GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Dec 2018, 00:52

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
  • GMATbuster's Weekly GMAT Quant Quiz, Tomorrow, Saturday at 9 AM PST

     December 14, 2018

     December 14, 2018

     09:00 AM PST

     10:00 AM PST

    10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.

Math Revolution DS Expert - Ask Me Anything about GMAT DS

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 03 Oct 2018, 17:30
Ask me Anything about GMAT Data Sufficiency


Hello, I am Max Lee, Founder and Lead Math Tutor at Math Revolution.

I have over 6,000 posts and almost 5,000 Kudos. This topic is a new feature on the DS Forum and a way for you to directly interact with me and ask anything about the DS, e.g. if you want a certain concept explained or have a particular you question you want me addressed, this is the place to post a link to it or your question. I intend to have this thread be as a "Everything You Need to Know about DS" type of thread. I will keep updating this post with links and resources that are helpful for the DS. Meanwhile, you can ask me anything ;-)


My other discussions you may be interested in:



Thank you all - good luck on the GMAT and look forward to seeing you in the DS forum!
- Max Lee.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post Updated on: 15 Oct 2018, 23:29
[Math Revolution GMAT math practice question]

(absolute value) If \(|x+1|=2|x-1|, x=?\)

\(1) x<1\)
\(2) x>0\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"


Originally posted by MathRevolution on 15 Oct 2018, 00:40.
Last edited by MathRevolution on 15 Oct 2018, 23:29, edited 1 time in total.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 15 Oct 2018, 23:29
1
[Math Revolution GMAT math practice question]

Is the sum of \(7\) different positive integers greater than or equal to \(48\)?

1) Their median is \(9\)
2) The largest number is \(12\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 16 Oct 2018, 23:35
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(absolute value) If \(|x+1|=2|x-1|, x=?\)

\(1) x<1\)
\(2) x>0\)


=>

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 original condition \(|x+1|=2|x-1|\) is equivalent to \(x=\frac{1}{3}\) or \(x=3\) as shown below:

\(|x+1|=2|x-1|\)
\(=> |x+1|^2=(2|x-1|)^2\)
\(=> (x+1)^2=4(x-1)^2\)
\(=> x^2+2x+1=4(x^2-2x+1)\)
\(=> x^2+2x+1=4x^2-8x+4\)
\(=> 3x^2-10x+3 = 0\)
\(=> (3x-1)(x-3) = 0\)
\(=> 3x-1=0\) or \(x-3 = 0\)
\(=> x=\frac{1}{3}\) or \(x=3\)

Thus, condition 1) is sufficient since it gives a unique solution.

Condition 2) is not sufficient, since it allows both possible solutions.

Therefore, A is the answer.
Answer: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 16 Oct 2018, 23:37
[Math Revolution GMAT math practice question]

(set) If \(|X|\) is the number of elements in set \(X\), and \(“∪”\) is the union and \(“∩”\) is the intersection of \(2\) sets, what is the value of \(|A∩B|\)?

\(1) |A∪B|=50\)
\(2) |B|=40\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 18 Oct 2018, 00:10
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is the sum of \(7\) different positive integers greater than or equal to \(48\)?

1) Their median is \(9\)
2) The largest number is \(12\)


=>

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 many variables (x1, x2, …, x7) 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)
We write the numbers as x1≤x2≤x3≤x4≤x5≤x6≤x7. Then x4 is their median.
From condition 1), x4 = 9 and the smallest possible number is 1 + 2 + 3 + 9 + 10 + 11 + 12 = 48. Therefore, the answer is ‘yes’.
Both conditions 1) & 2) together are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
Since we didn’t use condition 2) in the above argument, condition 1) is sufficient on its own.

By condition 1), x4 = 9 and the smallest possible number is 1 + 2 + 3 + 9 + 10 + 11 + 12 = 48. Therefore, the answer is ‘yes’.


