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

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.
Correct Answer: Option B
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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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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.

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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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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