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

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29 Dec 2019, 18:07
[GMAT math practice question]

(Inequalities) What is the minimum value of a?

1) The solution of 3 - 3x ≥ 2x - 7 and x + 3 > a is ø.
2) a 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

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

Condition 1)
3 - 3x ≥ 2x - 7
=> 10 ≥ 5x
=> x ≤ 2

X + 3 > a
=> x > a – 3

Looking at the intersection of x ≤ 2 and x > a - 3, we have a - 3 ≥ 2 or a ≥ 5.
Thus, the minimum value of a is 5.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Condition 2) tells us that a is an integer, which gives us an infinite number of possibilities.

Since condition 2) does not yield a unique solution, it is not sufficient.

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.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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01 Jan 2020, 02:20
[GMAT math practice question]

(Number Properties) a, b and c are positive integers with a ≤ b ≤ c. What is the value of a + b + c?

1) abc = a + b + c.
2) abc = 6.

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Since we have 3 variables (a, b, and c) and 0 equations, E is most likely 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 a, b, and c are positive integers and we have abc = 6 with a ≤ b ≤ c, we have a unique solution of a = 1, b = 2, c = 3.
Therefore, we have a + b + c = 6.

Since both conditions together yield a unique solution, they 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 2)
If a = 1, b = 2 and c = 3, then we have a + b + c = 1 + 2 + 3 = 6.
If a = 1, b = 1 and c = 6, then we have a + b + c = 1 + 1 + 6 = 8.

Since condition 2) does not yield a unique solution, it is not sufficient.

Condition 1)
Since abc = a + b + c and 1 ≤ a ≤ b ≤ c, we have c ≤ abc = a + b + c ≤ 3c or c ≤ abc ≤ 3c.
Therefore, we have 1 ≤ ab ≤ 3.
If ab = 1, then we have a = b = 1 and c = 2 + c, which doesn’t make sense.
If ab = 2, then we have a = 1, b = 2 and 2c = c + 3 or c = 3, which tells us that a + b + c = 6.
If ab = 3, then we have a = 1, b = 3 and 3c = 4 + c or c = 2, which doesn’t make sense since c < b.
Therefore, a = 1, b = 2 and c = 3 is the unique case and we have a + b + c = 6.

Since condition 1) yields a unique solution, it is sufficient.

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.

This question is a CMT 4(B) question: We easily figured out condition 2) is not sufficient, and condition 1) is difficult to work with. For CMT 4(B) questions, we assume condition 1) is sufficient. Then A is most likely an answer.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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02 Jan 2020, 18:16
[GMAT math practice question]

(Number Properties) A teacher distributes n apples to some students. If she gives 4 apples to each student, 7 apples remain. If she tried to give 5 apples to each student, 3 students would not get anything. What is the range of possible values of n?

A. 14
B. 16
C. 18
D. 20
E. 22

=>

Assume s is the number of students.
We have n = 4s + 7 and 5(s - 4) < n ≤ 5(s - 3).
Then we have 5s – 20 < 4s + 7 ≤ 5s – 15.
5s – 20 < 4s + 7 is equivalent to s < 27 and 4s + 7 ≤ 5s – 15 is equivalent to 22 ≤ s.
Therefore we have 22 ≤ s < 27 or 22 ≤ s ≤ 26.
We have 88 ≤ 4s ≤ 104 and 95 ≤ 4s + 7 ≤ 111.
The range is 111 – 95 = 16.

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

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05 Jan 2020, 17:58
[GMAT math practice question]

(Geometry) There is a point P(a, b). What is the value of a+b?

1) P is on the line x/3 + y/4 = 1.
2) The line x/3 + y/4 = 1 is parallel to the line (a/3)x + (b/4)y = 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 2 variables (a and b) and 0 equations, C is most likely 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 have a/3 + b/4 = 1 since the point P(a, b) is on the line x/3 + y/4 = 1.
We have a = b since x/3 + y/4 = 1 is parallel to the line (a/3)x + (b/4)y = 1 or 1/3 : a/3 = 1/4 : b/4.
Then, we have a/3 + a/4 = 1, 4a/12 + 3a/12 = 1, (7/12)a = 1 or a = 12/7.
Thus we have a + b = 12/7 + 12/7 = 24/7.

