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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

Note that we need approximate value of \(q\). Now, \(5^{28}\) is much, much, much bigger than \(3^{11}\). So adding \(3^{11}\) to \(5^{28}\) will be closer to \(5^{28}\) then to \(5^{29}\), basically \(3^{11}\) is negligible in this case. So \(q\approx{28}\).

thx i guess i need to go review my exponents haha. i was trying to actually do the problem until it started to get out of hand....sigh...
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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

The answer has to be at least 28 since you are adding something to 5^28.

Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:

The next possible answer is 5^30 which is greater than 5^28 5^30 = 25*5^28

But 5^28 + 5^28 = 2*5^28 Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28 In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.
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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

Note that we need approximate value of \(q\). Now, \(5^{28}\) is much, much, much bigger than \(3^{11}\). So adding \(3^{11}\) to \(5^{28}\) will be closer to \(5^{28}\) then to \(5^{29}\), basically \(3^{11}\) is negligible in this case. So \(q\approx{28}\).

Answer: C.

Bunuel, my approach for this question was:

I approximated \(3^{11}\) to \(30^{10}\) and thus \(3^{11}\) = \(5*6^{10}\) ----> factor ---> \(5^{10}\) (\(5^{18}\) + 6) .. Since the addition in the parenthesis is minescule, we can ignore it. And thus we have \(5^{10}\) * \(5^{18}\) = \(5^{28}\) .... so q = 28

But obviously 30^10 is about a third of the size of 3^11 so I do not know if these operations work in general. Do they?

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

Note that we need approximate value of \(q\). Now, \(5^{28}\) is much, much, much bigger than \(3^{11}\). So adding \(3^{11}\) to \(5^{28}\) will be closer to \(5^{28}\) then to \(5^{29}\), basically \(3^{11}\) is negligible in this case. So \(q\approx{28}\).

Answer: C.

Bunuel, my approach for this question was:

I approximated \(3^{11}\) to \(30^{10}\) and thus \(3^{11}\) = \(5*6^{10}\) ----> factor ---> \(5^{10}\) (\(5^{18}\) + 6) .. Since the addition in the parenthesis is minescule, we can ignore it. And thus we have \(5^{10}\) * \(5^{18}\) = \(5^{28}\) .... so q = 28

But obviously 30^10 is about a third of the size of 3^11 so I do not know if these operations work in general. Do they?

It seems that you need to brush up fundamentals on this topic, because unfortunately very little above is correct.

\(3^3=27\) which is pretty close to \(5^2\) \(3^1^1\) is 3 times \(3^3\) and one time \(3^2\) thus we can approximate to 3 times \(5^2\) and one 5

\(5^2^8+5^7=5^7(5^2^1+1)\).

we can conclude that the best approximation is \(5^2^8\) since \(5^2^1+1\) is a little bit more than \(5^2^1\). and \(5^7\) times (a little bit more than \(5^2^1\)) = around \(5^2^8\)

hope it helps.
_________________

learn the rules of the game, then play better than anyone else.

Last edited by gmat6nplus1 on 29 Dec 2013, 04:18, edited 1 time in total.

Re: Which of the following best approximates the value of q if [#permalink]

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29 Dec 2013, 03:35

vwjetty wrote:

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

We have: 5^28+3^11=5^q ==> because 3^11 > 0 --> 5^q MUST be equal or greater than 5^28 ==> q MUST be equal or greater than 28 ==> Option D and E are out immediately.

Divide both sides by 5^q and q >= 28 We have: 5^(28-q) + 3^11/5^q = 1

Because q >= 28 ==> 3^11/5^q = 0.0000xyz that is very small, we can ignore it. Thus, 5^(28-q) must be approximate 1 ==> 28-q = 0 ==> q is approximate 28 C is the answer.

Hope it helps.
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Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

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

Note that we need approximate value of \(q\). Now, \(5^{28}\) is much, much, much bigger than \(3^{11}\). So adding \(3^{11}\) to \(5^{28}\) will be closer to \(5^{28}\) then to \(5^{29}\), basically \(3^{11}\) is negligible in this case. So \(q\approx{28}\).

Answer: C.

I thought it this way:\(3^11=5^q-5^28\).Now if we take\(q>28\),we'll be able to take out \(5^28\) common from RHS;that cannot equal \(3^11\).And if we take \(q<28\),We'll get -ve RHS;that again cannot equal \(3^11\). So the closest value can be \(q=28\) only.But can this question be there in the GMAT?Even the closest/aprox. value in this case is quite far away!

Re: Which of the following best approximates the value of q if [#permalink]

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20 Feb 2016, 11:13

VeritasPrepKarishma wrote:

Smita04 wrote:

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

The answer has to be at least 28 since you are adding something to 5^28.

Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:

The next possible answer is 5^30 which is greater than 5^28 5^30 = 25*5^28

But 5^28 + 5^28 = 2*5^28 Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28 In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.

great explanation...I tried to solve it by logic..and eliminated right away D and E. A is way too much. Between B and C, went with B..now I see why I did the mistake..

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

The answer has to be at least 28 since you are adding something to 5^28.

Note that 3^11 is much much smaller than 5^28 so adding it will not change the value of 5^28 much. If it is hard to visualize, think of it this way:

The next possible answer is 5^30 which is greater than 5^28 5^30 = 25*5^28

But 5^28 + 5^28 = 2*5^28 Even if we add 5^28 to 5^28, all we get is 2*5^28 which is much much smaller than 25*5^28 In fact, what we are actually adding is only 3^11 so 5^28 + 3^11 must be much closer to 5^28. Hence its value must be approximately 5^28.

great explanation...I tried to solve it by logic..and eliminated right away D and E. A is way too much. Between B and C, went with B..now I see why I did the mistake..

B could've been easily eliminated as for increasing another power of 5, you will need to atleast multiply that number by 5 atleast. 3^11 can be approximated to (3^6)^2 and 3^6 will give you 5^4 so you will end up getting almost 5^8 and this when added to 5^28 will still not do anything.
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