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

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sandy
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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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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.
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D
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GreenlightTestPrep
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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
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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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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink] New post   19 May 2020, 05:46
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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] New post   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] New post   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
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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink] New post   18 Oct 2021, 05:01
Hi Brent, you mean we can have a negative ratio?

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

That means the ratio is possible to be 16:-28?

What is your understanding of this result?

GreenlightTestPrep wrote:
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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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink] New post   18 Oct 2021, 05:56
jantje wrote:
Hi Brent, you mean we can have a negative ratio?

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

That means the ratio is possible to be 16:-28?

What is your understanding of this result?



There's no rule that says ratios can't be negative.
So, for example 1 : -1 is equivalent to 2 : -2
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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink] New post   28 Aug 2023, 13:26
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Was going through the book and saw this excellent question:

Consider the stem only:

we know that

16/g=g/49
therefore:
g^2=4^2*7^2
g=28k
Notice that g is some multiple of 28, excluding 0. If we take the case of k=2, QA is larger. If we take the case of k=-1, QB is larger.
Without information on what type of number G is, it is not possible to solve.

D
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Re: The ratio of 16 to g is equal to the ratio of g to 49. [#permalink]
28 Aug 2023, 13:26
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