Since both conditions together yield a unique solution, they are sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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06 Jan 2020, 18:16
[GMAT math practice question]

(Geometry) As the figure below shows, line l is perpendicular to BD and CE. What is the length of DE?

1) △ABC is a right isosceles triangle with ∠BAC = 90
2) BD = 3, and CE = 4

Attachment:

1.2ds.png [ 8.15 KiB | Viewed 352 times ]

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 9 variables from 3 triangles and 2 equations from two right triangles, E is most likely 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 we have AB = AC from condition 1) and ∠DBA = ∠EAC, the triangles ADB and CEA are congruent.
Thus, DE = DA + AE = CE + BD = 3 + 4 = 7.

Since both conditions together yield a unique solution, they are sufficient.

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.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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08 Jan 2020, 23:44
[GMAT math practice question]

(Number Properties) Annie multiplied the date of her birthday by 5, then subtracted 4 from that. She multiplied it by 2 after that and added the month of her birthday again. She got the result of 232. When is her birthday?

A. Aug. 20th
B. Aug. 23rd
C. Sep. 21st
D. Sep. 22nd
E. Oct. 23rd

=>

Assume m and d are the month and date of Annie’s birthday.
Then we have 2(5d - 4) + m = 232 or m = 240 – 10d = 10(24-d).
Since m is a multiple of 10, we have m = 10. (Note that m cannot be 20, 30, etc. because there are only 12 months in a year.)
Then we have 10d = 240 – m, 10d = 240 – 10, 10d = 230 or d = 23.

Thus, Annie’s birthday is Oct. 23rd.

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

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09 Jan 2020, 19:35
[GMAT math practice question]

(Graphs) A line passes through two points (a, -2), and (2a-6, 2). This line is parallel to the y-axis. What is a?

A. 2
B. 4
C. 6
D. 8
E. 10

=>

The x-coordinate of all points on a vertical line must be equal.
Then we have a = 2a – 6 or a = 6.

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

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12 Jan 2020, 17:51
[GMAT math practice question]

(Geometry) The figure shows a parallelogram. What is the measure of ∠APC?

1) ∠B : ∠C = 2 : 3
2) ∠BAP = ∠DAP

Attachment:

1.7ds.png [ 11.78 KiB | Viewed 297 times ]

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have a parallelogram, we have 3 variables, and E is most likely 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)

∠B + ∠C = 180° and ∠C = ∠BAD = ∠BAP + ∠DAP.
Since ∠B : ∠C = 2 : 3 and ∠B + ∠C = 180° from condition 1), we have ∠B = 72° and ∠C = 108°, because:
∠B + ∠C = 180° can be rewritten as ∠B = 180° - ∠C
Substitute into ∠B : ∠C = 2 : 3
180 - ∠C : ∠C = 2 : 3
3(180° - ∠C) = 2C (by cross multiplying)
540° - 3∠C = 2∠C
540° = 5∠C (adding 3∠C to both sides)
∠C = 108° (dividing both sides by 5)
∠B = 180° - ∠C, B = 180° - 108°, or ∠B = 72°

Since ∠C = 108° = ∠BAP + ∠DAP and ∠BAP = ∠DAP, we have ∠BAP = 54°.
Thus the exterior angle ∠APC of the triangle ABP is the sum of ∠ABP and ∠BAP and we have ∠APC = ∠ABP + ∠BAP = 72° + 54° = 126°.

The answer is unique, and the conditions combined are sufficient.

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

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13 Jan 2020, 17:41
[GMAT math practice question]

(Inequalities) What is the value of y? ([x] denotes the greatest integer less than or equal to x.)