Condition 2)
When the numbers are 6,7,8,9,10,11,12, their sum is 6 + 7 + 8 + 9 + 10 + 11 + 12 = 63 > 48, and the answer is ‘yes’.
When the numbers are 6,7,8,9,10,11,12, their sum is 1 + 2 + 3 + 4 + 5 + 6 + 12 = 33 < 48, and the answer is ‘no’.
Since we don’t obtain a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 18 Oct 2018, 00:11
[Math Revolution GMAT math practice question]

(number property) If \(a\) and \(b\) are positive integers such that when \(a\) is divided by \(b\), the remainder is \(10\), what is the value of \(b\)?

\(1) b>10\)
\(2) b<12\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 19 Oct 2018, 00:03
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(set) If \(|X|\) is the number of elements in set \(X\), and \(“∪”\) is the union and \(“∩”\) is the intersection of \(2\) sets, what is the value of \(|A∩B|\)?

\(1) |A∪B|=50\)
\(2) |B|=40\)


=>

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.
Note that
\(|A∪B| = |A| + |B| - |A∩B|\) and \(|A∩B| = |A| + |B| - |A∪B|\).

Since we have \(4\) variables\((|A∩B|, |A|, |B|, |A∪B|)\) and \(1\) equation \((|A∩B| = |A| + |B| - |A∪B|)\), 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)
Suppose \(A\) and \(B\) are disjoint sets, \(|A∪B| = 50, |A| = 10,\) and \(|B| = 40.\) Then \(|A∩B| = |A| + |B| - |A∪B| = 0.\)
Suppose \(A\) contains \(B, |A∪B| = 50, |A| = 50,\) and \(|B| = 40.\) Then \(|A∩B| = |A| + |B| - |A∪B| = 40.\)
Since we don’t have a unique solution, both conditions together are not sufficient.


Therefore, E is the answer.
Answer: E
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 19 Oct 2018, 00:04
[Math Revolution GMAT math practice question]

(inequality) Is \(1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}\)?

\(1) x>0\)
\(2) x<1\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 21 Oct 2018, 17:51
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(number property) If \(a\) and \(b\) are positive integers such that when \(a\) is divided by \(b\), the remainder is \(10\), what is the value of \(b\)?

\(1) b>10\)
\(2) b<12\)


=>

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.

By the quotient-remainder theorem, we can write \(a = b * q + 10\), where the remainder \(10\) is less than \(b\), that is, \(b > 10\).

Thus, condition 2) \(“b<12”\) is sufficient since it gives the unique solution \(b = 11\).

Note: Condition 1) does not give a unique solution. For example, we might have \(b = 11\) or \(b = 12\). Thus, it is not sufficient.

Therefore, B is the answer.
Answer: B
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 21 Oct 2018, 17:53
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(inequality) Is \(1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}\)?

\(1) x>0\)
\(2) x<1\)


=>

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 \(1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}\) is equivalent to \(0 < x < 1\) as shown below:

For \(x ≠1\),
=>\(1+x+x^2+x^3+x^4+x^5+x^6<\frac{1}{(1-x)}\)
\(=> (1+x+x^2+x^3+x^4+x^5+x^6)(1-x)^2< (1-x)\)
\(=> (1 - x^7)(1 - x) < 1 – x\)
\(=> 1 - x^7 – x +x^8 < 1 - x\)
\(=> - x^7 + x^8 < 0\)
\(=> x^7( x – 1 ) < 0\)
\(=> x( x – 1 ) < 0\)
\(=> 0 < x < 1\)

Since both conditions must be applied together to obtain this inequality, both conditions 1) & 2) are sufficient, when applied together.

Therefore, C is the answer.
Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 22 Oct 2018, 00:30
[Math Revolution GMAT math practice question]

(inequality) Is \(x^3-y^>x^2+xy+y^2\)?

\(1) x > y + 1\)
\(2) 0 < y < x\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 22 Oct 2018, 23:44
[Math Revolution GMAT math practice question]

(function) In the xy-plane, does the graph of \(y=ax^2+c\) intersect the x-axis?

\(1) a>0\)
\(2) c>0\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 24 Oct 2018, 00:16
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(inequality) Is \(x^3-y^>x^2+xy+y^2\)?

