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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: 8435
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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27 Oct 2019, 19:55
[GMAT math practice question]

(algebra) What is the value of x + 1/y?

1) y + 1/z = 1
2) z + 1/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.
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 (x, y, and z) 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 y + 1/z = 1, we have y = 1 – 1/z, y = (z-1)/z and 1/y = z/(z-1).
Since z + 1/x = 1, we have 1/x = 1 - z or x = 1/(1-z).
Then x + 1/y = 1/(1-z) + z/(z-1) = 1/(1-z) - z/(1-z) = (1-z)/(1-z) = 1.

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

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

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30 Oct 2019, 18:26
[GMAT math practice question]

(geometry) In the figure, what is ∠a + ∠b + ∠c + ∠d + ∠e - ∠f + ∠g?

Attachment:

10.21PS.png [ 20.59 KiB | Viewed 418 times ]

A. 270°
B. 300°
C. 330°
D. 360°
E. 420°

=>

Attachment:

10.21PS(A).png [ 29.3 KiB | Viewed 419 times ]

We have <a + <b + 180° - <x = 180°.
<c + <d + <e + <y = 360°
<g + <z + <x = 180°
<f + <y + <z = 180°
When we add the first three equations and subtract the last equation, we have
<a + <b + 180° - <x + <c + <d + <e + <y + <g + <z + <x - (<f + <y + <z) = 180° + 360° + 180° - 180°
=><a + < b + <c + <d + <e - <f + < g + 180°= 540°
=><a + < b + <c + <d + <e - <f + < g = 360°

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

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31 Oct 2019, 18:40
[GMAT math practice question]

(geometry) The figure shows that the arc length AB and arc length AC are the same, and ∠BOC = 100°. What is ∠OCA?

Attachment:

10.24PS.png [ 11.72 KiB | Viewed 395 times ]

A. 15°
B. 20°
C. 25°
D. 30°
E. 35°

=>

Attachment:

10.24ps(a).png [ 17.3 KiB | Viewed 395 times ]

Since the length of the arc AB is equal to the length of the arc AC, <AOB = <AOC = (1/2)(360°-100°) = 130°.
Since OA=OC in the triangle AOC, we have <OCA = (1/2)(180°-130°) = 25°.

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

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03 Nov 2019, 19:40
[GMAT math practice question]

(number properties) x and y are positive integers. What is the value of x *y?

1) x^{x+y} = y^4
2) y^{x+y} = 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.
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)
x = 1 and y = 1 satisfies both conditions 1) & 2) together and we have x*y = 1.
x = 2 and y = 2 satisfies both conditions 1) & 2) together and we have x*y = 4.

Since both conditions together do not yield a unique solution, they are 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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05 Nov 2019, 19:12
[GMAT math practice question]

(number properties) x, y, and z are positive integers. What is the value of xyz?

1) xy + yz = 24
2) xz + yz = 13

=>

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 (x, y, and z) 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 we have (x+y)z = 13 from condition 2), we have x+y=13 and z = 1.
We have (x+z)y = (x+1)y = 24 from condition 1) since z = 1.

If x = 1, y = 12, z = 1, then xyz = 12.
If x = 11, y = 2, z = 1, then xyz = 22.

Since both conditions together do not yield a unique solution, they are not 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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06 Nov 2019, 21:37
[GMAT math practice question]

(geometry) The figure shows that OA is parallel to CB, and the arc length AB is 8 cm, and ∠AOB is 40. What is the arc length of BC?

Attachment:

10.29ps.png [ 14.7 KiB | Viewed 356 times ]

A. 20 cm
B. 22 cm
C. 24 cm
D. 26 cm
E. 28 cm

=>

Since ∠AOB and ∠OBC are alternate interior angles, they are equal to each other, and we have ∠OBC = 40.

Attachment:

10.29PS(A).png [ 15 KiB | Viewed 357 times ]

∠BOA = 100 and the length of the arc BC is 8*(100/40) = 20.

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

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07 Nov 2019, 19:37
[GMAT math practice question]

(geometry) An inner angle of an n-regular polygon is a positive integer. How many possible n’s are there less than or equal to 20?

A. 10
B. 11
C. 12
D. 13
E. 14

=>

Since the sum of all interior angles of an n-polygon is 180(n-2), an interior angle of an n-regular polygon = 180(n-2)/n = (180n – 360)/n = 180 – (360/n).
In order for 180 - (360/n) to be an integer, n must be a factor of 360.
Then the possible values of n are 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, and 20.
We have 11 possible values of n.

