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

Question

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

KarishmaB · Accepted Answer

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.

Bunuel · Answer

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.

kraizada84 · Answer

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

Bunuel · Answer

gmat6nplus1 · Answer

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.

arunspanda · Answer

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)

GMATGuruNY · Answer

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.

C

Solas · Answer

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

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

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