What is the value of t?

jjjinapinch wrote:What is the value of t?
(1) s + t = 6 + s
(2) t^3 = 216

Official Guide question
Answer: D

Target question: What is the value of t?

Statement 1: s + t = 6 + s
Subtract s from both sides to get: t = 6...DONE!
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: t^3 = 216
Only one value satisfies this equation: t = 6...DONE!
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent

jjjinapinch wrote:What is the value of t?

(1) s + t = 6 + s
(2) t^3 = 216

Official Guide question
Answer: D

While the first statement is easy, let's discuss the second statement.

If the exponent of a number is an odd integer, you get a unique value of the number.

Let's take the following examples.

1. t^2 = 36; exponent 2 is even

= t^2 = 6^2; or t^2 = (–6)^2;

In this case t = 6 or –6. No unique value.

2. t^3 = 216; exponent 3 is odd

= t^3 = 6^3; or t^3 ≠ (–6)^3;

In this case t = 6. A unique value.

The correct answer: D

Hope this helps!

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Hi jjjinapinch,

This prompt is built around a couple of standard Arithmetic rules. We're asked for the value of T.

1) S + T = 6 + S

If we subtract S from both sides of the equation, we get... T = 6
Fact 1 is SUFFICIENT.

2) T^3 = 216

While equations that involve exponents sometimes result in more than one solution, this equation has JUST one solution. Here's why:

(positive)^3 = positive
(negative)^3 = negative
(0)^3 = 0

Since T^3 = +216, there can be JUST ONE solution - one positive solution (and while T=6 is that solution, you don't have to technically calculate it to KNOW that there's just one solution). Thus....
Fact 2 is SUFFICIENT.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich