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bilv23
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Bunuel
5. For a certain set of numbers, if x is in the set, then both -x^2 and -x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ?

I. -1/64
II. 1/64
III. 1/2^(1/3)

A. I only,
B. II only,
C. III only,
D. I and II only
E. I, II and III

Since 1/2 is in the set, the so must be:
-x^2 = -1/4;
-x^3 = -1/8.

Since -1/4 is in the set, the so must be:
-x^3 = 1/64;

Since -1/8 is in the set, the so must be:
-x^2 = -1/64.

The only number we cannot get is 1/2^(1/3).

Answer: D.
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Lets say if x = 1/2^(1/3), then -x^3 = -1/2

Now since -1/2 is in the set, shouldn't 1/2^(1/3) also be in the set?
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Bunuel
5. For a certain set of numbers, if x is in the set, then both -x^2 and -x^3 are also in the set. If the number 1/2 is in the set , which of the following must also be in the set ?

I. -1/64
II. 1/64
III. 1/2^(1/3)

A. I only,
B. II only,
C. III only,
D. I and II only
E. I, II and III

Since 1/2 is in the set, the so must be:
-x^2 = -1/4;
-x^3 = -1/8.

Since -1/4 is in the set, the so must be:
-x^3 = 1/64;

Since -1/8 is in the set, the so must be:
-x^2 = -1/64.

The only number we cannot get is 1/2^(1/3).

Answer: D.

Lets say if x = 1/2^(1/3), then -x^3 = -1/2

Now since -1/2 is in the set, shouldn't 1/2^(1/3) also be in the set?
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Why is -1/2 necessarily in the set? Also, "x is in the set, then both -x^2 and -x^3 are also in the set" does not necessarily mean that if x is there then -x^(1/3) must also be there: if x then y, does not mean if y then x.

Hope it's clear.
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4. A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?
A. 9 liters
B. 18 liters
C. 27 liters
D. 36 liters
E. 45 liters

My thought process was quite dumb so putting it here incase any one else is thinking in the same direction:

I was misguided by the mention of 3 ltrs per hour and I ended up thinking additional water in the pool was emptied in the extra 2 hours (additional water due to rain was 3 ltr * 2 hrs=6 ltrs)

It rained for 6 hours in fact and additional water in the pool was 3 ltrs * 6 hours =18 ltrs

In each additional hour 9 ltr water was emptied. 9 ltr/ hour

So, in 4 hours (without rain) emptied water (capacity of the pool) is 9 ltr * 4 hours= 36 ltrs (D)
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Hi Bunuel,
what confused me in the solution is that if -x^2 and -x^3 are -1/4 and -1/8, then how are we again treating them as x individually. The way question is written it seems that the set has 3 numbers, x, -x^2, and -x^3

Please help me out with this, thanks :)
Bunuel
5. For a certain set of numbers, if \(x\) is in the set, then both \(-x^2\) and \(-x^3\) are also in the set. If the number \(\frac{1}{2}\) is in the set, which of the following must also be in the set?

I. \(-\frac{1}{64}\)

II. \(\frac{1}{64}\)

III. \(\frac{1}{\sqrt[3]{2}}\)

A. I only,
B. II only,
C. III only,
D. I and II only
E. I, II and III

Since \(\frac{1}{2}\) is in the set, the following must also be in the set:


\(-x^2 = -\frac{1}{4}\);

\(-x^3 = -\frac{1}{8}\).

Since \(-\frac{1}{4}\) is in the set, the following must also be in the set:


\(-x^3 =\frac{1}{64}\)

Since \(-\frac{1}{8}\) is in the set, the following must also be in the set:


\(-x^2 =-\frac{1}{64}\)

The only number we cannot obtain is \(\frac{1}{\sqrt[3]{2}}\).

Answer: D.
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Bunuel
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saransh2797
Hi Bunuel,
what confused me in the solution is that if -x^2 and -x^3 are -1/4 and -1/8, then how are we again treating them as x individually. The way question is written it seems that the set has 3 numbers, x, -x^2, and -x^3

Please help me out with this, thanks :)
Bunuel
5. For a certain set of numbers, if \(x\) is in the set, then both \(-x^2\) and \(-x^3\) are also in the set. If the number \(\frac{1}{2}\) is in the set, which of the following must also be in the set?

I. \(-\frac{1}{64}\)

II. \(\frac{1}{64}\)

III. \(\frac{1}{\sqrt[3]{2}}\)

A. I only,
B. II only,
C. III only,
D. I and II only
E. I, II and III

Since \(\frac{1}{2}\) is in the set, the following must also be in the set:


\(-x^2 = -\frac{1}{4}\);

\(-x^3 = -\frac{1}{8}\).

Since \(-\frac{1}{4}\) is in the set, the following must also be in the set:


\(-x^3 =\frac{1}{64}\)

Since \(-\frac{1}{8}\) is in the set, the following must also be in the set:


\(-x^2 =-\frac{1}{64}\)

The only number we cannot obtain is \(\frac{1}{\sqrt[3]{2}}\).

Answer: D.
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The set's rule means each number generates new elements based on the pattern. Here, -x^2 and -x^3 are treated as elements in the set, not individual variables. They follow the same rule to generate further numbers.
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