square root in ratio

[GmatGreen]

Which of the following ratios is most nearly equal to the ratio 1 + sqrt(5) to 2?

A) 8 to 5
B) 6 to 5
C) 5 to 4
D) 2 to 1
E) 1 to 1

[Patrick_GMATFix]

The solution below is taken from the GMATFix App (this is QID 5263).



-Patrick

[GMATGuruNY]

Which of the following ratios is most nearly equal to the ratio 1 + sqrt(5) to 2?

A) 8 to 5
B) 6 to 5
C) 5 to 4
D) 2 to 1
E) 1 to 1

The LCM of the denominators in the answer choices = 5*4 = 20.
Approximate the value of (1 + √5)/2 with a denominator of 20.
√5 is between 2 and 3.
Thus:
(1 + √5)/2 is between 3/2 = 30/20 and 4/2 = 40/20.

The correct answer choice must be between 30/20 and 40/20.
Only A works:
8/5 = 32/20.

The correct answer is A.

[Brent@GMATPrepNow]

Which of the following ratios is most nearly equal to the ratio 1 + √5 to 2?

A) 8 to 5
B) 6 to 5
C) 5 to 4
D) 2 to 1
E) 1 to 1

There are 3 root evaluations that all GMAT students should memorize:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

So, 1 + √5 to 2 ≈ 1 + 2.2 to 2
≈ 3.2 to 2
≈ 1.6 to 1

At this point, if we multiply both sides by 5, we get: ≈ 8 to 5 (answer choice A)

Aside: Notice that, once we get to the equivalent ratio 1.6 to 1, we can automatically eliminate answer choices D and E.
Then, if we multiply both sides by 4, we get ≈ 6.4 to 4, which means we can eliminate C

Cheers,
Brent