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# Overview of GMAT Math Question Types and Patterns on the GMAT

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6375
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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20 Jul 2017, 18:43
When n is divided by 4, what is the remainder?

1) When n is divided by 3, the remainder is 1
2) When n+1 is divided by 4, the remainder is 2

==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, you can directly substitute. Therefore, for con 1), from n=3p+1=1,4,…, the remainder when divided by 4 becomes 1=4(0)+1, which makes remainder=1, and from 4=4(1)+0, you get remainder=0, hence it is not unique and not sufficient. For con 2), from n+1=4q+2 and n=4q+1, the remainder when divided by 4 always becomes 1, hence it is unique and sufficient.

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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 23 Jul 2017, 18:32 Is 3x greater than x-6? 1) x is greater than -4 2) x is greater than 0 ==> If you modify the original condition and the question, you get 3x>x-6?, 2x>-6?, x>-3?. There is 1 variable (x) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from x>-4, the range of the question doesn’t include the range of the condition, hence it is not sufficient. For con 2), from x>0, the range of the question includes the range of the condition, hence it is 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$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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26 Jul 2017, 18:16
Is u>w?
1) u=∣w∣
2) w=∣u∣

==> For con 2), w=|u|≥u for all u is established, so you get w≥ur, which is always no and sufficient.

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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 30 Jul 2017, 19:02 When x is divided by 7, the remainder is 3. When x3 is divided by 7, what is the remainder? A. 2 B. 3 C. 4 D. 5 E. 6 ==> For remainder questions, it is important to use direct substitutions. From X=7p+3=3,10,17,…., if you substitute x=3, from x^3=3^3=27=7(3)+6, you get a remainder of 6. 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$99 for 3 month Online Course"
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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30 Jul 2017, 20:41
MathRevolution wrote:
When x+y is integer, is y an integer?

1) x is an integer.
2) x+2y is an integer.

==> In the original condition, there are 2 variables (x,y) and 1 equation (x+y=integer). In order to match the number of variables to the number of equations, there must be 1 more equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), from x=integer and x+y=integer, integer+y=integer, you get y=integer, which is yes and sufficient. For con 2), from x+2y=x+y+y=integer, integer+y=integer, you get y=integer, which is also yes and sufficient.

st 2. x+2y is an integer- y can be 0.5, 2.5, 1 or 2 etc so st 2 is not sufficient

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Math Revolution GMAT Instructor
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Posts: 6375
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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31 Jul 2017, 18:13
What is the units digit of a positive integer n?

1) The units digit of n^2 is 4
2) The units digit of n^3 is 8

==> In the original condition, there is 1 variable (n) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For con 1), you get n=~2, ~8, hence it is not unique and not sufficient. For con 2), you only get n=~2, hence it is unique and sufficient.

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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 03 Aug 2017, 18:10 If m and n are non-negative integers, mn=? 1) 9^n=3^m 2) 2^n=5^m ==> In the original condition, there are 2 variables (m,n) and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2), from con 1), you get 9^n=(3^2)^n=3^{2n}=3^m, which becomes 2n=m. In order for con 2) to satisfy as well, you only get m=n=0, hence it is unique and sufficient. The answer is C. However, this is an integer question, one of the key questions, so you apply CMT 4 (A: if you get C too easily, consider A or B). For con 1), the way to satisfy 9^n=(3^2)^n=3^{2n}=3^m to 2n=m is not unique and not sufficient. For con 2), from 2^n=5^m, you get 2^n=even and 5^m=odd, so even≠odd. Only m=n=0 satisfies this, hence it is unique and sufficient. Therefore, the answer is B, not C. 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"
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06 Aug 2017, 18:21
If you are flipping the coin 4 times, what is the probability of landing on head two times?

A. 3/5
B. 4/5
C. 3/7
D. 4/7
E. 3/8

==> Probability=Want/Total. Total=since the number of ways when throwing the coins each becomes head or tail 2 times, you get 2*2*2*2=16. Want=if it lands on head 2 times, it lands on tail 2 times, so you get 4!/2!2!=6. Thus, the probability=6/16=3/8.

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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 09 Aug 2017, 18:11 Is $$x>(-3)^\frac{1}{3}$$? 1) $$x>(-2)^\frac{1}{3}$$ 2) $$x>(-4)^\frac{1}{3}$$ Attachment: 8.9.png [ 15.33 KiB | Viewed 929 times ] _________________ 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"
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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10 Aug 2017, 18:06
The percent of employees participated in A program is 80% of the total employees. What is the total number of employees in the company?