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

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10 Nov 2019, 21:34
[GMAT math practice question]

(algebra) What is the value of 1/(2x-1) + 1/(2y-1)?

1) 1/(2x+1) + 1/(2y+1) = 1
2) x = 4y = 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 1/(2x-1) + 1/(2y-1) is equivalent to (2x+2y-2)/(4xy-2x-2y+1) for the following reason.
1/(2x-1) + 1/(2y-1)
= (2y-1)/[(2x-1)(2y-1)] + (2x-1)/[(2x-1)(2y-1)]
= (2x+2y-2)/(4xy-2x-2y+1)

Condition 2)
Since x = 4y = 1, we have 4xy = 1 and (2x+2y-2)/(4xy-2x-2y+1) = (2x+2y-2)/(1-2x-2y+1) = (2x+2y-2)/(-2x-2y+2) = {2(x+y-1)}/{(-2)(x+y-1)} = -1.
Since condition 2) yields a unique solution, it is sufficient.

Condition 1)
1/(2x+1) + 1/(2y+1) = 1
=> (2y+1)/[(2x+1)(2y+1)] + (2x+1)/[(2x+1)(2y+1)] = 1
=> (2x+1+2y+1)/[(2x+1)(2y+1)] = 1
=> (2x+2y+2)/(4xy+2x+2y+1) = 1
=> 2x+2y+2 = 4xy+2x+2y+1
=> 4xy = 1.
Then we have (2x+2y-2)/(4xy-2x-2y+1) = (2x+2y-2)/(1-2x-2y+1) = (2x+2y-2)/(-2x-2y+2) = {2(x+y-1)}/{(-2)(x+y-1)} = -1.
Since condition 1) yields a unique solution, it is sufficient.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

This question is a CMT4(B) question: condition 2) is easy to work with, and condition 1) is difficult to work with. For CMT4(B) questions, D is most likely to be the answer.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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11 Nov 2019, 22:22
[GMAT math practice question]

(algebra) a≠b and b≠c are given. Is it true that a=c?

1) (a-b)(b-c)(c-a) = 0
2) (a^2+3a)/(a+1) = (b^2+3b)/(b+1) = (c^2+3c)/(c+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.

Condition 1) tells that a = b or b =c or c = a. However, we have a≠b and b≠c from the original condition, so we have a = c.
Thus, condition 1) is sufficient.

Condition 2)
Assume (a^2+3a)/(a+1) = (b^2+3b)/(b+1) = (c^2+3c)/(c+1) = k
We have (a^2+3a) = k(a+1), (b^2+3b) = k(b+1) and (c^2+3c) = k(c+1)

When we subtract the first two equations, we have
(a^2+3a) - (b^2+3b) = k(a+1) - k(b+1)
=> (a^2-b^2+3a-3b) = ka+k-kb-k
=> (a^2-b^2) + 3(a-b) = ka-kb
=> (a^2-b^2) + 3(a-b) = k(a-b)
=> (a+b)(a-b) + 3(a-b) = k(a-b)
=> (a+b+3)(a-b) = k(a-b)
=> a+b+3 = k since a≠b

When we subtract the last two equations, we have
(b^2+3b) - (c^2+3c) = k(b+1) - k(c+1)
=> b^2-c^2+3b-3c = kb+k-kc-k
=> (b^2-c^2) + 3(b-c) = kb-kc
=> (b^2-c^2) + 3(b-c) = k(b-c)
=> (b+c)(b-c) + 3(b-c) = k(b-c)
=> (b+c+3)(b-c) = k(b-c)
=> b+c+3 = k since b≠c

Since we have a+b+3 = k and b+c+3 = k, we have a = c.
Thus condition 1) is sufficient.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that D is most likely to be the answer to this question, since each condition includes a ratio.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).

This question is a CMT4(B) question: condition 2) is easy to work with, and condition 1) is difficult to work with. For CMT4(B) questions, D is most likely to be the answer.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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14 Nov 2019, 18:43
[GMAT math practice question]

(geometry) The figure shows the square with a side length of 10 cm, and a circle is inscribed by the square. What is the area of the shaded region?

Attachment:

11.6ps.png [ 34.1 KiB | Viewed 280 times ]

A. 40 cm^2
B. 44 cm^2
C. 46 cm^2
D. 48 cm^2
E. 50 cm^2

=>

If we consider moving the areas of A and B to C and D, respectively, we have two squares with a side length of 5. Thus the sum of the areas of two squares is 25 + 25 = 50.
Thus the area of the shaded region is 50.