1) y = 2[x] + 3
2) y = 3[x - 2] + 5

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 2 variables (x and y) and 0 equations, C is most likely 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)

Assume we have n = [x].
Since we have y = 2n + 3 and y = 3(n - 2) + 5 since we have [x - 2] = [x] - 2.
Then, substituting the first equation into the second equation we have
2n + 3 = 3(n – 2) + 5
2n + 3 = 3n - 6 + 5
2n +3 = 3n - 1
-n = -4
n = 4

Then:
y = 2n + 3
y = 2(4) + 3
y = 11.

Since both conditions together yield a unique solution, they are sufficient.

Since this question is an integer 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)
x = 1, y = 5 and x = 2, y = 7 are solutions.
Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
x = 1, y = 2 and x = 2, y = 5 are solutions.
Since condition 2) does not yield a unique solution, it is not sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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15 Jan 2020, 17:25
[GMAT math practice question]

(Function) The function is defined as follows: f(x+1) = 3x + 2. What is f(1) + f(2) + f(3) +…+ f(9) + f(10)?

A. 149
B. 153
C. 155
D. 157
E. 159

=>

Since f(x+1) = 3x + 2, we have f(x) = f((x-1) + 1) = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1.
f(1) + f(2) + f(3) + … + f(9) + f(10)
= ( 3*1 – 1 ) + ( 3*2 – 1 ) + … + ( 3*10 – 1 )
= 3(1 + 2 + … + 10) – (1 + 1 +…+ 1)
= 3*55 – 10 = 155.

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

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16 Jan 2020, 17:27
[GMAT math practice question]

(Coordinate Geometry) A quadrilateral P has (1, 1), (3, 1), (3, 5) and (1, 5) as 4 vertices and another quadrilateral Q has (-1, -1), (-5, -1), (-5, -5) and (-1, -5) as 4 vertices. A line divides these two quadrilaterals evenly at the same time. What is this line?

A. y = - 1/6x + 5/6
B. y = - 5/6x + 1/6
C. y = 6/5x + 3/5
D. y = 1/3x + 5/6
E. y = - 1/6x + 7/5

=>

Attachment:

1.9ps(a).png [ 29.51 KiB | Viewed 252 times ]

The quadrilaterals are rectangles, and bisecting lines of rectangles pass through the center of the rectangles.
Thus we have to find the line passing through the centers of those two rectangles.
The centers of the rectangles are (2, 3) and (-3, -3).
The slope of the line passing through (2, 3) and (-3, -3) is (3- (-3)) / (2 - (-3)) = 6/5.
The line passing through them is y – 3 = (6/5)(x - 2) or y = (6/5)x + (3/5).
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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19 Jan 2020, 17:54
[GMAT math practice question]

(Inequality) Which is greater between (a + 2b)2 and 9ab?

1) 1 < a < 2
2) 1/2 < b < 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

The question is equivalent to the statement (a - b)(a - 4b) is greater than or less than 0 for the following reason:

(a + 2b)^2 - 9ab > 0
=> a^2 + 4ab + 4b^2 – 9ab > 0
=> a^2 - 5ab + 4b^2 > 0
=> (a - b)(a - 4b) > 0

Since we have 2 variables (a and b) and 0 equations, C is most likely 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 1 < a < 2 and 1/2 < b < 1, we have 1/2 < b < 1 < a < 2 or b < a.
Since 1 < a < 2 and 2 < 4b < 4 (by multiplying the equation given in condition 2) by 4), we have 1 < a < 2 < 4b < 4 or a < 4b.

Then we have a – b > 0, and a – 4b < 0 or (a - b)(a - 4b) < 0.
Thus, we have (a + 2b)^2 - 9ab > 0 and (a + 2b)^2 is greater than 9ab.