\(1) x > y + 1\)
\(2) 0 < y < x\)


=>

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 original condition \(x^3-y^3>x^2+xy+y^2\) is equivalent to \(x > y + 1\) as shown below:
\(x^3-y^3 > x^2+xy+y^2\)
\(=> (x-y)(x^2+xy+y^2)>x^2+xy+y^2\)
\(=> x – y > 1\) after dividing both sides by \(x^2+xy+y^2\), since \(x^2+xy+y^2 > 0.\)

Since the final inequality is equivalent to \(x > y + 1\), condition 1) is sufficient.

Condition 2)
If \(x = 3\) and \(y = 1\), then \(x – y = 2 > 1\), and the answer is ‘yes’.
If \(x = 1\) and \(y = \frac{1}{2},\) then \(x – y = \frac{1}{2} < 1,\) and the answer is ‘no’.
Since it doesn’t give a unique answer, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 24 Oct 2018, 00:17
[Math Revolution GMAT math practice question]

(algebra) For integers \(m\) and \(n\), the operation \(△\) is defined by \(m△n = (m-1)^2 + (n+1)^2\). What is the value of the integer \(x\)?

\(1) x△1 = 4\)
\(2) 1△x = 4\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 25 Oct 2018, 00:20
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(function) In the xy-plane, does the graph of \(y=ax^2+c\) intersect the x-axis?

\(1) a>0\)
\(2) c>0\)


=>

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 “does the graph of \(y=ax^2+c\) intersect the x-axis” is equivalent to asking “does the equation \(ax^2+c = 0\) have a root”.
Note that the statement “\(ax^2 + bx + c = 0\) has a root” is equivalent to \(b^2-4ac ≥ 0.\)
Thus, the question asks if \(-4ac ≥ 0,\) or \(ac ≤ 0\), since \(b = 0\) in this problem.

When we consider both conditions together, we obtain \(ac > 0\) and the answer is “no”, since \(a > 0\) and \(c > 0.\)
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions together are sufficient.

Note: Neither condition on its own provides enough information for us to determine whether \(ac ≤ 0.\)

Therefore, C is the answer.
Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 25 Oct 2018, 00:20
[Math Revolution GMAT math practice question]

(statistics) If the average (arithmetic mean) of \(5\) numbers is \(20\), what is their standard deviation?

1) Their minimum is \(20\).
2) Their maximum is \(20\).
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 25 Oct 2018, 23:52
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(algebra) For integers \(m\) and \(n\), the operation \(△\) is defined by \(m△n = (m-1)^2 + (n+1)^2\). What is the value of the integer \(x\)?

\(1) x△1 = 4\)
\(2) 1△x = 4\)


=>

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 (\(x\)) 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)
\(x△1 = (x-1)^2 + (1+1)^2 = (x-1)^2 + 2^2 = 4.\)
Thus, \((x-1)^2 = 0\) and \(x = 1.\)
Since we have a unique solution, condition 1) is sufficient.

Condition 2)
\(1△x = (1-1)^2 + (x+1)^2 = (x+1)^2 = 4.\)
So, \(x+1 = ±2\) or \(x = -1 ± 2.\)
Thus, \(x = -3\) or \(x = 1\).
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 25 Oct 2018, 23:53
[Math Revolution GMAT math practice question]

(number property) \(n\) is an integer. Is \(n(n+2)\) a multiple of \(8\)?

1) \(n\) is an even integer
2) \(n\) is a multiple of \(4\)
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS  [#permalink]

Show Tags

New post 28 Oct 2018, 18:16
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

(statistics) If the average (arithmetic mean) of \(5\) numbers is \(20\), what is their standard deviation?

1) Their minimum is \(20\).
2) Their maximum is \(20\).


=>

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.

Note that if the average and the maximum of a data set are the same, then all of the data values are the same and the standard deviation is 0. Similarly, if the average and the minimum of a data set are the same, all of the data values are the same and the standard deviation is 0.

Thus, each of conditions is sufficient on its own since the minimum and the maximum are the same as the average.

Therefore, D is the answer.
Answer: D
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: Math Revolution DS Expert - Ask Me Anything about GMAT DS &nbs [#permalink] 28 Oct 2018, 18:16

Go to page    1   2   3   4   5   6    Next  [ 106 posts ] 

Display posts from previous: Sort by

Math Revolution DS Expert - Ask Me Anything about GMAT DS

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.