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MGMAT

by cvs » Mon Nov 19, 2007 7:52 am
Which of the following best approximates the value of q if 5^28+3^11=5^q ?

39
30
28
27
17

Pls post your answers with explanations.
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Re: MGMAT

by gabriel » Mon Nov 19, 2007 9:27 am
cvs wrote:Which of the following best approximates the value of q if 5^28+3^11=5^q ?

39
30
28
27
17

Pls post your answers with explanations.
The answer is B 30.

First the basics .. 5^n when divided by 3 has a remainder 1 if n is even and a remainder 2 if n is odd ..

Now, the given equation can also be written as 3^11=5^q-5^28, looking at the equation we can say that 5^q-5^28 has to be a multiple of 3(that means when (5^q-5^28) is divided by 3 the remainder is 0) that means 5^q and 5^28 should have similar remainders when divided by 3, so that when we subtract them they cancel out and the overall remainder is 0.

Now, we know that 5^28 has a remainder 1 when divided by 3 (as 28 is even), so 5^q should also have a remainder 1 when divided by 3 and hence we can say that q should also be even. The given answer choices have just 2 even options 30 and 28, obviously 28 cant be the answer therefore we can conclude q has to be 30.

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by cvs » Mon Nov 19, 2007 12:42 pm
Any more thoughts.. The answer is not 30!!!
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by samirpandeyit62 » Mon Nov 19, 2007 9:43 pm
IMO 28

now 5^28 would be a huge nos itself

& 3^11 = 27*27*27 * 9

to approx we can say it is 30^3 *10 which is 180000

this when added to such a huge nos as 5^28 would not make much of a diff

so q =28
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by gabriel » Tue Nov 20, 2007 12:10 am
samirpandeyit62 wrote:IMO 28

now 5^28 would be a huge nos itself

& 3^11 = 27*27*27 * 9

to approx we can say it is 30^3 *10 which is 180000

this when added to such a huge nos as 5^28 would not make much of a diff

so q =28
Well I had thot about it ... but if we choose q = 28 then we are considering the value of 3^11 as 0, which does not make a lot of sense to me .. but then again the question does say approximate value of q, but dont u think we would be pushing it a bit by assuming 3^11 equal to 0 ..
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by gabriel » Tue Nov 20, 2007 12:17 am
On second thought I agree the answer should be 28 .. I was sure that the answer should be either 30 or 28, 28 makes more sense now .. good going Samir

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by samirpandeyit62 » Tue Nov 20, 2007 2:58 am
Hi Gabriel,
My reasoning was like this

5^28 = very large nos say X

3^11 = 180000 approx

now q can be 28 or more, i.e next nos is 30

so if we line them up it would be

X X+180000 25X

now obviously X+180000 would be closer to X
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by cvs » Tue Nov 20, 2007 12:23 pm
Thanks Samir/Gabrial.

The official answer is 28.

Samir explanation is identical to MGMAT's explanation.
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by xcise_science » Wed Nov 21, 2007 10:47 am
Hi samirpandeyit62,

I don't understand this approximation:
3^11 = 27*27*27 * 9
to approx we can say it is 30^3 *10 which is 180000

Also, can you clarify on this as well:

5^28 = very large nos say X
3^11 = 180000 approx
now q can be 28 or more, i.e next nos is 30
so if we line them up it would be
X X+180000 25X
now obviously X+180000 would be closer to X

Also, I see what you wrote before that adding 3^11 to 5^28 will not make a major difference, so then why can't Q be 30.....to account for the slight increase when we add to 5^28?

Thanks
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