Attachment:

11.6PS(A).png [ 34.84 KiB | Viewed 281 times ]

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

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17 Nov 2019, 18:45
[GMAT math practice question]

(arithmetic) What is the maximum value of 2^a + 2^b + 2^c?

1) a + b + c = 5
2) for any a, b ≥ 0, 2^a + 2^b ≤ 1 + 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.
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)
2^a + 2^b + 2^c
≤1 + 2^{a+b} + 2^c
≤1 + 1 + 2^{a+b+c}, since 2^{a+b} + 2^c ≤ 1 + 2^{a+b+c}
≤1 + 1 + 25 = 34

So, the maximum value of 2^a + 2^b + 2^c is 34.

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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19 Nov 2019, 18:59
[GMAT math practice question]

(Geometry) The figure shows that AB is parallel to FE. What is ∠ABC + ∠BCD + ∠CDE + ∠DEF?

Attachment:

11.11ps.png [ 12.1 KiB | Viewed 235 times ]

A. 380°
B. 440°
C. 540°
D. 600°
E. 720°

=>

Draw two lines GK and HO parallel to AB and FE as follows.

Attachment:

11.11ps(a).png [ 21.56 KiB | Viewed 234 times ]

Then we have ∠ABC + ∠BCG = 180°, ∠GCD + ∠CDH = 180°, ∠HDE + ∠DEF = 180°, and the pairs of two angles are supplementary, respectively.
∠ABC + ∠BCD + ∠CDE + ∠DEF = ∠ABC + (∠BCG + ∠GCD) + (∠CDH + ∠HDE) + ∠DEF = (∠ABC + ∠BCG) + (∠GCD + ∠CDH) + (∠HDE + ∠DEF) = 180° + 180° + 180° = 540°,

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

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24 Nov 2019, 19:24
[GMAT math practice question]

(Number Properties) What is the solution to 4x + 3y = 13?

1) x and y are positive integers
2) x and y are real numbers

=>

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.

Review the following property.
When we have solve an equation ax + by = c in terms of x and y, we can presume this equation has a unique solution under the following conditions.
1) x and y are positive integers.
2) coefficients a and b are relative primes.
3) c is not a big number.

Since condition 1) tells us that x and y are positive integers. The coefficients 4 and 3 are relative primes and the constant term c is not a big number.
Thus we can presume this equation has a unique solution.

The logical reason is as follows.
We can substitute positive integers from 1 into the variable x of the equation 3y = 13 – 4x and we should notice that 13 – 4x must be a multiple of 3 since we have 3y on the left hand side.
The unique possible value of x is 1 in order to have a positive value of y from the equation.
Then we have a unique solution x = 1 and y = 3.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since condition 2) allows all real numbers, there many possibilities for solutions to this equation 4x + 3y = 13.
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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27 Nov 2019, 18:25
[GMAT math practice question]

(Speed) The distance between Jane’s home and her school is 24km. It takes 4 hours and 50 minutes for Jane to walk from home to school and it takes 5 hours to come back. The road consists of an uphill section, a downhill section and a flat section. How long is the flat section?

1) The speed on the uphill section is 4km/hr, on the downhill section is 6km/hr and on the flat section is 5km/h.
2) The speed on the flat section is the arithmetic average of the speeds on the uphill and downhill sections.

=>

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 f, u and d are distances on the flat sections, uphill sections and downhill sections when she travels from home to school.
Then we have f + u + d = 24.
Even though we have 3 variables and 1 equation, condition 1) has 3 equations. So we should check condition 1) first.

Condition 1)
The time she travels from home to school is f/5 + u/4 + d/6 = 4(50/60) = 29/6.
The time she travels from school to home is f/5 + u/6 + d/4 = 5 since uphill sections becomes downhill sections and downhill sections becomes uphill when she travels back.
Adding the equations together, we have (2/5)f + (5u + 5d)/12 = (2/5)f + (5/12)(u+d) = 29/6 + 5 = 59/6.
Substituting in u + d = 24 – f, we have (2/5)f +(5/12)(24 - f) = 59/6, (2/5)f + 10 - (5/12)f = 59/6, or (24/60)f - (25/60)f = 59/6 - 60/6. Then we have (-1/60)f = -1/6, or f = 10.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since the speed on the flat section is the arithmetic average of the speeds on the uphill and downhill sections, we can assume that s is the speed on the flat sections, s – a is the speed on the uphill sections and s + a is the speed on the downhill sections.
Then we have the time she takes when she travels from home to school, f/s + u/(s-a) + d/(s+a) = 29/6 and we have the time she takes when she travels from home to school, f/s + u/(s+a) + d/(s-a) = 5.
When we add those equations, we have (2f/s) + (u+d)(1/(s-a)+1/(s-b)) = 59/6.
We can notice that there must be many possibilities for solutions.