Since both conditions together yield a unique solution, they are sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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20 Jan 2020, 17:38
[GMAT math practice question]

(Algebra) Thomas went to a grocery store and bought some fruit with \$25. The prices of the fruit are \$5, \$1, and \$0.50 for each watermelon, pear, and apple, respectively. How many apples did he buy?

1) He bought 10 pieces of fruit, and he didn’t get any change back.
2) He had at least one of each fruit.

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Assume x, y and z are the number of watermelons, pears, and apples, respectively.
Then we have 5x + y + 0.5z = 25 or 10x + 2y + z = 50.

Since we have 3 variables (x, y, and z) and 1 equation, C is most likely 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 have x + y + z = 10 and 5x + y + 0.5z = 25 or 10x + 2y + z = 50. Subtracting the first equation from the second equation gives us (10x + 2y + z) – (x + y + z) = 50 - 10, or 9x + y = 40.
Then y = 40 – 9x.
Then the possible values of (x, y) are (1, 31), (2, 22), (3, 13), and (4, 4).
If x = 1, and y = 31, then z = 10 – x – y = -22 doesn’t make sense, since z must be positive.
If x = 2, and y = 22, then z = 10 – x – y = -14 doesn’t make sense, since z must be positive.
If x = 3, and y = 13, then z = 10 – x – y = -6 doesn’t make sense, since z must be positive.
If x = 4, and y = 4, then we have z = 10 – x – y = 2.

Since both conditions together yield a unique solution, they are sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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27 Jan 2020, 06:06
[GMAT math practice question]

(Probability) Among integers from 1 to 50, inclusively, what is the number of the multiples of 4 or 5?

A. 14
B. 16
C. 18
D. 20
E. 22

=>

The number of multiples of 4 is 12 = (48 – 4)/4 + 1 = 11 + 1, since 4, 8, …, 48 are the multiples of 4 between 1 and 50, inclusive.
The number of multiples of 5 is 10 = (50 – 5)/5 + 1 = 9 + 1, since 5, 10, …, 50 are the multiples of 5 between 1 and 50, inclusive.
Multiples of 20 are double-counted, and the number of multiples of 20 is 2 since 20 and 40 are multiples of 20 between 1 and 50, inclusive.
Then we have 12 + 10 - 2 = 20.

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

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28 Jan 2020, 17:48
[GMAT math practice question]

(Geometry) In the figure below, is triangle AEF an isosceles triangle?

1) AB = AC
2) DF is perpendicular to BC.

Attachment:

1.22ds.png [ 8.57 KiB | Viewed 561 times ]

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since triangle AEF has three sides, we have 3 variables (AE, AF, and EF) and 0 equations, and E is most likely 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 have ∠B = ∠C since AB = AC, and the triangle is isosceles.
Assume ∠B = ∠C = x.
Then ∠DEC = ∠AEF = 90 – x since the triangle is a right triangle, and ∠DEC is congruent to ∠AEF.
Since triangle BDF is a right triangle, we have ∠AFE = 90 – x.
Thus we have ∠AEF = ∠AFE, which means the triangle is isosceles, and we have AE = AF.

Since both conditions together yield a unique solution, they are sufficient.

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.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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02 Feb 2020, 18:33
[GMAT math practice question]

(Geometry) What is the measure of ∠BIC in the figure?

1) Point I is the incenter (the point where the three angle bisectors meet) of triangle ABC.
2) ∠BAC = 50°

Attachment:

1.28ds.png [ 4.2 KiB | Viewed 538 times ]

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 4 variables (∠BIC, ∠ABC, ∠BCA, and ∠CAB) and 1 equation (∠ABC + ∠BCA + ∠CAB = 180°), C is most likely 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 point O is the incenter of triangle ABC from condition 1), the segments IA, IB, and IC are bisectors of ∠BAC, ∠ABC and ∠BCA, respectively.

∠BIC = 180° – (∠IBC + ∠ICB), ∠BIC = 180° – (1/2)(180° - ∠BAC), ∠BIC = 180° – (1/2)(180° - 50°), ∠BIC = 180° – 65° = 115°.

Since both conditions together yield a unique solution, they are sufficient.

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 in which the answer is A, B, C, or D.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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05 Feb 2020, 17:21
[GMAT math practice question]

(Number Properties) If 100! = 100 x 99 x…x 2 x 1 can be written as 2^a3^b5^c7^d…., what is a?

A. 86
B. 97
C. 108
D. 119
E. 131

=>

We need to count the number of prime factors 2 in the prime factorization of 100!. We can do it by counting:

The number of multiples of 2 is [100/2] = 50.
The number of multiples of 4 is [100/4] = 25.
The number of multiples of 8 is [100/8] = 12.
The number of multiples of 16 is [100/16] = 6.
The number of multiples of 32 is [100/32] = 3.
The number of multiples of 64 is [100/64] = 1.

Thus the number of prime factors 2 is 50 + 25 + 12 + 6 + 3 + 1 = 97.

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

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09 Feb 2020, 17:29
[GMAT math practice question]

(Geometry) The figure below shows the dimensions of triangle ABC. What is ∠BIC?

1) Point I is the incenter of △ABC.
2) Line DE is parallel to line BC.

Attachment:

2.4DS.png [ 8.92 KiB | Viewed 483 times ]

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

Condition 1)

Since we can find an incenter of a triangle by the intersection of lines bisecting interior angles, ∠DBI is equal to ∠IBC, and ∠ECI is equal to ∠ICB.

Attachment:

2.4DS(A).png [ 10.96 KiB | Viewed 482 times ]

Then we have ∠IBC = 22° and ∠ICB = 30°.
Thus, we have ∠BIC = 180° - ∠IBC - ∠ICB = 180° – 22° – 30° = 128°.

Since condition 1) yields a unique solution, it is sufficient.

Condition 2)

Since we don’t know the position of I on segment DE, condition 2) does not yield a unique solution, and it is not sufficient.

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

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11 Feb 2020, 18:11
[GMAT math practice question]

(Algebra) What is the value of [x] + [-x]? ([x] means the greatest integer less than or equal to x.)

1) 0 ≤ x.
2) x is not 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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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

If x = n + h where n is an integer and 0 ≤ h < 1, then [x] = n. Here n is the integer part of n, and h is the decimal part of n.

If x is an integer, then we have x = n + h where h = 0, [x] = n, [-x] = -n and [x] + [-x] = n + (-n) = 0.

Assume x is not an integer.
Then we have x = n + h where 0 < h < 1, [x] = n.
We have -x = -n - h, -x = -n - 1 + 1 - h, -x = -(n + 1) + (1 - h) where 0 < 1 - h < 1.
Thus [-x] = -n - 1 and we have [x] + [-x] = n + (-n - 1) = -1.

Condition 2) tells us that x is not an integer. Therefore [x] + [-x] = -1 and condition 2) yields a unique solution.

Condition 2) is sufficient.

Condition 1)
If x = 0 which is an integer, then we have [x] + [-x] = 0.
If x = 1.5 which is not an integer, then we have [x] + [-x] = -1.

Since condition 1) does not yield a unique solution, it is not sufficient.

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

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13 Feb 2020, 18:26
[GMAT math practice question]

(Geometry) In the figure below, point I is the incenter of △ABC and line AH is perpendicular to BC. If ∠ABC = 80 and ∠ACB = 50 what is ∠x + ∠y?

Attachment:

2.4PS.png [ 17.52 KiB | Viewed 449 times ]

A. 55
B. 60
C. 65
D. 75
E. 80

=>

∠BAC = 180 – 80 – 50 = 50.
An incenter of a triangle is the intersection of lines bisecting all interior angles.
∠x = ∠CAH - ∠CAI = 40 – 25 = 15.
∠y = ∠CAI + ∠ACI = 25 + 25 = 50.
Thus ∠x + ∠y = 15 + 50 = 65.

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 13 Feb 2020, 18:26

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