Last visit was: 19 Nov 2025, 12:44 It is currently 19 Nov 2025, 12:44
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
User avatar
ShankSouljaBoi
User avatar
Joined: 21 Jun 2017
Last visit: 17 Apr 2024
Posts: 622
Own Kudos:
603
Given Kudos: 4,090
Location: India
Concentration: Finance, Economics
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 1: 660 Q49 V31
GMAT 2: 620 Q47 V30
GMAT 3: 650 Q48 V31
GPA: 3.1
WE:Corporate Finance (Non-Profit and Government)
Products:
My Reviews
Schools: Rotman '23 (D) IIMA PGPX'22 (D) Desautels '23 (D) Schulich Sept '23 (D) WBS (D) IIML IPMX'25 (A)
GMAT 3: 650 Q48 V31
Posts: 622
Kudos: 603
Math Revolution DS Expert - Ask Me Anything about GMAT DS 23 Dec 2018, 11:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
MathRevolution
[Math Revolution GMAT math practice question]

(number property) If \(n\) is an integer greater than \(1\), what is the value of \(n\)?

1) \(n\) is a prime number
2) \(\frac{(n+2)}{n}\) is an integer

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If \(n = 1\), then \(\frac{(n+2)}{n} = 3\) is an integer.
If \(n = 2,\) then \(\frac{(n+2)}{n} = 2\) is an integer.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If \(n = 2\), then \(\frac{(n+2)}{n} = 2\) is an integer.
If \(n = 3\), then \(\frac{(n+2)}{n} = \frac{5}{2}\) is not integer.
If \(n\) is a prime number bigger than \(2\), \(\frac{(n+2)}{n}\) is not an integer.
Thus \(n = 2\) is the unique solution and both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
Show more
Please check the OA, Highlighted text is wrong. Stem alreay mention n as > 1.

Regards
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 23 Dec 2018, 19:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(absolute value) Is \(|m-n|=|m|-|n|\) ?

\(1) m-n = 0\)
\(2) n = 0\)
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Squaring both sides of \(|m – n| = |m| - |n|\) yields
\(|m-n|^2=(|m|-|n|)^2\)
\(=> (m-n)^2=(|m|-|n|)^2\)
\(=> m^2+n^2-2mn=|m|^2+|n|^2-2|mn|\)
\(=> m^2+n^2-2mn=m^2+n^2-2|mn|\)
\(=> -2mn=-2|mn|\)
\(=> mn=|mn|\)
\(=> mn ≥ 0\)

Condition 1):
\(m – n = 0\) implies that \(m = n.\) So \(mn = n^2 ≥ 0\) for all values of \(n\).
Condition 1) is sufficient.

Condition 2):
If \(n = 0\), then \(0 = mn ≥ 0.\)
Condition 2) is sufficient.
Therefore, the correct answer is D.
Answer: D
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 23 Dec 2018, 19:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(integer) \(n\) is a positive integer. Is \(\frac{n(n+1)(n+2)}{4}\) an even integer?

1) \(n\) is an even integer
2) \(1238 ≤ n ≤ 1240\)
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Asking for \(\frac{n(n+1)(n+2)}{4}\) to be an even integer is equivalent to asking for \(n(n+1)(n+2)\) to be a multiple of \(8\). If \(n\) is an even integer, \(n\) and \(n+2\) are consecutive even integers and a product of two consecutive even integers is a multiple of \(8\). Thus, condition 1) is sufficient.

Condition 2)
If \(n = 1238, n(n+1)(n+2)=1238*1239*1240\) is a multiple of \(8\) since \(1240\) is a multiple of \(8\).
If \(n = 1239, n(n+1)(n+2)=1239*1240*1241\) is a multiple of \(8\) since \(1240\) is a multiple of \(8\).
If \(n = 1240, n(n+1)(n+2)=1240*1241*1242\) is a multiple of \(8\) since \(1240\) is a multiple of \(8\).
Thus, condition 2) is sufficient.

