If a, b, and c are different integers greater than 1, is b a multiple

Question

If a, b, and c are different integers greater than 1, is b a multiple of a?

(1)  3ac + 10a^2 = b

(2)  5b^2 + a = c

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AKJK · Answer

The question is if we can write b as a times x; x being any integer

Statement 1
3ac+10^2=b
this can be written as b = a (10a+3c) ; let (10a+3c)=x
so b=a.x => statement 1 is sufficient

Statement 2
5b^2+a=c
can be written as b = ((c+a)/5)^1/2
which cannot be reduced to the form b=a.x => statement 2 is insufficient

Hence the answer is A

arahim · Answer

statement 1:
can be rewritten as a(3c+10a)=b
c, a, and b are all integers, 3c+10a is therefore an integer, thus a is a multiple of b

Statement 2:
Cannot rearrange formula into the format a(x) = b, so inconclusive.

Correct answer is A

If a, b, and c are different integers greater than 1, is b a multiple

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