kumarneupane4344 wrote:
If the difference between the product and sum of five integers a, b, c, d, e is an even integer, then the number of even integers among these five numbers CANNOT be?
Indicate all that are true.
A. 0
B. 1
C. 2
D. 3
E. 4
F. 5
(a)(b)(c)(d)(e) - (a + b + c + d + e) = even
Case I: (a)(b)(c)(d)(e) = odd
(a + b + c + d + e) = odd
Case II: (a)(b)(c)(d)(e) = even
(a + b + c + d + e) = even
A. Number of even integers 0 - Case I(odd + odd + odd + odd + odd) = odd
B. Number of even integers 1 - Case II(even + odd + odd + odd + odd) = even
C. Number of even integers 2 - Neither Case I or II(even + even + odd + odd + odd) = odd
D. Number of even integers 3 - Case II(even + even + even + odd + odd) = even
E. Number of even integers 4 - Neither Case I or II(even + even + even + even + odd) = odd
F. Number of even integers 5 - Case II(even + even + even + even + even) = even
Hence, option C and E