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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]  19 Aug 2018, 03:02
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Question Stats:

32% (00:32) correct 67% (00:43) wrong based on 119 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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Sandy
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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
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

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]  19 May 2020, 05:46
1
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My question :
If the variable is given as ratio, we don't assume directly that it is positive ?
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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink]  24 Sep 2020, 10:29
Hi!
I like to find whatever clues the GRE question gives us, and this one is found by attempting to find the LCM of 16 and 49. By finding their respective prime number roots (2^4 and 7^2), we have no choice but to multiply them together! Multiplying 16*49= 784. This means that the first ratio is 16:784 where g=784. Remember that ratios can be increased or decreased by a factor so long as the ratio remains consistent which is why we can reduce that factor to 1:49 which is where we get our second g value. Notice how we got g= 784 and 1? This means that the answer choice is D! Cheers!
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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink]  24 Sep 2020, 21:16
16/g=g/49
or, g^2=16*49
or, g= (+/-) (4*7)
so, g= 28 or -28.
So, we can not determine. D
Re: The ratio of 16 to g is equal to the ratio of g to 49.   [#permalink] 24 Sep 2020, 21:16
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