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What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and

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What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and  [#permalink]

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New post 20 Feb 2020, 14:56
3
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:11) correct 29% (01:10) wrong based on 28 sessions

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What is the units digit of \(x^3\)?

(1) x is even

(2) \(x^3\) is between 10 and 100
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Re: What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and  [#permalink]

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New post 20 Feb 2020, 15:31
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OhMy wrote:
What is the units digit of \(x^3\)?

(1) x is even

(2) \(x^3\) is between 10 and 100


OhMy :- Can you please explain how B could be an answer?

i) x is even -> x could be 2,4 -> x^3 = 8, 64 - Multiple values - Not Sufficient

ii) x^3 is between 10 and 100 -> x could be 3 or 4 -> x^3 can be 27 or 64 -> Units digit can be 7 or 4 - Insufficient

Combining i) and ii) x^3 can only be 64 -> Units digit is 4

Hence C should be an answer.
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Re: What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and  [#permalink]

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New post 20 Feb 2020, 23:11
shameekv1989 wrote:
OhMy wrote:
What is the units digit of \(x^3\)?

(1) x is even

(2) \(x^3\) is between 10 and 100


OhMy :- Can you please explain how B could be an answer?

i) x is even -> x could be 2,4 -> x^3 = 8, 64 - Multiple values - Not Sufficient

ii) x^3 is between 10 and 100 -> x could be 3 or 4 -> x^3 can be 27 or 64 -> Units digit can be 7 or 4 - Insufficient

Combining i) and ii) x^3 can only be 64 -> Units digit is 4

Hence C should be an answer.


Edited the OA. It's C, not B.
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Re: What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and  [#permalink]

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New post 21 Feb 2020, 04:40
shameekv1989 Bunuel

You are right guys. sorry, my mistake.
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Re: What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and  [#permalink]

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New post 21 Feb 2020, 09:59

Solution



To find
We need to determine
    • The units digit of \(x^3\)

Analysing Statement 1
As per the information given in statement 1, x is even
However, from this information, we cannot determine the exact units digit of x.
    • For example, if x = 2, then units digits of \(x^3\) is 8
    • Alternatively, if x = 4, then units digit of \(x^3\) is 4

Hence, statement 1 is not sufficient to answer the question.

Analysing Statement 2
As per the information given in statement 2, \(x^3\) is between 10 and 100
Hence, value of \(x^3\) can be either 27 or 64 – but we cannot uniquely determine the exact value of \(x^3\)

Hence, statement 2 is not sufficient to answer the question.

Combining Both Statements Together
We know \(x^3\) can be either 27 and 64, and x is also even (means \(x^3\) is even)
    • Hence, \(x^3\) is equal to 64 only, and units digit is 4

Thus, option C is the correct answer.

Correct Answer: Option C
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Re: What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and  [#permalink]

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New post 21 Feb 2020, 18:07
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Why is the answer C and not E? It never says that X is an integer. Unless we are to assume that by definition the word "even" implicitly refers to integers.

(2.66)^3 = 18.821. This is an "even" decimal value for instance, but isn't an integer.
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Re: What is the unit digit of x^3? (1) x is even (2) x^3 is between 10 and   [#permalink] 21 Feb 2020, 18:07
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