Last visit was: 20 Jul 2024, 09:11 It is currently 20 Jul 2024, 09:11
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3711
Own Kudos [?]: 17343 [10]
Given Kudos: 165
Send PM
VP
VP
Joined: 07 Jan 2016
Posts: 1248
Own Kudos [?]: 466 [0]
Given Kudos: 126
Location: United States (MO)
GMAT 1: 710 Q49 V36
Send PM
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3711
Own Kudos [?]: 17343 [1]
Given Kudos: 165
Send PM
SVP
SVP
Joined: 27 May 2012
Posts: 1697
Own Kudos [?]: 1495 [0]
Given Kudos: 639
Send PM
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
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 .
SVP
SVP
Joined: 26 Mar 2013
Posts: 2456
Own Kudos [?]: 1369 [0]
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Send PM
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
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.
Correct Answer: Option B



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.
Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642518 [1]
Given Kudos: 86706
Send PM
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
1
Kudos
Expert Reply
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.
Senior Manager
Senior Manager
Joined: 13 Feb 2018
Posts: 377
Own Kudos [?]: 390 [1]
Given Kudos: 50
GMAT 1: 640 Q48 V28
Send PM
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
1
Kudos
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
Math Expert
Joined: 02 Sep 2009
Posts: 94430
Own Kudos [?]: 642518 [0]
Given Kudos: 86706
Send PM
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
Expert Reply
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.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: If M and x are positive integers greater than 1, what is the units dig [#permalink]
Moderator:
Math Expert
94430 posts