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# Which of the following best approximates the value of q if

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VP
Joined: 14 May 2006
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Which of the following best approximates the value of q if [#permalink]  08 Aug 2006, 17:43
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Which of the following best approximates the value of q if 5^28+3^11=5^q ?

A 39
B 30
C 28
D 27
E 17

Manager
Joined: 08 May 2004
Posts: 158
Location: Pittsburgh
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Kudos [?]: 0 [0], given: 0

Really, if I could understand how to factor these questions, I would have a 50 math score. I still have yet to find a good source on the net on how to do these. I had limited math as undergrad, only bus calc, so some of this is puzzling...
VP
Joined: 02 Jun 2006
Posts: 1266
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Kudos [?]: 48 [0], given: 0

ok.. After trying for more than 20 minutes... I have no explanation but the following.

q has to be greater than 28 otherwise 3^11 ~ approximates to zero.

Eliminating A. 39 because.. no idea.

Sorry thats the best I could not. I am not that smart...
VP
Joined: 29 Dec 2005
Posts: 1348
Followers: 7

Kudos [?]: 37 [0], given: 0

haas_mba07 wrote:
q has to be greater than 28 otherwise 3^11 ~ approximates to zero.(

are you sure? seems you have not taken fruit..

ok. q would be 29, if the equation is as under: 5^28 + [5 (5^28)] = 5^q?
q would be 30, if the equation is as under: 5^28 + [24 (5^28)] = 5^q?

note the red part.
in first eq... how bigger is 5 (5^28) than 3^11?

hope its clear.
CEO
Joined: 20 Nov 2005
Posts: 2910
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 19

Kudos [?]: 132 [0], given: 0

C

3^11 is too small as compared to 5^28

3^11 have 8 or 9 digits
5^28 have around 25 digits.
So 3^11 is billionth billionth of 5^28.

Hence q will be 28.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

SVP
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 127 [0], given: 39

here is a more detailed explanation,

3^11 = 3^3*3^3*3^3*3^2..

and .3^3 = 27 approx 25 ie: 5^2

therfore 3^11 approx =( 5^2)^3 * 3^2.... substitute

5^28+3^11 = 5^28+5^6*3^2 ie: 5^6(5^22 + 3^2) if we compared 3^2 (ie: 9) to such a huge exponent as 5^22 we can see that it approximately has negligable effect if added to it

Thus 5^22+3^2 approx = 5^22

So, 5^6(5^22 + negligabel) = 5^28

therfore 5^28+3^11 = 5^28

Hence q is approx = 28

I hope i helped.....take care
SVP
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 127 [0], given: 39

Hi Haas , i think you ve got a very valid point of view about approximation,

However when we approximate we should always ask ourslves we are approximating .............compared to what?????

ie: if we are approximating 0.42

We actually compared 2 to ten so we answere 0.42 is approx = 0.4

Similarly if we compared 3^11 to 5^28 we have a bigger (exponantial)reason to neglect the 3^11.

Take care.
VP
Joined: 02 Jun 2006
Posts: 1266
Followers: 2

Kudos [?]: 48 [0], given: 0

I don't think any amount of fruit would have helped me on that one...

Professor wrote:
are you sure? seems you have not taken fruit..
SVP
Joined: 05 Jul 2006
Posts: 1516
Followers: 5

Kudos [?]: 127 [0], given: 39

Hass ...trust me when i tell you that a day after day i face more than 10 to 15 Q problems that i dont have a reply to except a very big big smile

We are learning and trying to beat the Gmat all mighty. and sure we will.

Take care
Senior Manager
Joined: 13 Jul 2006
Posts: 327
Followers: 1

Kudos [?]: 4 [0], given: 0

5^28 + 3^11 = 5^q
so 28 log5 + 11 log3 = qlog5
(q-28) log5 = 11log3

log5 is 1.6 (log5 to the base e) log3 is approx 1.1
log5 is .7(log5 to the base of 10) log3 is .5(log3 to the base of 10)

solving this i am getting q is approx 35 or 36.
SVP
Joined: 30 Mar 2006
Posts: 1737
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Kudos [?]: 46 [0], given: 0

C 28.

3^11 is too small compared to 5^28. hence adding 5^28 + 3^11 wont be much greater than 5^28.
Intern
Joined: 04 May 2006
Posts: 40
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5^28 + 3^11 = 5^q ( therefore q is >0 and greater than 28)

3^11 = 5^q - 5^28

3^11 = 5^28*(5^(q-28)-1) (since q >28 from above)

1+3^11/5^28=5^(q-28)

3^11/5^28 = approx(0) ( since 5^28 is so much larger than 3^11)

1 = 5^(q-28)

q - 28 = approx (0)

q = 28.
Current Student
Joined: 28 Dec 2004
Posts: 3387
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 186 [0], given: 2

god..i cant belive some of u r doing logrithmic calculations on this problem..this question shud be done under 12 sec....

5^28 is considerably bigger than 3^11...therefore q=28

30 will be too large...

C it is..
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