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
Number Properties | The functions f and g are defined for al
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- richachampion
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OA : C
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
- richachampion
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Thanks Mr. Rich,
I find this question quite irritating. whats your Opinion about this question?
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This question is a little boring, and it's not very sophisticated.richachampion wrote:I find this question quite irritating. whats your Opinion about this question?
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.
Enjoy the game!!!
Marty Murray
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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
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
- richachampion
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__________________[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
Thanks Mr. Rich and Mr. Murray. This question was not tough, but a boring one.Marty Murray wrote:
This question is a little boring, and it's not very sophisticated.
R I C H A,
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