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It is known that (1.1)^{17} is approximately equal to 5.05.

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by Max@Math Revolution » Wed Jun 12, 2019 12:18 am

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[GMAT math practice question]

It is known that (1.1)^{17} is approximately equal to 5.05. What is the approximate value of (1.1)^{50}?

A. 20
B. 40
C. 80
D. 120
E. 160
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by GMATGuruNY » Wed Jun 12, 2019 2:11 am
Max@Math Revolution wrote:[GMAT math practice question]

It is known that (1.1)^{17} is approximately equal to 5.05. What is the approximate value of (1.1)^{50}?

A. 20
B. 40
C. 80
D. 120
E. 160
1,1¹� ≈ 5
(1.1¹�)³ ≈ 5³
1.1�¹ ≈ 125
Thus:
1.1�� = a bit less than 125

The correct answer is D.
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Solutions

by Max@Math Revolution » Thu Jun 13, 2019 10:51 pm
Answer: D

(1.1)^50
= (1.1)^(51 - 1)
= (1.1)^51 / (1.1)
= ((1.1)^17)^3 / (1.1)
≈ 5^3/1.1
= 125/1.1
≈ 120

Therefore, the answer is D.
Last edited by Max@Math Revolution on Sun Jun 16, 2019 10:02 pm, edited 1 time in total.
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by Scott@TargetTestPrep » Fri Jun 14, 2019 2:41 pm
Max@Math Revolution wrote:[GMAT math practice question]

It is known that (1.1)^{17} is approximately equal to 5.05. What is the approximate value of (1.1)^{50}?

A. 20
B. 40
C. 80
D. 120
E. 160
We see that (1.1)^50 ≈ (1.1)^51 = [(1.1)^17]^3

Since (1.1)^17 ≈ 5.05, we can round it to 5 and we have:

[(1.1)^17]^3 ≈ 5^3 = 125

Therefore, (1.1)^50 ≈ 125. Since 120 is the closest to 125, choice D is the correct answer.

Answer: D

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