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10 Jul 2018, 20:18
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E
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If a,b and c are positive integers and only one out of them is even, which of the following must be even?
I. \(\frac{ab}{c}\), where ab/c is an integer.
II. abc
III. a+b+c
A. Only I
B. Only II
C. Only III
D. Only II and III
E. I, II and III
New question
I. \(\frac{ab}{c}\), where ab/c is an integer.
II. abc
III. a+b+c
A. Only I
B. Only II
C. Only III
D. Only II and III
E. I, II and III
New question
10 Jul 2018, 20:42
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the answer is E.
with one of the numbers even and two of them odd, the product of abc HAS to be even.
Since Odd + Odd = Even and Even + Even = Even; the sum of abc will also be even.
If ab/c is an integer, it means that an odd denominator is cancelling an odd numerator, finally leading to an even integer.
with one of the numbers even and two of them odd, the product of abc HAS to be even.
Since Odd + Odd = Even and Even + Even = Even; the sum of abc will also be even.
If ab/c is an integer, it means that an odd denominator is cancelling an odd numerator, finally leading to an even integer.
10 Jul 2018, 21:25
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chetan2u
If a,b and c are positive integers and only one out of them is even, which of the following must be even?
I. \(\frac{ab}{c}\), where ab/c is an integer.
II. abc
III. a+b+c
A. Only I
B. Only II
C. Only III
D. Only II and III
E. I, II and III
New question
I. \(\frac{ab}{c}\), where ab/c is an integer.
II. abc
III. a+b+c
A. Only I
B. Only II
C. Only III
D. Only II and III
E. I, II and III
New question
Given, a,b and c are positive integers & only one out of them is even.
I.\(\frac{ab}{c}\),
Since ab/c is an integer, hence \(Rem(\frac{numerator}{denominator})=0\), so, when one of the integers is even, then numerator/denominator must be a multiple of 2.hence the expression must be even.
II.abc
Since only one out of a,b, and c is odd; hence even*(odd)=Even. hence abc is Even.
Must be even.
III. a+b+c
when a=even, b, c=odd; a+b+c=even+odd+odd=even+even=even
Since a,b, and c are added ;same results would be obtained when b or c is even.
Must be even.
Ans. (E)
