Which of the following could be equal to

Question

Which of the following could be equal to  x^{18}  for an integer x?

A.  x^9 + x^9

B.  (x^2)^9

C.  (x^9)^9

D.  (x^3)^{15}

E. More than one of the above answers

GMATBusters Collection

GMATBusters · Accepted Answer

This is a classic  "Could be"  type trap:
Here we need to reject only those answer options, which can never be equal to  x^{18}  for any integer x.
it can be seen than for x = 0 or 1, all answer options A, B, C, D are equal to equal to  x^{18}  
hence, we have more than one answer correct.
Answer E

yashikaaggarwal · Answer

A. X^9+X^9 = 2(x^9) { not equal to x^18 }

B. (X^2)^9 = x^18 { power multiplies when base is same }

C. (X^9)^9 = x^81 { power multiplies when base is same }

D. (X^3)^15 = x^45 { power multiplies when base is same }

There could be a confusion between A and B for the first instance when one see it. But both yields different results.

So supposedly answer is B.

Posted from my mobile device

GMATinsight · Answer

Let's check Options

A.  x^9 + x^9 = x^9(1+1) = 2*x^9 ≠ x^{18}

B.  (x^2)^9 = x^{2*9} = x^{18}

C.  (x^9)^9 = x^{9*9} = x^{81} ≠ x^{18}

D.  (x^3)^{15} = x^{3*15} = x^{45} ≠ x^{18}

So the answer looks like Option B

Bust since the question does NOT mention what is the possible value of x

and for x = 0

all the option would result in same value i.e. 0 hence all option could be equivalent to  x^{18}  for x = 0 hence

answer: Option E

globaldesi · Answer

GMATBusters  Can you confirm its answer?
It seems to be B bu how come OA is E

GMATBusters · Answer

Solution posted, hope it is clear. if there is any doubt, feel free to tag me.

SunilSwain · Answer

X is integer, hence x can be 1. 
In that case x power 18 => (1) power of 18 = 1.

Hence, when X =1 ; options B,C,D results 1. Hence more than one answers (Option E)

CrackverbalGMAT · Answer

Since the question mentions integers, it actually makes our life easy. Since this is a ‘Could be’ question, we can solve this question easily by plugging in simple integer values like 0, 1, etc.,
A couple of great values we can try are 0 and 1.

If x = 0,  0^{18}  = 0. This can be satisfied by answer options A, B, C and D. This should be enough proof that E might be the right answer. If you wish to play safe, try the value of 1.

If x = 1,  1^{18}  = 1. This can be satisfied by answer options B, C and D. Again, we see that more than one options can be equal to x^18.

This is sufficient to conclude that answer option E is the right answer.

The correct answer option is E .

Hope that helps!

globaldesi · Answer

Thanks GMATBusters . Did not realize the word could be tricky word

Makes sense now

bumpbot · Answer

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Which of the following could be equal to

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Which of the following could be equal to

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