Therefore, the answer is D.
Answer: D

Note: This question is a CMT4(B) question. Condition 1) is easy to understand and condition 2) is hard. When one condition is easy to understand, and the other is hard, D is most likely to be the answer.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 24 Dec 2018, 01:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[Math Revolution GMAT math practice question]

(number property) \(f(x)\) is the greatest prime factor of \(x\). If \(n\) is a positive integer less than \(10\), what is the value of \(n\)?

\(1) f(n) = f(1000)\)
\(2) f(n) = 5\)
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 24 Dec 2018, 11:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShankSouljaBoi
MathRevolution
MathRevolution
[Math Revolution GMAT math practice question]

(number property) If \(n\) is an integer greater than \(1\), what is the value of \(n\)?

1) \(n\) is a prime number
2) \(\frac{(n+2)}{n}\) is an integer

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since there are many prime numbers, condition 1) is not sufficient.

Condition 2)
If \(n = 1\), then \(\frac{(n+2)}{n} = 3\) is an integer.
If \(n = 2,\) then \(\frac{(n+2)}{n} = 2\) is an integer.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If \(n = 2\), then \(\frac{(n+2)}{n} = 2\) is an integer.
If \(n = 3\), then \(\frac{(n+2)}{n} = \frac{5}{2}\) is not integer.
If \(n\) is a prime number bigger than \(2\), \(\frac{(n+2)}{n}\) is not an integer.
Thus \(n = 2\) is the unique solution and both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
Please check the OA, Highlighted text is wrong. Stem alreay mention n as > 1.

Regards
Show more

You are right.
The question should be changed to the followings.

If \(n\) is a positive integer, what is the value of \(n\)?

Thank you for your comments.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
 [1]
Math Revolution DS Expert - Ask Me Anything about GMAT DS 25 Dec 2018, 02:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[Math Revolution GMAT math practice question]

(number properties) If \(n\) is a positive integer, is \(\sqrt{n+1}\) an even integer?

1) \(n\) is the product of \(2\) consecutive odd numbers
2) \(n\) is an odd number
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 01:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number property) \(f(x)\) is the greatest prime factor of \(x\). If \(n\) is a positive integer less than \(10\), what is the value of \(n\)?

\(1) f(n) = f(1000)\)
\(2) f(n) = 5\)
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have \(1\) variable (\(n\)) and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since \(1000 = 2^3*5^3, f(1000) = 5.\)
So, \(f(n) = 5\) and \(n = 5.\)
Thus, condition 1) is sufficient, since it gives a unique solution.

Condition 2)
Condition 2) is the same as condition 1).
Thus, condition 2) is also sufficient.

FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, D is the answer.
Answer: D

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 01:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number?

1) \(\frac{m}{n}\) is an even number
2) \(m\) or \(n\) is an even number
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 19 Nov 2025
Posts: 8,422
Own Kudos:
4,982
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,422
Kudos: 4,982
 [1]
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 02:30
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number?

1) \(\frac{m}{n}\) is an even number
2) \(m\) or \(n\) is an even number
Show more


#1:
m/n = even no
m=6, n= 3 m/n= 2 ; m+n= 6+3= 9 sufficient

m=4, n=2 ; m/n= 2 ; m+n=4+2 = 6 not sufficient

#1 not sufficient

#2 :
m or n is an even no

property of odd no in addition : even+ odd = odd no
so since m & n are + integers so either of m or n being even other has to be odd integer hence we would get m+n= odd only

sufficient

IMO B
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
1,801
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,801
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 07:19
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number?

