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GMAT 1: 760 Q51 V42
Posts: 10,057
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:41) correct
41%
(02:38)
wrong
based on 194
sessions
History
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[GMAT math practice question]
\(f(x)\) denotes the number of prime numbers less than or equal to a positive integer \(x\), and \(m(a, b)\) denotes the maximum of \(a\) and \(b.\) What is the summation of all the values of \(x\) which satisfy \(m(f(x), 5)=5\)?
\(A. 70\)
\(B. 72\)
\(C. 74\)
\(D. 76\)
\(E. 78\)
\(f(x)\) denotes the number of prime numbers less than or equal to a positive integer \(x\), and \(m(a, b)\) denotes the maximum of \(a\) and \(b.\) What is the summation of all the values of \(x\) which satisfy \(m(f(x), 5)=5\)?
\(A. 70\)
\(B. 72\)
\(C. 74\)
\(D. 76\)
\(E. 78\)
Posts: 1
MathRevolution please share approach foe question.
m(f(x),5)=5
hence f(x) can be 0,1,2,3,4,or 5
x can take value of all positive integers less than 6th prime number, that is 13.
Sum of all values of x= 1+2+........11+12= 12*13/2=78
hence f(x) can be 0,1,2,3,4,or 5
x can take value of all positive integers less than 6th prime number, that is 13.
Sum of all values of x= 1+2+........11+12= 12*13/2=78
Adarshtgmat
MathRevolution
any good explanation for this question??
GMAT 1: 760 Q51 V42
Posts: 10,057
=>
Since \(m(f(x),5)=5\), we have \(f(x) ≤ 5\) or \(f(x) = 0, 1, 2, 3, 4\) or \(5.\)
\(f(1) = 0, f(2) = 1, f(3) = 2, f(4) = 2, f(5) = 3, … , f(11) = 5, f(12) = 5, f(13) = 6. f(13) = 6\) is out of the range of \(f(x) ≤ 5.\)
So, all possible values of \(x\) are \(1, 2, 3, … , 12\) and we have \(1 + 2 + 3 + … + 12 = 78\).
Therefore, E is the answer.
Answer: E
Since \(m(f(x),5)=5\), we have \(f(x) ≤ 5\) or \(f(x) = 0, 1, 2, 3, 4\) or \(5.\)
\(f(1) = 0, f(2) = 1, f(3) = 2, f(4) = 2, f(5) = 3, … , f(11) = 5, f(12) = 5, f(13) = 6. f(13) = 6\) is out of the range of \(f(x) ≤ 5.\)
So, all possible values of \(x\) are \(1, 2, 3, … , 12\) and we have \(1 + 2 + 3 + … + 12 = 78\).
Therefore, E is the answer.
Answer: E
Posts: 1,324
F(x) ———-> gives the count of all the Primes less than or equal to X
Max of ( f(x). ; 5) = 5
This means every value of X that will satisfy this function must have 5 or less prime values that are less than or equal to X
First 5 prime numbers
2, 3, 5, 7, 11
Next prime number 13——-> f(13) = 6 prime numbers including 13
If x = 13, the max number would be 6, not 5
Thus every Positive integer from 1 thru 12, inclusive, will satisfy X
Then just need to sum the first 12 consecutive integers
(12) (13) * (1/2) = 78
E
Posted from my mobile device
Max of ( f(x). ; 5) = 5
This means every value of X that will satisfy this function must have 5 or less prime values that are less than or equal to X
First 5 prime numbers
2, 3, 5, 7, 11
Next prime number 13——-> f(13) = 6 prime numbers including 13
If x = 13, the max number would be 6, not 5
Thus every Positive integer from 1 thru 12, inclusive, will satisfy X
Then just need to sum the first 12 consecutive integers
(12) (13) * (1/2) = 78
E
Posted from my mobile device
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