Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 18 Jul 2019, 23:02

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

Overview of GMAT Math Question Types and Patterns on the GMAT

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

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 27 Jan 2019, 18:31
[Math Revolution GMAT math practice question]

If y=|x-1|+|x+1|, then y=?

1) x>-1
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.

There are three ranges of values of x to consider.
If x > 1, then y = | x – 1 | + | x + 1 | = x – 1 + x + 1 = 2x and we don’t have a unique value of y.
If -1 ≤ x ≤ 1, then y = | x – 1 | + | x + 1 | = - ( x – 1 ) + x + 1 = 2 and we have a unique value of y.
If x < 1, then y = | x – 1 | + | x + 1 | = -( x – 1 ) – ( x + 1 ) = -2x and we don’t have a unique value of y.

Asking for the value of y is equivalent asking if -1 ≤ x ≤ 1.
Both conditions yield the inequality -1 < x < 1, when applied together. Therefore, both conditions are sufficient, when taken together.

In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 29 Jan 2019, 21:44
[Math Revolution GMAT math practice question]

m+n=?

1) (4^m)(2^n)=16
2) (2^{2m})(4^n)=64

=>

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.

Condition 2) is equivalent to m + n = 3 as shown below:
(2^{2m})(4^n)=64
=> (2^{2m})(2^{2n})=2^6
=> 2^{2m+2n}=2^6
=> 2m+2n = 6
=> m + n = 3
Condition 2) is sufficient.

Condition 1)
(4^m)(2^n)=16
=> (2^{2m})(2^n)=2^4
=> 2^{2m+n}=2^4
=> 2m+n = 4
If m = 1 and n =2, then m + n = 3.
If m = 0 and n = 4, then m + n = 4.
Since it does not yield a unique solution, condition 1) is not sufficient.

Therefore, the answer is B.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 31 Jan 2019, 17:31
[Math Revolution GMAT math practice question]

What is the measure of each interior angle of a regular decagon?

A. 72°
B. 108°
C. 120°
D. 135°
E. 144°

=>

The sum of all interior angles of n-gon is (n-2)*180°.
A decagon is a 10-gon.
The sum of all interior angles is (10-2)* 180° = 8*180°.
And each interior angle of a regular decagon has measure 8*180° / 10 = 8*18° = 144°.

Therefore, the answer is E.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 04 Feb 2019, 21:14
[GMAT math practice question]

If operation # represents one of addition, subtraction, multiplication, and division, what is the value of 0#1?

1) 2#1 = 2
2) 4#2 = 2

=>

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 operation is considered as a variable. Since we have 1 variable and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
Since 2#1 = 2, # is one of the operations, multiplication and division.
If # is the multiplication operation, then 0#1 = 0.
If # is the division operation, then 0#1 = 0.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since 4#2 = 2, # is one of the operations, subtraction and division.
If # is the subtraction operation, then 0#1 = -1.
If # is the division operation, then 0#1 = 0.
Since condition 2) doesn’t yield a unique solution, it 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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 07 Feb 2019, 18:30
[GMAT math practice question]

What is the value of (2^8 + 2^9 + 2^{10} + 2^{11}) / 32?

A. 80
B. 96
C. 100
D. 120
E. 160

=>

(2^8 + 2^9 + 2^{10} + 2^{11}) / 32
= (2^8 + 2^82^1 + 2^82^2 + 2^82^3) / 2^5
= 2^8(1 + 2^1 + 2^2 + 2^3) / 2^5
= 2^3(1+2+4+8)
= 8*15
= 120

Therefore, the answer is D.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 10 Feb 2019, 18:19
[GMAT math practice question]

If a>b>c>d>0, is d<4?

1) 1/c + 1/d > 1/2
2) (1/a)+(1/b)+(1/c)+(1/d)=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 original condition a>b>c>d>0 is equivalent to 0 < 1/a < 1/b < 1/c < 1/d. The question asks if d < 4. This is equivalent to asking if 1/d > 1/4.

By condition 1, 1/d > 1/4 since 1/c < 1/d. So, d < 4. Condition 1) is sufficient.

Condition 2)
Since 0 < 1/a < 1/b < 1/c < 1/d and (1/a)+(1/b)+(1/c)+(1/d)=1, we have 1/a<1/d, 1/b<1/d, 1/c<1/d and 1/a +1/b + 1/c + 1/d < 1/d +1/d +1/d + 1/d = 4/d. Therefore, 1 < 4/d and d < 4.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

Note: This question is a CMT4(B) question: condition 1) is easy to work with and condition 2) is hard. For CMT4(B) questions, D is most likely to be the answer.
_________________
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 13 Feb 2019, 18:23
[GMAT math practice question]

What is the number of the x-intercepts of y=x^4-3x^3+2x^2?

