Bunuel wrote:
What is the value of integer a ?
(1) \(1 ≤ a^3 ≤ 54\)
(2) \(|3a| = a^2\)
Project DS Butler Data Sufficiency (DS3)
For DS butler Questions Click Here Given: a is an integer Target question: What is the value of a? Statement 1: \(1 ≤ a^3 ≤ 54\) This equation tells us that
a = 1, a = 2 or a = 3 (since 1³ = 1, 2³ = 8, 3³ = 27, but 4³ ≠ 64)
Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: \(|3a| = a^2\)Key property: If |something| = k (where k is positive), then something = k or something = -kWhen we apply the property we get: 3a = a² or 3a = -a²
Let's solve each equation separately.
Take 3a = a² and subtract 3a from both sides to get: 0 = a² - 3a
Factor get: 0 = a(a - 3)
So, either
a = 0 or
a = 3 Take 3a = -a² and add a² to both sides to get: 3a + a² = 0
Factor get: a(3 + a) = 0
So, either
a = 0 or
a = -3 Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that
a = 1, a = 2 or a = 3Statement 2 tells us that
a = -3, a = 0 or a = 3Since both statements must be true, it must be the case that
a = 3, because this is the only solution shared by both statements
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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