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# If M and x are positive integers greater than 1, what is the units dig

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If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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Updated on: 13 Aug 2018, 01:04
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Difficulty:

25% (medium)

Question Stats:

74% (01:24) correct 26% (01:15) wrong based on 190 sessions

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e-GMAT Question:

If $$M$$ and $$x$$ are positive integers greater than 1, what is the units digit of $$M^x$$?

(1) $$M$$ when divided by $$5$$ gives a remainder of $$1$$.
(2) $$M = 21$$

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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Originally posted by EgmatQuantExpert on 27 Feb 2018, 09:17.
Last edited by EgmatQuantExpert on 13 Aug 2018, 01:04, edited 4 times in total.
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Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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27 Feb 2018, 11:41
EgmatQuantExpert wrote:

Question:

If $$M$$ and $$x$$ are positive integers greater than 1, what is the units digit of $$M^x$$?

(1) $$M$$ when divided by $$5$$ gives a remainder of $$2$$.
(2) $$M = 21$$

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) m = 5k +2
m can be 2 or 7
insufficient as the unit digit varies

2) m =21

we know that 1^x unit digit is 1
sufficient

(B) imo
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Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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28 Feb 2018, 01:25

Solution:

Step 1: Analyse Statement 1:
$$X$$, when divided by $$5$$, leaves a remainder of $$2$$.
• Per our conceptual understanding, when a number is divided by $$5$$, the remainder is equal to the units digit of the number (if the units digit is $$<5$$) and when the units digit is greater than $$5$$, the remainder is: (Units digit -5).
o Here, when $$M$$ is divided by $$5$$, the remainder is $$2$$.
o Hence, the possible units digit of $$M$$ can be $$2$$ or $$7$$.
• But to calculate the units digit of the expression, $$M^x$$, we need more information on the value of $$x$$.
Since we do not have that information,
Statement 1 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choices A and D.
Step 4: Analyse Statement 2:
$$X = 21$$.
It is also given that “x” is a positive integer.
$$21^{Any Positive integer}$$ will end with a $$1$$ because $$1^{ Any positive integer}$$ ends with a $$1$$.

Since we could figure out the units digit of $$M^x$$
Statement 2 alone is SUFFICIENT to answer the question.
Step 5: Combine both Statements:
This step is not required since we already arrived at an answer from statement 2.
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Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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28 Feb 2018, 05:38
EgmatQuantExpert wrote:

Question:

If $$M$$ and $$x$$ are positive integers greater than 1, what is the units digit of $$M^x$$?

(1) $$M$$ when divided by $$5$$ gives a remainder of $$2$$.
(2) $$M = 21$$

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

Doesn't statement 1 and statement 2 contradict each other !
if the value of M is 21 then divided by 5 it gives a remainder of 1 rather than 2.

Hope moderator will look into this .
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- Stne

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Joined: 26 Mar 2013
Posts: 1904
Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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28 Feb 2018, 06:13
EgmatQuantExpert wrote:

Solution:

Step 1: Analyse Statement 1:
$$X$$, when divided by $$5$$, leaves a remainder of $$2$$.
• Per our conceptual understanding, when a number is divided by $$5$$, the remainder is equal to the units digit of the number (if the units digit is $$<5$$) and when the units digit is greater than $$5$$, the remainder is: (Units digit -5).
o Here, when $$M$$ is divided by $$5$$, the remainder is $$2$$.
o Hence, the possible units digit of $$M$$ can be $$2$$ or $$7$$.
• But to calculate the units digit of the expression, $$M^x$$, we need more information on the value of $$x$$.
Since we do not have that information,
Statement 1 alone is NOT sufficient to answer the question.
Hence, we can eliminate answer choices A and D.
Step 4: Analyse Statement 2:
$$X = 21$$.
It is also given that “x” is a positive integer.
$$21^{Any Positive integer}$$ will end with a $$1$$ because $$1^{ Any positive integer}$$ ends with a $$1$$.

Since we could figure out the units digit of $$M^x$$
Statement 2 alone is SUFFICIENT to answer the question.
Step 5: Combine both Statements:
This step is not required since we already arrived at an answer from statement 2.

Hi,

I have same concern above. If M =21 then does it give reminder 2 when dividing 5. Both statement should not contradict each other.
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Posts: 51073
Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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28 Feb 2018, 06:42
1
stne wrote:
EgmatQuantExpert wrote:

Question:

If $$M$$ and $$x$$ are positive integers greater than 1, what is the units digit of $$M^x$$?

(1) $$M$$ when divided by $$5$$ gives a remainder of $$2$$.
(2) $$M = 21$$

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

Doesn't statement 1 and statement 2 contradict each other !
if the value of M is 21 then divided by 5 it gives a remainder of 1 rather than 2.

Hope moderator will look into this .

Yes, the statements contradict each other. On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. The question should be revised.
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Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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26 Jul 2018, 00:45
1
EgmatQuantExpert Bunuel

Now the statements don't contradict each other but the answer is wrong in my opinion.
Instead of B, it should be D

1 statement:$$M$$ when divided by 5 gives a remainder of 1 --> The units digit of $$M$$ is 6 or 1, in both cases doesn't matter what's the power of $$M$$

Please clarify If I'm missing something
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Joined: 02 Sep 2009
Posts: 51073
Re: If M and x are positive integers greater than 1, what is the units dig  [#permalink]

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26 Jul 2018, 00:58
LevanKhukhunashvili wrote:
EgmatQuantExpert Bunuel

Now the statements don't contradict each other but the answer is wrong in my opinion.
Instead of B, it should be D

1 statement:$$M$$ when divided by 5 gives a remainder of 1 --> The units digit of $$M$$ is 6 or 1, in both cases doesn't matter what's the power of $$M$$

Please clarify If I'm missing something

There are two types of data sufficiency questions:

1. YES/NO DS Questions:

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

2. VALUE DS QUESTIONS:

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

This question is a VALUE question, so a statement to be sufficient it should give the single numerical value of the units digit. As you said, from (1) it could be 1 or 6, so (1) is not sufficient.

Hope it's clear.
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Re: If M and x are positive integers greater than 1, what is the units dig &nbs [#permalink] 26 Jul 2018, 00:58
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