanks.

The first question: factors-104757.html
The second question: gmat-prep-2-remainder-86155.html
The third question: square-root-and-modulus-100303.html (OA: A)
The fourth question: probability-question-gmatprep-85802.html

Topic locked.
_________________
Re: Three questions from the gmat prep   [#permalink] 19 Dec 2010, 17:06
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