A, B, C, D, E, F and G are seven positive integers. And given a. AB is odd. b.…
2025
A, B, C, D, E, F and G are seven positive integers. And given
a. AB is odd.
b. C+ DE is odd.
c. AD is odd.
d. FACG is odd.
How many of the above integers are odd?
- A.
5
- B.
4
- C.
3
- D.
6
Attempted by 1125 students.
Show answer & explanation
Correct answer: D
Key idea: A product is odd only if every factor is odd; a sum is odd only if the two terms have opposite parity.
From AB is odd: both A and B are odd.
From AD is odd: both A and D are odd. (A was already known odd.)
From FACG is odd: F, A, C, and G are odd. (A already odd.)
So far A, B, C, D, F, G are odd.
Consider C + DE odd: C is odd, D is odd, so DE has the same parity as E. For odd + (parity of DE) to be odd, DE must be even, hence E is even.
Conclusion: Exactly six integers (A, B, C, D, F, G) are odd and one (E) is even. Answer: 6