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Which of the following best approximates the value of q if 5^28+3^11=5

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vwjetty
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Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   Updated on: 13 Dec 2017, 01:02
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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
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C

Originally posted by vwjetty on 23 Aug 2010, 09:32.
Last edited by Bunuel on 13 Dec 2017, 01:02, edited 3 times in total.
Edited the question.
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   01 Apr 2012, 23:51
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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.
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   23 Aug 2010, 10:12
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Question should read:

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.
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   Updated on: 29 Dec 2013, 04:18
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I solved it this way:

\(5^2^8+3^1^1=5^q\)

\(3^3=27\) 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.

Originally posted by gmat6nplus1 on 28 Dec 2013, 11:02.
Last edited by gmat6nplus1 on 29 Dec 2013, 04:18, edited 1 time in total.
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   Updated on: 29 Sep 2014, 05:48
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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

\(5^{28} + 3^{11} = 5^q\)

Or, \(5^{28}( 1 + \frac{3^{11}}{5^{28}}) = 5^q\)

Since, \(\frac{3^{11}}{5^{28}} << 1\), the term \((1 + \frac{3^{11}}{5^{28}})\)can be approximated to 1.

Thus, \(5 ^ {28} = 5 ^q\)

Or, \(q = 28\).

Answer: (C)

Originally posted by arunspanda on 29 Dec 2013, 03:34.
Last edited by arunspanda on 29 Sep 2014, 05:48, edited 1 time in total.
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   16 Apr 2020, 17:31
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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


\(5^q - 5^{28} = 3^{11}\)

We can PLUG IN THE ANSWERS, which represent the approximate value of q.

B: q=30
\(5^{30} - 5^{28} = 3^{11}\)
\(5^{28}(5^2 - 1) = 3^{11}\)
\(5^{28}(24) = 3^{11}\)
Not viable.
The left side is MUCH GREATER than the right side.
Eliminate B.

D: q=27
\(5^{27} - 5^{28} = 3^{11}\)
Not viable.
The left side is negative and thus is MUCH SMALLER than the right side.
Eliminate D.

Since B makes the left side too big, while D makes the left side too small, the correct answer must be BETWEEN B AND D.

Show Spoiler
C
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   01 Apr 2012, 23:56
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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


Pay attention to the funda here that 3^11 is much less than 5^28 (obviously its superlarge number)

hence q can be approximated to 28.

ANALOGY: suppose you need to add 10...... trillion to 100 then obviously the result after addition can be approximated to 10......trillion.

Hence C
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   02 Apr 2012, 00:25
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Hope it helps.
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   12 Sep 2021, 08:05
Please could you help me tell if the below solution is an acceptable approach?

5^28 will yield a value with units digit 0
3^11 will yield a vaule with units digit 1

The sum of these two values will yield a number with units digit 1. Since 5^q would yield a value only with units digit 0 or 5, the closest approximation to '1' above would be '0' - and only an even power for 5 would give us a unit digit '0'. Therefore, q=EVEN -> hence C

Appreciate your help in advance
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink] New post   03 Jan 2024, 11:03
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Re: Which of the following best approximates the value of q if 5^28+3^11=5 [#permalink]
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