DS Number properties

[tonebeeze]

If a, b, and c are positive integers and 4a = 2b + 4c, which of the following must be true?

I. a = c
II. b ≠ c
III. a > c

a. None
b. I only
c. II only
d. III only
e. I and III

[srcc25anu]

IMO D

lets take an example
4(6)=2(6) + 4(3)
4(6) = 2(2) + 4(5)
4(6) = 2(4) + 4(4)

contition 1: a=c (not necessarily true) - case 1 and 2
b not equal to c (again not necessarily true) - case 3
a > c always true since given that a,b,c > 0

[manpsingh87]

If a, b, and c are positive integers and 4a = 2b + 4c, which of the following must be true?

I. a = c
II. b ≠ c
III. a > c

a. None
b. I only
c. II only
d. III only
e. I and III

4a=2b+4c;
4a-4c=2b;
2(a-c)=b; as a,b and c are positive integers therefore right hand side is positive; if right hand side is positive then left hand side must also be positive such that quantities on both the sides becomes equal. therefore, (a-c)>0 i.e a>c;
hence D

[maihuna]

2A=B+2C
since b>0 2(a-c) = b > 0 =< a>c, it is also obvious since 2a = b+2c, => a!=c, as otherwise b should be 0, a!<c, as b should be negative.

If a, b, and c are positive integers and 4a = 2b + 4c, which of the following must be true?

I. a = c
II. b ≠ c
III. a > c

a. None
b. I only
c. II only
d. III only
e. I and III

[force5]

yes Manpsingh explained it well... i also feel D by same explanation.