A. one
B. two
C. three
D. four
E. five

=>

y = x^4-3x^3+2x^2
=> y = x^2(x^2-3x+2)
=> y = x^2(x-1)(z-2)
The x-intercepts occur when y = 0. This occurs when x = 0, x = 1 and x = 2.
There are three x-intercepts.

Therefore, the answer is C.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 14 Feb 2019, 18:30
[GMAT math practice question]

We define the harmonic mean of a set of numbers as the reciprocal of the average (arithmetic mean) of the reciprocals of the numbers. What is the harmonic mean of 20 and 30?

A. 22
B. 24
C. 25
D. 26
E. 28

=>

1 / { ( 1/20 + 1/30 ) / 2 } = 1 / { ( 3/60 + 2/60 ) / 2 } = 1 / { (5/60) / 2 } = 1 / { 5 / 120 } = 120 / 5 = 24.

Therefore, the answer is B.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 17 Feb 2019, 18:42
[GMAT math practice question]

Is 3(a-b)>0?

1) a^3>b^3
2) a>b

=>

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 if 3(a-b)>0 is equivalent to asking if a – b > 0, or, equivalently, if a > b.
Thus, condition 2) is sufficient.

Condition 1)
a^3>b^3
=> a^3-b^3 > 0
=> (a-b)(a^2+ab+b^2) > 0
=> a - b > 0 since a^2+ab+b^2 > 0
=> a > b
Thus, condition 1) is sufficient too.

Therefore, D is the answer.
Answer: D

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.

_________________
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 18 Feb 2019, 18:37
[GMAT math practice question]

Is |a|<1?

1) a^2<1
2) 1/(1-a^2)>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.

|a|<1
=> |a|^2 < 1
=> a^2 < 1
=> a^2-1 < 0
=> (a+1)(a-1) < 0
=> -1 < a < 1

Condition 1) is sufficient, since it is equivalent to the question.

Condition 2)
1/(1-a^2) > 0
=> (1-a^2) > 0
=> a^2-1 < 0
=> (a+1)(a-1) < 0
=> -1 < a < 1
Thus, condition 2) is sufficient, since it is also equivalent to the question.

Therefore, the answer is D.
Answer: D

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.
_________________
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 20 Feb 2019, 18:28
[GMAT math practice question]

Which of the following expressions is equal to 2^{32}-2^{31}-2^{30}?

A. 3*2^{29}
B. 5*2^{29}
C. 2^{30}
D. 3*2^{30}
E. 2^{31}

=>

2^{32}-2^{31}-2^{30}?
= (2^2)(2^{30})- (2^1)(2^{30})-2^{30}
= 4(2^{30})- 2(2^{30})-2^{30}
= (4-2-1)(2^{30})
=1(2^{30})=2^{30}

Therefore, the answer is C.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 24 Feb 2019, 18:29
If the median of 5 positive integers is 10, is their average (arithmetic mean) greater than 10?

1) The largest number is 40
2) The smallest number is 1

Answer: A

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.

Suppose the numbers satisfy a ≤ b ≤ 10 ≤ c ≤ d. The question asks if ( a + b + 10 + c + d ) / 5 > 10 or a + b + c + d + 10 > 50.
This is equivalent to the inequality, a + b + c + d > 40.
If a question includes the words “greater than”, then it asks us to look for a minimum.
Since a, b c, and d are positive, and d = 40 by condition 1), we must have a + b + c + d > 40.
Condition 1) is sufficient.

Condition 2)
If a = 1, b = 2, c = 11, and d = 40, then a + b + c + d > 40, and the answer is ‘yes’.
If a = 1, b = 2, c = 11, and d = 12, then a + b + c + d < 40, and the answer is ‘no’.
Thus, condition 2) is not sufficient since it does not yield a unique solution.

Therefore, A is the answer.
_________________
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 26 Feb 2019, 00:19
f(x)=x^2n+x^n+1, where n is an integer. Is f(x)=1?

1) x=-1
2) n is a multiple of 5.

Answer: E

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.
f(x)=1
⇔ x^2n+x^n+1=1
⇔ x^2n+x^n=0
⇔ x^n(x^n +1)=0
⇔ xn= 0 or xn =-1
⇔ ( x = 0 ) or ( x = -1 and n is odd )

Conditions 1) and 2)
If x = -1 and n = 5, then f(x) = (-1)10 + (-1)5 + 1 = 1 + (-1) + 1 = 1 and the answer is ‘yes’.
If x = -1 and n = 10, then f(x) = (-1)20 + (-1)10 + 1 = 1 + 1 + 1 = 1 and the answer is ‘no’.

Thus, both conditions together are not sufficient, since they do not yield a unique solution.

Therefore, E is the answer.
_________________
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 27 Feb 2019, 05:09
The squares of two consecutive positive integers differ by 55. What is the smaller of the two integers?

A. 27
B. 29
C. 30
D. 32
E. 35


Answer: A

Let the two consecutive positive integers be n and n+1.
Then (n+1)^2 – n^2 = 55, so 2n+1 = 55.
It follows that 2n = 54 and n = 27.

