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The functions f and g are defined for all the positive

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The functions f and g are defined for all the positive [#permalink]

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The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of perfect squares less than n and g(n) is the number of primes 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
[Reveal] Spoiler: OA

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Re: The functions f and g are defined for all the positive [#permalink]

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f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.
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Re: The functions f and g are defined for all the positive [#permalink]

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New post 09 May 2014, 05:41
farful wrote:
f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.



Than why not not f(x)=6 and g(x)=10?
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Re: The functions f and g are defined for all the positive [#permalink]

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New post 09 May 2014, 05:48
ronr34 wrote:
farful wrote:
f(n) = number of perfect squares less than n
1,4,9,16,25,36

f(25) = 4
f(26)=f(27)=...=f(35)=f(36) = 5
f(37) = 6

g(n) = number of prime numbers less than n
2,3,5,7,11,13,17,19,23,29,31,37

g(31)=10
g(32)=g(33)=...=g(36)=g(37) = 11
g(38)=12


f(x)+g(x)=16 implies that f(x)=5 and g(x)=11.

So, x = 32,33,34,35,or36.

Answer C, 31 < x < 37.



Than why not not f(x)=6 and g(x)=10?



f(x) >= 6 implies x > 36.
g(x) <= 10 implies x < 32.
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Re: The functions f and g are defined for all the positive [#permalink]

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New post 09 May 2014, 05:58
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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 primes 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

Perfect squares: 1, 4, 9, 16, 25, 36, ..,
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15.
If x = 32, then f(32) = 5 and g(32) = 11: f(x) + g(x) = 5 + 11 = 16.
...
If x = 36, then f(36) = 5 and g(36) = 11: f(x) + g(x) = 5 + 11 = 16.
If x = 37, then f(37) = 6 and g(37) = 11: f(x) + g(x) = 6 + 11 = 17.

Thus x could be 32, 33, 34, 35 or 36: 31<x<37.

Answer: C.

P.S. This is GMAT Club's question, not Grockit's.
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Re: The functions f and g are defined for all the positive [#permalink]

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Re: The functions f and g are defined for all the positive   [#permalink] 11 Dec 2017, 09:50
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