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05 Dec 2016, 03:05
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E
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Difficulty:
15%
(low)
Question Stats:
83% (01:25) correct
17%
(01:21)
wrong
based on 65
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Are there any prime numbers between the integers m and n?
(1) m – n is even.
(2) There is only one odd number between m and n.
(1) m – n is even.
(2) There is only one odd number between m and n.
05 Dec 2016, 03:47
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Bunuel
M-N = EVEN , both M and N are even or both are odd ... clearly insuff , (8,9,,10,11 12) , (4,5,6) or (1,2,3) (7,8,9) YES AND NO
from 2
m and n are successive even numbers (4,5,6) yes or (8,9,10) no... insuff
both
m and n are successive even numbers (4,5,6) yes or (8,9,10) no... insuff
E
05 Dec 2016, 03:55
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Statement 1: for m-n to be even, either both should be odd or even. There can or cannot be a prime number between two even or two odd integers. For instance, Between 4 and 6, 5 is a prime number, but there is no prime number between 45 or 47.
This statement is not sufficient to solve the problem
Statement 2: There is only one odd number between m and n.
In this case, m and n can be even/odd but only one odd number should be between them
Case 1: 5, 6, 7, 8, 9
possible values of m and n are : m=5, n=8
m=6, n=8
m=5, n=9
m=6, n=9
For any of the above values of m and n , there is a prime number, 7 between m and n
Case 2: 7, 8, 9 , 10, 11
possible values of m and n are : m=7, n=10
m=7, n=11
m=8, n=10
m=8, n=11
For any of the above values of m and n , there is no prime number between m and n
This statement is not sufficient to solve the problem
Combining both statements:
Both m and n are either odd or even and there is only one odd between m and n
Case 1: 5, 6, 7, 8, 9
possible values of m and n are :
m=6, n=8
m=5, n=9
For any of the above values of m and n , there is a prime number, 7 between m and n
Case 2: 7, 8, 9 , 10, 11
possible values of m and n are :
m=7, n=11
m=8, n=10
For any of the above values of m and n , there is no prime number between m and n
Combining both statements does not resolve the problem, so the correct answer is E.
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This statement is not sufficient to solve the problem
Statement 2: There is only one odd number between m and n.
In this case, m and n can be even/odd but only one odd number should be between them
Case 1: 5, 6, 7, 8, 9
possible values of m and n are : m=5, n=8
m=6, n=8
m=5, n=9
m=6, n=9
For any of the above values of m and n , there is a prime number, 7 between m and n
Case 2: 7, 8, 9 , 10, 11
possible values of m and n are : m=7, n=10
m=7, n=11
m=8, n=10
m=8, n=11
For any of the above values of m and n , there is no prime number between m and n
This statement is not sufficient to solve the problem
Combining both statements:
Both m and n are either odd or even and there is only one odd between m and n
Case 1: 5, 6, 7, 8, 9
possible values of m and n are :
m=6, n=8
m=5, n=9
For any of the above values of m and n , there is a prime number, 7 between m and n
Case 2: 7, 8, 9 , 10, 11
possible values of m and n are :
m=7, n=11
m=8, n=10
For any of the above values of m and n , there is no prime number between m and n
Combining both statements does not resolve the problem, so the correct answer is E.
------------
+1 Kudos if you like the post
