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03 Jun 2020, 23:02
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For distinct positive integers x and y, where x < y, the function FP(x, y) returns the smallest prime number between x and y, exclusive, or the text string ‘NULL’ if no such number is found. If FP(a, b) +FP(c, d) = FP(e, f), where a, b, c, d, e and f are distinct positive integers, what is the value of c^a ?
(1) FP(g, h) = a, where g and h are distinct positive integers
(2) c is less than the minimum possible value of the function FP(x,y).
Are You Up For the Challenge: 700 Level Questions
(1) FP(g, h) = a, where g and h are distinct positive integers
(2) c is less than the minimum possible value of the function FP(x,y).
Are You Up For the Challenge: 700 Level Questions
04 Jun 2020, 04:12
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Even+Odd = Odd
Hence, between FP(a, b) and FP(c, d), one must be equal to 2. So, either a = 1 or c=1
Statement 1-
a is prime number; Hence, c must be equal to 1.
It doesn't matter what's the value of a, \(c^a\) is always equal to 1
Sufficient
Statement 2 - It also tells us that c is smaller than 2 or c=1.
Hence, \(c^a\) is equal to 1
Sufficient
D
Hence, between FP(a, b) and FP(c, d), one must be equal to 2. So, either a = 1 or c=1
Statement 1-
a is prime number; Hence, c must be equal to 1.
It doesn't matter what's the value of a, \(c^a\) is always equal to 1
Sufficient
Statement 2 - It also tells us that c is smaller than 2 or c=1.
Hence, \(c^a\) is equal to 1
Sufficient
D
Bunuel
For distinct positive integers x and y, where x < y, the function FP(x, y) returns the smallest prime number between x and y, exclusive, or the text string ‘NULL’ if no such number is found. If FP(a, b) +FP(c, d) = FP(e, f), where a, b, c, d, e and f are distinct positive integers, what is the value of ca ?
(1) FP(g, h) = a, where g and h are distinct positive integers
(2) c is less than the minimum possible value of the function FP(x,y).
(1) FP(g, h) = a, where g and h are distinct positive integers
(2) c is less than the minimum possible value of the function FP(x,y).
HoneyLemon
04 Jun 2020, 19:30
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Bunuel
For distinct positive integers x and y, where x < y, the function FP(x, y) returns the smallest prime number between x and y, exclusive, or the text string ‘NULL’ if no such number is found. If FP(a, b) +FP(c, d) = FP(e, f), where a, b, c, d, e and f are distinct positive integers, what is the value of ca ?
(1) FP(g, h) = a, where g and h are distinct positive integers
(2) c is less than the minimum possible value of the function FP(x,y).
(1) FP(g, h) = a, where g and h are distinct positive integers
(2) c is less than the minimum possible value of the function FP(x,y).
Wow . Such a good ques . Kudos to this ques !! Took me >3 min to deduce the logic .
Ans is E IMO .
FP(a, b) +FP(c, d) = FP(e, f) , a, b, c, d, e and f are distinct positive integers ..
Prime + Prime = Prime
we know that addition of 2 prime can only yield prime number if one of them is 2 .
so either a or c must be 1 .
We need to find value of ac .
(1) FP(g, h) = a, where g and h are distinct positive integers
a must be a prime number .
So now c must be 1 . But a can be any prime 3 or 2 .
FP(2, 4) +FP(1, 3) = FP(4, 6) ===> 3 + 2 = 5
or
FP(3, 6) +FP(1, 9) = FP(5,8 ) ===> 5 + 2 = 7
ac can be 2 or 3 .
So statement 1 is not sufficient .
(2) c is less than the minimum possible value of the function FP(x,y).
minimum possible value of the function FP(x,y) is 2 .
Now
C < 2 and C > 0
so C = 1 .
But a can be anything .
So statement 2 is not sufficient .
Now Combining both
we have c=1 and a can be still 2 or 3 .
So statement 1 and 2 , combing is not sufficient .
Ans E