1) 168 employees participated in this program.
2) 42 employees did not participate in this program.

==> If you modify the original condition and the question and set the number of people who participated in the program as a and number of people who did not participate in the program as b, from a=80%(a+b), there are 2 variables and 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer.
For con 1), from 168=80%(a+b) and a+b=168/80%=210, it is unique and sufficient.
For con 2), from 42=20%(a+b) and a+b=42/20%=210, it is unique and sufficient.

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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 13 Aug 2017, 18:26 What is the value of (-2)^2+(1/3)^{-3}+(-4)^3? A. -27 B. -29 C. -33 D. 33 E. 29 ==> From (-2)^2+(1/3)^{-3}+(-4)^3=4+(3^{-1})^{-3}+(-4)^3=4+33-64=4+27-64=-33, 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$99 for 3 month Online Course"
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17 Aug 2017, 00:56
If the average (arithmetic mean) of 7 numbers is 21, what is the standard deviation of the numbers?

1) The smallest number of them is 21
2) The greatest number of them is 21

=>Condition 1)
Since the minimum number and the average are same, all numbers should be 21.

Condition 2)
Since the maximum number and the average are same, all numbers should be 21.

Ans: D
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"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" Manager Joined: 08 Jun 2017 Posts: 59 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 17 Aug 2017, 19:09 Is Circular question type and Race type frequently tested in GMAT? Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 20 Aug 2017, 19:21 An alarm of a certain clock rings every 20 minutes. If the clock's alarm first rings at 15:20, when will the 12th alarm of the clock ring? A. 17:30 B. 18:00 C. 18:30 D. 19:00 E. 19:30 =>The third alarm rings at 16:00, the sixth alarm rings at 17:00. Thus every third alarm rings every hour on the hour. The 12th alarm rings at 19:00. Ans: 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"
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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22 Aug 2017, 18:47
If xy≠0, is |x|>|y|？

1) x=-2y
2) x=y^4

=>
Condition 1)

|x| = |-2y| = 2|y| > |y|.
Thus this is sufficient.

Condition 2)

If y = 2, then x = 16 and so |x| > |y|.
If y = ½, then x = 1/16 and so |x| < |y|.
This is not sufficient.

Ans: A
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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 24 Aug 2017, 18:03 What is the value of a positive integer k? 1) When k is divided by 5, the remainder is 3. 2) When k is divided by 3, the remainder is 2. => Condition 1) & 2) k = 8, 23, … Both conditions together are not sufficient either. Ans: 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"
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27 Aug 2017, 19:18
If x, y, and z are positive integers, is x+y divisible by 5?

1) x+z is divisible by 5
2) y+z is divisible by 5

=>Consider 1) & 2)

x = 1, y = 1, z = 4 : x + y is not divisible by 5
x = 5, y = 5, z = 0 : x + y is divisible by 5

Ans: E
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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 30 Aug 2017, 01:30 What is the median of 12, y, and x? 1) x+y=24 2) y=6 =>Condition 1) If x = y = 12, then the median of them is 12. If x < y, then the median of them 12, since x < 12 < y. If x > y, then the median of them 12, since y < 12 < x. This is sufficient. Condition 2) Since we don’t know x, we don’t identify their median. This is not sufficient. Ans: 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"
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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03 Sep 2017, 18:46
If x-7=√x+√7, x=?

A. 8+2√7
B. 8-2√7
C. 8+√7
D. 8-√7
E. 7+2√6

=>x-7=√x+√7
(√x+√7)(√x-√7)=√x+√7
√x-√7 = 1
√x = √7 + 1
x = (√7 + 1)^2
x = 7 + 2√7 + 1 = 8 + 2√7

Ans: A
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"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 Joined: 16 Aug 2015 Posts: 6375 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink] ### Show Tags 06 Sep 2017, 19:01 If |x+3|=|y+3|, what is the value of x+y? 1) xy<0 2) x>3 and y<3 => 1) xy < 0 We can assume x > 0 and y < 0 without loss of generality. Then we have x + 3 = -y - 3 x + y = -6 This is sufficient. 2) x > 3 and y < 3 Then we have x + 3 = -y - 3 x + y = -6 This is sufficient. Ans: 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"
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT &nbs [#permalink] 06 Sep 2017, 19:01

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