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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}.

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.

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.

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Last edited by gmat6nplus1 on 29 Dec 2013, 03:18, edited 1 time in total.

Re: Which of the following best approximates the value of q if [#permalink]
29 Dec 2013, 02:35

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.

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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.

I thought it this way:3^11=5^q-5^28.Now if we takeq>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!