1) \(\frac{m}{n}\) is an even number
2) \(m\) or \(n\) is an even number
Show more
\(m,n\,\,\, \geqslant 1\,\,\,{\text{ints}}\,\,\,\,\left( * \right)\)

\(m + n\,\,\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\boxed{\,\,\,?\,\,\,:\,\,\,\left( {m\,\,{\text{odd}}\,,\,\,n\,\,{\text{even}}} \right)\,\,\,{\text{or}}\,\,\,{\text{vice - versa}\,\,}\,\,}\)


\(\left( 1 \right)\,\,\,\frac{m}{n} = {\text{even}}\,\,\,\,\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\\\
\,{\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,\,m\,\,{\text{even}}\,\,\,{\text{or}}\,\,\,n\,\,{\text{even}}\,\,\,\,\left\{ \begin{gathered}\\
\,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\\\
\,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\text{E}} \right)\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S.: "A or B" means "only A", "only B" or BOTH.
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
1,801
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,801
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 07:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(n\) is a positive integer, is \(\sqrt{n+1}\) an even integer?

1) \(n\) is the product of \(2\) consecutive odd numbers
2) \(n\) is an odd number
Show more
Beautiful problem, Max. Congrats (and kudos)!

\(n \geqslant 1\,\,\,\operatorname{int}\)

\(\sqrt {n + 1} \,\,\,\mathop = \limits^? \,\,{\text{even}}\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\boxed{\,\,n + 1\,\,\,\mathop = \limits^? \,\,\,{{\left( {{\text{even}}} \right)}^2}\,\,}\)


\(\left( 1 \right)\,\,\,n = \left( {2M - 1} \right)\left( {2M + 1} \right) = {\left( {2M} \right)^2} - {\left( 1 \right)^2}\,\,\,\,\,\left[ {M\,\,\operatorname{int} \,} \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,n + 1 = {\left( {2M} \right)^2}\,\,\,,\,\,\,\,M\,\,\operatorname{int} \,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\)

\(\left( 2 \right)\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,n = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \\
\,{\rm{Take}}\,\,n = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\,\,\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 19 Nov 2025
Posts: 8,422
Own Kudos:
4,982
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,422
Kudos: 4,982
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 08:21
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fskilnik
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number?

1) \(\frac{m}{n}\) is an even number
2) \(m\) or \(n\) is an even number
\(m,n\,\,\, \geqslant 1\,\,\,{\text{ints}}\,\,\,\,\left( * \right)\)

\(m + n\,\,\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\boxed{\,\,\,?\,\,\,:\,\,\,\left( {m\,\,{\text{odd}}\,,\,\,n\,\,{\text{even}}} \right)\,\,\,{\text{or}}\,\,\,{\text{vice - versa}\,\,}\,\,}\)


\(\left( 1 \right)\,\,\,\frac{m}{n} = {\text{even}}\,\,\,\,\left\{ \begin{gathered}\\
\,{\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\\\
\,{\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \\
\end{gathered} \right.\)

\(\left( 2 \right)\,\,\,m\,\,{\text{even}}\,\,\,{\text{or}}\,\,\,n\,\,{\text{even}}\,\,\,\,\left\{ \begin{gathered}\\
\,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\\\
\,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\text{E}} \right)\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

P.S.: "A or B" means "only A", "only B" or BOTH.
Show more


fskilnik

#2 says m or n even ; why have you taken both as even while proving statement as insufficient?
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
1,801
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,801
Math Revolution DS Expert - Ask Me Anything about GMAT DS 26 Dec 2018, 09:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Archit3110

#2 says m or n even ; why have you taken both as even while proving statement as insufficient?
Show more
Hi Archit3110 ,

Thank you for your interest in my solution.

As I explained in my post scriptum (PS), the word "OR" has not the everyday common use of "exclusive or".

In other words, when it is given that "m is even or n is even", there are three possibilities available:

(i) m is even and n is not even
(ii) m is not even and n is even
(iii) m is even and n is also even

Regards and success in your studies,
Fabio.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 27 Dec 2018, 02:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(n\) is a positive integer, is \(\sqrt{n+1}\) an even integer?

