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Number Properties | The functions f and g are defined for al

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Number Properties | The functions f and g are defined for al

by richachampion » Thu Oct 06, 2016 4:15 pm
The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of positive perfect squares less than n and g(n) is the number of prime numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38
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by richachampion » Thu Oct 06, 2016 4:16 pm
OA : C
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by [email protected] » Thu Oct 06, 2016 6:24 pm
Hi All,

We can use the answer choices to our advantage on this question (by determining if number of possible or impossible, we can eliminate answer choices).

Let's start by TESTing X=31. According to the prompt...

f(31) = number of perfect squares less than 31 = {1, 4, 9, 16, 25] = 5
g(31) = number of primes less than 31 = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} = 10

f(31) + g(31) = 15; we're told that it's SUPPOSED to be 16 though, so X CANNOT be 31. Eliminate Answers A and B.

Next, let's TEST X = 37. According to the prompt...

f(37) = number of perfect squares less than 31 = {1, 4, 9, 16, 25, 36] = 6
g(37) = number of primes less than 31 = {2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 3} = 11

f(37) + g(37) = 17; we're told that it's SUPPOSED to be 16 though, so X CANNOT be 37. Eliminate Answers D and E.

Final Answer: C

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by richachampion » Thu Oct 06, 2016 7:00 pm
[email protected] wrote: Final Answer: C

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Thanks Mr. Rich,

I find this question quite irritating. whats your Opinion about this question?
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by MartyMurray » Thu Oct 06, 2016 9:20 pm
richachampion wrote:I find this question quite irritating. whats your Opinion about this question?
This question is a little boring, and it's not very sophisticated.

At the same time, the GMAT is often a test of skill in just plain getting things done, and answering this question is about pretty much just getting something done.

So maybe the thing to do with a question like this one is just to see it for what it is, come up with a way to get to the answer, and GET IT DONE.

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by [email protected] » Fri Oct 07, 2016 9:13 am
Hi richachampion,

Regardless of whether you 'like' a question or not, you have to remember that the Quant section of the GMAT is NOT, strictly-speaking, a "math test." As such, you're going to face questions that really are NOT about 'testing' you math skills - they're about testing your 'critical thinking' skills (a variety of DS questions exist for exactly this purpose). Ultimately, when dealing with a Quant question, I consider every piece of information that I'm given to work with (including the answer choices) and look for the easiest/most-efficient approach to get to the correct answer. In some cases, that means "just do math", but more often there's a Tactic, pattern or logic-based approach that will work really well. Even the nastiest questions are still based on patterns and rules, so even if I don't immediately see an obvious approach, there are details in the prompt that will remind me of OTHER questions that I've already answered - so I can 'play around' a bit with the prompt and likely find the pattern that I need to know to properly answer the question.

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by richachampion » Fri Oct 07, 2016 2:12 pm
[email protected] wrote:Hi richachampion,

Regardless of whether you 'like' a question or not, you have to remember that the Quant section of the GMAT is NOT, strictly-speaking, a "math test." As such, you're going to face questions that really are NOT about 'testing' you math skills - they're about testing your 'critical thinking' skills (a variety of DS questions exist for exactly this purpose). Ultimately, when dealing with a Quant question, I consider every piece of information that I'm given to work with (including the answer choices) and look for the easiest/most-efficient approach to get to the correct answer. In some cases, that means "just do math", but more often there's a Tactic, pattern or logic-based approach that will work really well. Even the nastiest questions are still based on patterns and rules, so even if I don't immediately see an obvious approach, there are details in the prompt that will remind me of OTHER questions that I've already answered - so I can 'play around' a bit with the prompt and likely find the pattern that I need to know to properly answer the question.

GMAT assassins aren't born, they're made,
Rich
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This question is a little boring, and it's not very sophisticated.
Thanks Mr. Rich and Mr. Murray. This question was not tough, but a boring one.
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