Therefore, the answer is 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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 28 Feb 2019, 21:49
[GMAT math practice question]

What is the greatest positive three-digit number that is divisible by 2, 3, 4, 5, 6 and 7?

A. 120
B. 140
C. 210
D. 420
E. 840

=>

The question asks for the value of the greatest positive three-digit multiple of lcm(2,3,4,5,6,7), where lcm(2,3,4,5,6,7) is the least common multiple of 2, 3, 4, 5, 6 and 7.
lcm(2,3,4,5,6,7) = 22*3*5*7 = 420.
There are two positive three-digit integers that are multiples of 420: 420 and 840.
The greatest positive three-digit number that is a multiple of 420 is 840.

Therefore, the answer is E.
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 03 Mar 2019, 18:37
[GMAT math practice question]

If n is an integer, is (n+1)(n+2)(n+3) divisible by 12?

1) n is an even number.
2) n is a multiple of 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.

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

Since n+1, n+2 and n+3 are three consecutive integers, (n+1)(n+2)(n+3) is a multiple of 3.

Condition 2) tells us that n+1 and n+3 are odd integers, and n+2 is an even number which is not a multiple of 4. Thus, (n+1)(n+2)(n+3) is not a multiple of 4.
CMT(Common Mistake Type 1) states “no” is also an answer and a condition giving rise to the unique answer “no” is sufficient. Thus, condition 2) is sufficient.

Condition 1)
If n = 2, then (n+1)(n+2)(n+3) = 3*4*5 = 60 is a multiple of 12 and the answer is “yes”.
If n = 4, then (n+1)(n+2)(n+3) = 5*6*7 = 210 is not a multiple of 12 and the answer is “no”.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 06 Mar 2019, 18:27
[GMAT math practice question]

A is the set of 6-digit positive integers whose first three digits are same as their last three digits, written in the same order. Which of the following numbers must be a factor of every number in the set A?

A. 7
B. 11
C. 17
D. 19
E. 23

=>

Each number n in the set A is an integer of the form “xyz,xyz”. So,
n = 10^5x + 10^4y + 10^3z + 10^2x + 10y + z
= 10^3(10^2x + 10y + z) + (10^2x + 10y + z )
= 1000(10^2x + 10y + z) + (10^2x + 10y + z )
= 1001(10^2x + 10y + z )
= 11*91(10^2x + 10y + z )

Thus, n is a multiple of 11.

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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 10 Mar 2019, 18:25
[GMAT math practice question]

Is a triangle, with one side of length 12, inscribed in a circle a right triangle?

1) The area of the circle is 36π.
2) The circumference of the circle is 12π.

=>

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.

Attachment:
3.8.png
3.8.png [ 7.42 KiB | Viewed 285 times ]


If a side of a triangle is the diameter of its circumscribed circle, then the triangle is a right triangle.

Condition 1)
A circle with area 36π has radius 6 and diameter 12. So, the answer is ‘yes’ and condition 1) is sufficient.

Condition 2)
A circle with circumference 12π has diameter 12. So, the answer is ‘yes’ and condition 2) is sufficient.


Therefore, D is the answer.
Answer: D

Note that if conditions 1) and 2) yield the same information, Tip 1 of the VA method tells us that D is most likely to be the answer.
_________________
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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 13 Mar 2019, 18:27
[GMAT math practice question]

If x and y are positive integers and (x-y)^2+y^2=25, which of the following could be the value of x?

A. 6
B. 7
C. 8
D. 9
E. 10

=>

The possible values of the pair (x-y,y), with x and y positive, are (0,5), (3,4), (-3,4), (4,3) and (-4,3).
So, (x,y) = (5,5), (7,4), (1,4), (7,3) or (-1,3).
Thus, x could be 5, 7 or 1.

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 $79 for 1 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: 7605
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

Show Tags

New post 17 Mar 2019, 18:23
[GMAT math practice question]

If x and y are positive integers, x/y=?

1) 2^{x+y}3^{xy}=72
2) 2^x3^y=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.

Condition 2) tells us that 2^x3^y=12 = 2^23^1 and x = 2, y = 1.
Thus x/y = 2/1 = 2, and condition 2) is sufficient.

Condition 1)
2^{x+y}3^{xy}=72 = 2^33^2 yields the equations x+y=3 and xy=2.
So, x = 1 and y = 2, or x =2 and y = 1.
Thus, x/y = 1/2 or x/y = 2/1 = 2.
Condition 1) is not sufficient since it does not yield a unique solution.

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 $79 for 1 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: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 17 Mar 2019, 18:23

Go to page   Previous    1  ...  11   12   13   14   15   16   17   18   19   20   21   22    Next  [ 434 posts ] 

Display posts from previous: Sort by

Overview of GMAT Math Question Types and Patterns on the GMAT

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





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