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What is the units digits of N?

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EgmatQuantExpert
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What is the units digits of N? [#permalink] New post   Updated on: 31 Jan 2018, 22:56
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A
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E

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55% (hard)

Question Stats:

58% (01:53) correct 42% (01:36) wrong based on 118 sessions
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Q.)

What is the units digits of N?

(I) The units digit of \(N^4\) is \(6\)
(II) The units digit of\((N - 2)^2\) is \(6\)

    A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
    B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
    C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D. EACH statement ALONE is sufficient.
    E. Statements (1) and (2) TOGETHER are NOT sufficient
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Official Answer
E

Originally posted by EgmatQuantExpert on 31 Jan 2018, 06:19.
Last edited by EgmatQuantExpert on 31 Jan 2018, 22:56, edited 1 time in total.
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Re: What is the units digits of N? [#permalink] New post   31 Jan 2018, 06:19
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Reserving this space to post the official solution. :)
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amanvermagmat
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Re: What is the units digits of N? [#permalink] New post   31 Jan 2018, 08:25
EgmatQuantExpert wrote:
Q.)

What is the units digits of N?

(I) The units digit of \(N^4\) is \(6\)
(II) The units digit of\((N - 2)^2\) is \(6\)

    A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
    B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
    C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D. EACH statement ALONE is sufficient.
    E. Statements (1) and (2) TOGETHER are NOT sufficient


(1) If units digit of N^4 is 6, then the unit digit of N could be 2 or 4 or 6 or 8 (all these even numbers have their fourth power ending in 6). So there is no single value for units digit of N. Not sufficient.

(2) If units digit of (N-2)^2 is 6, then the unit digit of (N-2) could be 4 or 6 (both 4 and 6 have their squares ending in 6). Now if (N-2) ends in 4, then N will end in 6 and if (N-2) ends in 6, then N will end in 8. Still two possibilities for units digit of N. Not sufficient.

Combining the two statements, units digit of N could still be 6 or 8. Still no unique value. Not sufficient.

Hence E answer
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Re: What is the units digits of N? [#permalink] New post   31 Jan 2018, 09:34
EgmatQuantExpert wrote:
Q.)

What is the units digits of N?

(I) The units digit of \(N^4\) is \(6\)
(II) The units digit of\((N - 2)^2\) is \(6\)

    A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
    B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
    C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
    D. EACH statement ALONE is sufficient.
    E. Statements (1) and (2) TOGETHER are NOT sufficient


The numbers with their unit digit as 2, 4, 6 & 8 raised to power of 4 will have their unite digit as 6.

Statement I: Here, N = 2/4/6/8.... So, Insufficient.
Statement II: Here, N = 6/8..... So, Insufficient.

Combining the two statements we get... N = 6/8.

So, E.
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Re: What is the units digits of N? [#permalink] New post   07 Feb 2020, 01:32
The units digit of \(N^4\) can be 6 when the units digit of N is 2 or 4 or 6 or 8. Clearly, statement I alone is insufficient to find out a unique value for the units digit of N.
Answer options A and D can be eliminated. The possible answer options are B, C or E.

The units digit of \((N-2)^2\) is 6. This means that the units digit of (N-2) is 4 or 6 which means that the units digit of N is 6 or 8. Statement II alone is insufficient to find out a unique value for the units digit of N.
Answer option B can be eliminated. The possible answer options are C or E.

Combining both statements I and II, we can say that the units digit of N can be either 6 or 8. We still do not have a unique value for the units digit of N. The combination of statements is insufficient.

Answer option C can be eliminated, the correct answer option is E.

Hope that helps!
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Re: What is the units digits of N? [#permalink]
07 Feb 2020, 01:32
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