What is the value of integer a ? (1) 1 a^3 54 (2) |3a| = a^2

Question

What is the value of integer a ?

(1)  1 ≤ a^3 ≤ 54

(2)  |3a| = a^2

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Cyryl · Answer

Do you need both statements? I think (1) alone says a must be positive since an odd exponent is between 2 positive values and (2) alone gives you the actual value that could be positive or negative.

GaryIndiana · Answer

Cyryl , I can't figure out how to respond directly, (I am new to using the forum), but the issue with A is that multiple positive integers are all valid responses. 1,2, and 3, all are valid under statement 1 only.

For that reason, I answered C.

Fdambro294 · Answer

Statement 1:
Any odd integer power will have a result that keeps the sign of the base

Thus according to statement 1, a > 0

We also know a = integer 
Which means that (a)^3 = perfect cube

a = 1, 2, or 3 
All there values satisfy the given inequality

Statement 2:

(1st) a term with the variable (a) is set equal to a term with the variable (a)
Therefore, we know that: (a) = 0 will satisfy the equation

(2nd)
PROPERTY:
(X)^2 = |X| * |X|

so we can rewrite (a)^2 as the product of two absolute values

|3a| = |a| * |a|

Which is the same as:
3 * |a| = |a| * |a|

Since we already found that (a = 0) is one possible solution, let us assume that a is not equal to 0 and divide by the absolute value of a

3 = |a|

So we can find two more solutions: 
a = 3 
Or
a = — 3

(S1 & S2 together)

S1: a = 1, 2, or 3
S2: a = 0, —3, or 3

Positive 3 is the only value that works when both statements are used together

*C*

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What is the value of integer a ? (1) 1 a^3 54 (2) |3a| = a^2

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