1) \(n\) is the product of \(2\) consecutive odd numbers
2) \(n\) is an odd number
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The question is equivalent to asking if \(\sqrt{n+1} = 2k\) for some positive integer \(k\).
\(\sqrt{n+1} = 2k\)
\(=> n+1 = 4k^2\)
\(=> n = 4k^2-1\)
\(=> n = (2k-1)(2k+1)\)
\(n\) is a product of two consecutive odd integers.
Thus, condition 1) is sufficient.

Condition 2)
If \(n = 3\), then \(\sqrt{3+1} = \sqrt{4}=2\) and the answer is ‘yes’.
If \(n = 1\), then \(\sqrt{1+1} = 2\) is not an integer and the answer is ‘no’.
Condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 27 Dec 2018, 02:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(3^{4m+2}+n\) divisible by \(5\)?

\(1) m=3\)
\(2) n=1\)
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 25 Jul 2021, 03:02
Originally posted by MathRevolution on 28 Dec 2018, 03:17.
Last edited by MathRevolution on 25 Jul 2021, 03:02, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number?

1) \(\frac{m}{n}\) is an even number
2) \(m\) or \(n\) is an even number
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have \(2\) variables (\(m\) and \(n\)) and \(0\) equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since \(\frac{m}{n}\) is even, \(\frac{m}{n} = 2k\) and \(m = (2k)n\) for some positive integer \(k\).
If \(m = 2\) and \(n = 1\), then \(m + n = 3\), is an odd integer and the answer is ‘yes’.
If \(m = 4\) and \(n = 2\), then \(m + n = 6\) is an even integer and the answer is ‘no’.
Since we do not obtain a unique answer, conditions 1) & 2) are not sufficient when considered together.

Therefore, E is the answer.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 28 Dec 2018, 03:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[Math Revolution GMAT math practice question]

(function) In the \(xy\)-coordinate plane, does \(y=a(x-h)^2+k\) intersect the \(x\)-axis?

\(1) h=1\)
\(2) k=2\)
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS Updated on: 25 Jul 2021, 03:03
Originally posted by MathRevolution on 30 Dec 2018, 18:28.
Last edited by MathRevolution on 25 Jul 2021, 03:03, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(number properties) If \(m\) and \(n\) are positive integers, is \(3^{4m+2}+n\) divisible by \(5\)?

\(1) m=3\)
\(2) n=1\)
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The units digits of \(3^k\) have period \(4\) as they form the cycle \(3 -> 9 -> 7 -> 1.\)
\(3^{4m+2}\) has \(9\) as its units digit if \(3^{4m+2}\) has units digit \(9\), regardless of the value of \(m\).
Thus, the divisibility of \(3^{4m+2}+n\) by \(5\) relies on the variable n only.

Therefore, the correct answer is B.
Answer: B
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 30 Dec 2018, 18:30
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[Math Revolution GMAT math practice question]

(function) In the \(xy\)-coordinate plane, does \(y=a(x-h)^2+k\) intersect the \(x\)-axis?

\(1) h=1\)
\(2) k=2\)
Show more

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have \(3\) variables (\(a, h\) and \(k\)) and \(0\) equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
If \(a = 1\), then the graph doesn’t intersect the \(x\)-axis shown as below.

Attachment:
1231.png
1231.png [ 5.04 KiB | Viewed 1588 times ]

If \(a = -1\), then the graph intersects the \(x\)-axis shown as below.

Attachment:
12311.png
12311.png [ 5.23 KiB | Viewed 1605 times ]

Since neither condition gives us information about the value of \(a\), conditions 1) & 2) are not sufficient, when considered together.

Therefore, the answer is E.
Answer: E

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,391
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,391
Math Revolution DS Expert - Ask Me Anything about GMAT DS 31 Dec 2018, 02:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[Math Revolution GMAT math practice question]

(absolute value) Is \(\sqrt{(x+1)^2}=x+1\) ?

\(1) x(x-2) = 0\)
\(2) x(x+2) = 0\)
   1  ...  5   6   7   8   9  ...  64   
Moderators:
Bunuel
Math Expert
105390 posts
GMATBusters
GMAT Tutor
1924 posts