A cube has length x, a surface area y, and a volume z. Which of the

Question

A cube has length x, a surface area y, and a volume z. Which of the following must be true?

A.  \frac{xy}{z} - \frac{y}{x} = 0

B.  \frac{x^2y}{z} - \frac{y}{x} = 0

C.  \frac{xz}{x^2y} - \frac{x^2}{xy} = 0

D.  \frac{x√y}{√z} - \frac{x^2}{y} = 0

E.  \frac{√z}{xy} -\frac{√y}{x^2} = 0

Abhishek009 · Answer

Let x = 2 , So Survaface Area of Cube is y = 6*2^2 = 24 , Volume is z = 2^3 = 8

Now, check the options only (B) fits in ...

\frac{2^224}{8} - \frac{24}{2}

= 4*3 - 12

= 0 , Answer must hence be (B)

asmba · Answer

Length = x
Surface Area of Cube = 6x^2 = y
Volume = x^3 = z

Substituting these values in answer options gives B as the right answer as below:
x^2 * 6x^2/x^3 - 6x^2/x = 6x - 6x = 0

rishabhg2712 · Answer

Why does this not work, when x=1 ?

Posted from my mobile device

Bunuel · Answer

Check below. Pay attention to the highlighted part.

"MUST BE TRUE" ("ALWAYS TRUE"/"IS TRUE") questions:
 These questions ask which statement is always true for  every  valid set of numbers. If you can find just one valid set of numbers where a statement is not true, it means the statement is not always true and therefore not the correct answer.

So, for 'MUST BE TRUE' questions, the plug-in method is good for eliminating an option, but it does not provide a 100% guarantee that an option is always true.

For "MUST BE TRUE" questions, when using the plug-in method, if you find that more than one option appears to be correct for a particular number or set of numbers, try using different numbers to double-check. Reevaluate only those options that were previously considered correct.

"COULD BE TRUE" questions:
 The questions that ask which of the following statements could be true are different. If you can demonstrate that a statement is true for a specific set of numbers, it implies that the statement could be true and therefore is a correct answer.

So, for "COULD BE TRUE" questions, the plug-in method can be used to demonstrate that an option could be true. However, it's important to note that if you find that an option is not true for a particular set of numbers, it does not necessarily mean that there isn't another set of numbers where that option would be true.

For this specific question, if we substitute x = 1, we find that y = 6 and z = 1. These values satisfy three options: A, B, and C. Let's consider a different value for x: x = 2. By substituting x = 2 into the equations, we find that y = 6 * 2^2 = 24, and z = 2^3 = 8. Now, let's examine only options A, B, and C using this new set of values. After evaluation, we see that only option B is true.

I would like to share two final thoughts. Firstly, when dealing with "must be true" or "could be true" questions, it is generally not ideal to use 1, -1, or 0 as values to plug in since the question designers often create multiple options that satisfy these values. It is better to use numbers like 2 or 3 or fractions for some questions. Secondly, this question can arguably be solved more easily using algebra. By expressing both the surface area and the volume in terms of x (y = 6x^2 and z = x^3), we can determine that only option B must be true.

Hope it helps.

A cube has length x, a surface area y, and a volume z. Which of the

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GMAT Problem Solving (PS) Questions

A cube has length x, a surface area y, and a volume z. Which of the

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