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f, g, and h are consecutive prime numbers such that f < g

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sandy
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f, g, and h are consecutive prime numbers such that f < g [#permalink] New post   22 Oct 2016, 10:24
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f, g, and h are consecutive prime numbers such that f < g < h.

Quantity A
Quantity B
f + g + h
3g


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


Drill 2
Question: 6
Page: 287
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D
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Re: f, g, and h are consecutive prime numbers such that f < g [#permalink] New post   22 Oct 2016, 10:25
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Explanation

The intervals between consecutive prime numbers does not follow a consistent, predictable pattern. Prove it by Plugging In: Try f = 2, g = 3, and h = 5. Now f + g + h = 10 and 3g = 9.

Quantity A is greater; eliminate choices (B) and (C). Now try f = 7, g = 11, and h = 13. This time, f + g + h = 31, and 3g = 33. Quantity B is now greater. Eliminate choice A, and you’re left with choice D.
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f, g, and h are consecutive prime numbers such that f < g [#permalink] New post   23 Apr 2019, 05:56
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sandy wrote:
f, g, and h are consecutive prime numbers such that f < g < h.

Quantity A
Quantity B
f + g + h
3g


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


Drill 2
Question: 6
Page: 287


Let's test some possible values of f, g, and h

Case i: f = 2, g = 3 and h = 5
We get:
QUANTITY A: f + g + h = 2 + 3 + 5 = 10
QUANTITY B: 3g = 3(3) = 9
In this case, Quantity A is greater


Case ii: f = 3, g = 5 and h = 7
We get:
QUANTITY A: f + g + h = 3 + 5 + 7 = 15
QUANTITY B: 3g = 3(5) = 15
In this case, the two quantities are equal

Answer: D

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Re: f, g, and h are consecutive prime numbers such that f < g [#permalink] New post   01 Jun 2019, 03:22
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sandy wrote:
f, g, and h are consecutive prime numbers such that f < g < h.

Quantity A
Quantity B
f + g + h
3g


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


Drill 2
Question: 6
Page: 287


----PLUG IN VALUES--------
Take 2,3,5
3 times 3 < 2 + 3 + 5

Take 3,5,7
3 times 5 = 3 + 5 + 7

Thus contradicting statemements gives us D answer
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Re: f, g, and h are consecutive prime numbers such that f < g [#permalink] New post   08 Jun 2020, 07:34
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Re: f, g, and h are consecutive prime numbers such that f < g [#permalink] New post   08 Jun 2020, 17:04
To equal a and b.

f + g + h = 3g

The difference between f, g and h, have to be equal to 'g'. So, there must be an arithmetic succession (pattern) to obtain this. This occurs in the case os 3,5,7 (prime numbers with an arithmetic succession) but we need that in general prime numbers don't have a pattern. In conclusion, we have a case that meets a = b, but in other cases we need that a will be different than b. So the answer is D.
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Re: f, g, and h are consecutive prime numbers such that f < g [#permalink]
08 Jun 2020, 17:04
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