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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29 Nov 2019, 01:48
[GMAT math practice question]

(Algebra) There is a gram of sugared water with a% density. If x grams of water is poured into the sugared water, then the density becomes (a-5)% (a > 5). What is the value of x?

A. 5a
B. (a+5)/(a-5)
C. (a+5)/5
D. (5a)/(a-5)
E. (a-5)/a

=>

The amount of sugar in a gram of a% sugared water is (a/100)*a grams.
When we add x gram of water, we have [(a/100)*a]/(a + x) = (a - 5)/100 or a^2/(a + x) = a - 5.
Then we have a^2 = (a - 5)(a + x) or a^2 = a^2 + ax – 5a – 5x.
This can be rearranged to get 5a = ax - 5x, or x(a-5) = 5a. So x = (5a)/(a - 5).

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

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01 Dec 2019, 21:10
[GMAT math practice question]

(number properties) There are 6 bags. Each bag contains 18, 19, 21, 23, 25, and 34 beads, respectively. All the beads in one bag are broken, and no other bags have any broken beads. How many beads are broken?

1) Adam has 3 bags, and Betty has 2 bags, and no one has the bag of broken beads.

=>

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 there are 6 bags, we have many variables 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)
Assume a and b are the numbers of beads that Adam and Betty have, respectively.
Since Adam chooses 3 bags and Betty chooses 2 bags, one bag is not chosen by Adam or Betty.
Since we have a = 2b, a + b = 2b + b = 3b, then a + b is a multiple of 3.
18 + 19 + 21 + 23 + 25 + 34 = 140 has a remainder 2 when 140 is divided by 3. When we subtract the number of beads in 1 of the 6 bags from 140, it must be a multiple of 3 and only 23 satisfies this condition, since 140 – 23 = 117, which is a multiple of 3.
23 is the number of broken beads.
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 1)
There are 6 possibilities for the bag with broken beads.
Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
Since condition 2) doesn’t give us any information about the number of broken beads, it is obviously not 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 Dec 2019, 18:50
[GMAT math practice question]

(inequalities) Which one of (a + c)/(b + d) and ac/bd is greater than the other one?

1) d > c and b > a.
2) a, b, c, and d are positive.

=>

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.

(a + c)/(b + d) – ac/bd
= {(a + c)bd – ac(b+d)}/{bd(b+d)} (by adding fractions with a common denominator)
= {abd + cbd – acd – acd}/{bd(b+d)} (by multiplying through the brackets in the numerator)
= {ab(d - c) + cd(b - a)}/{bd(b + d)} (by taking out common factors)

Since we have 4 variables (a, b, c, and d) 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, c and d is positive and we have d > c and b > a, we have {ab(d - c) + cd(b - a)}/{bd(b + d)} > 0.
It means we have (a + c)/(b + d) > ac/bd.

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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05 Dec 2019, 18:36
[GMAT math practice question]

(inequalities) For the equation 3 - 2[x] = 3[x] - 12, x satisfies p ≤ x < q. What is the value of p + q? ([x] denotes the greatest integer less than or equal to x.)

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

=>

Since [x] is the greatest integer less than or equal to x, if we have n ≤ x < n + 1, where n is an integer, we define [x] = n.

3 - 2[x] = 3[x] - 12
=> 15 = 5[x]
=> [x] = 3
=> 3 ≤ x < 4
Then we have p = 3 and q = 4.
So p + q = 7.

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

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06 Dec 2019, 23:01
math revolution, is here any source or link to get monthly update of gmat exam questions?

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

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08 Dec 2019, 18:42
[GMAT math practice question]

(algebra) A and B are polynomials. What polynomial is 3A + B?

1) A + B = 3x^2 - 3xy + 4y^2.
2) A – B = x^2 + xy - 6y^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.
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)
3A + B
=> = 2(A + B) + (A - B) (rearranging the equation to suit the conditions)
=> = 2(3x^2 - 3xy + 4y^2) + (x^2 + xy - 6y^2) (substituting in the conditions)
=> = 6x^2 - 6xy + 8y^2 + x^2 + xy - 6y^2 (multiplying 2 through the bracket)
=> = 7x^2 - 5xy + 2y^2 (adding like terms)
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] 08 Dec 2019, 18:42

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