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The ratio of 16 to g is equal to the ratio of g to 49.

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The ratio of 16 to g is equal to the ratio of g to 49. [#permalink] New post 19 Aug 2018, 03:02
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Question Stats:

33% (01:13) correct 66% (00:32) wrong based on 9 sessions
The ratio of 16 to g is equal to the ratio of g to 49.

Quantity A
Quantity B
g
\(28\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink] New post 21 Aug 2018, 11:26
Expert's post
sandy wrote:
The ratio of 16 to g is equal to the ratio of g to 49.

Quantity A
Quantity B
g
\(28\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


GIVEN: The ratio of 16 to g is equal to the ratio of g to 49.
In other words, 16/g = g/49
Cross multiply to get: g² = (16)(49) [Let's not find this product yet. You'll see why shortly]

Notice that 16 = 4² and 49 = 7²
So, we get: g² = (4²)(7²)

We have a nice rule that says (a^x)(b^x) = (ab)^x

So we can write: g² = 28²

IMPORTANT: Many people will conclude (incorrectly) that g must equal 28
However, we should also note that (-28)² = 28², so g could also equal -28

If g = 28, then Quantity A EQUALS Quantity B
If g = -28, then Quantity B is GREATER THAN Quantity B

Answer: D

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: The ratio of 16 to g is equal to the ratio of g to 49.   [#permalink] 21 Aug 2018, 11:26
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The ratio of 16 to g is equal to the ratio of g to 49.

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