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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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[Math Revolution GMAT math practice question]

What is the range of 10 numbers?

1) The average (arithmetic mean) of the 10 numbers is 10
2) The greatest of the 10 numbers is 15

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since Range = Max – Min, we have 3 variables and 1 equation, so C is most likely to be the answer. There is no equation relating the range, the average and the maximum, so the answer is most likely to be E).

Conditions 1) & 2):
If the data set is { 5, 5, 5, 5, 5, 15, 15, 15, 15, 15 }, then its range is 10.
If the data set is { 4, 5, 5, 5, 6, 15, 15, 15, 15, 15 }, then its range is 11.
Since we don’t have a unique solution, both conditions are not sufficient, when taken together.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

What is the area of a triangle?

1) The triangle is isosceles.
2) Two sides of the triangle are 10.

=>

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.

When we apply the VA (Variable Approach) method to a triangle, we have 3 variables corresponding to the side-lengths of the triangle. Since each condition provides only one equation, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2):

Attachment: 9.3.png [ 11.02 KiB | Viewed 389 times ]

If the triangle is a right-angled isosceles triangle with two legs of length 10, then its area is (1/2)10*10 = 50.
If the triangle is an equilateral triangle with all sides of length 10, then its area is (√3/4)10^2 = 25√3.
Since we don’t have a unique solution, both conditions are not sufficient, when taken together.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Is xy<1?

1) x^2+y^2 < 1
2) x + 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.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2):

x^2 + y^2 < 1
=> x^2< 1 - y^2 ≤ 1 since y^2 ≥ 0
=> x^2< 1
=> -1 < x < 1
and
x^2 + y^2 < 1
=> y^2< 1 - x^2 ≤ 1 since x^2 ≥ 0
=> y^2< 1
=> -1 < y < 1

Combining these two inequalities yields -1 < xy < 1, so xy < 1. Both conditions are sufficient, when taken together.

Since this question is an inequality 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)

The argument showing that conditions 1 and 2 are sufficient, when taken together, only used condition 1. Therefore, condition 1 is sufficient.

Using the same argument as above,

x^2 + y^2 < 1
=> x^2< 1 - y^2 ≤ 1 since y^2 ≥ 0
=> x^2< 1
=> -1 < x < 1
and
x^2 + y^2 < 1
=> y^2< 1 - x^2 ≤ 1 since x^2 ≥ 0
=> y^2< 1
=> -1 < y < 1.

So, -1 < xy < 1, and condition 1) is sufficient.

Condition 2)

If x = 1/3 and y = 1/3, then xy = 1/9 < 1 and the answer is ‘yes’
If x = -2 and y = -2, then xy = 4 > 1 and the answer is ‘no’
Since we don’t have a unique solution, condition 2) 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Is n an odd number?

1) n is the sum of 2 prime numbers
2) n is a multiple of 11

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If n = 2 + 3, then n = 5 is odd and the answer is ‘yes’.
If n = 3 + 5, then n = 8 is even and the answer is ‘no’.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
If n = 11, then n is odd and the answer is ‘yes’.
If n = 22, then n is even and the answer is ‘no’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If n = 2 + 31, then n = 33 is odd and the answer is ‘yes’.
If n = 13 + 31, then n = 44 is even and the answer is ‘no’
Since we don’t have a unique solution, both conditions 1) and 2) are not sufficient, when taken together.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value of x?

1) y = 16
2) The difference between y and z is 4

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method I s 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 gives the proportion x : y : z = 3 : 4 : 5, so we can write x = 3k, y = 4k and z = 5k. We have 4 variables and 3 equations.
Therefore, D is most likely to be the answer.

Condition 1) is sufficient since 16 = y = 4k, and so k = 4. Then x = 3k = 12.

Condition 2) is also sufficient since 4 = z – y = 5k – 4k = k. So, x = 3k = 12.

Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) give similar information.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Attachment: 9.8.png [ 2.42 KiB | Viewed 351 times ]

What is the area of the above triangle?

1) y=z
2) y+z=10

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)

Attachment: 9.10.png [ 13.33 KiB | Viewed 350 times ]

If x = y = z = 5, then the triangle is equilateral, and its area is (√3/4)*52 = (25/4) √3.
If x = 6 and y = z = 5, then the area of the triangle is (1/2)6*4 = 12.
Since the answer is not unique, conditions 1) & 2) are not sufficient, when taken together.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

What is the value of the 2-digit positive integer n if its tens digit is four times its units digit?

1) n is an even number
2) The units digit of n is greater than 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 only positive two-digit integers n satisfying the original condition are 82 and 41.

Condition 1) is sufficient since 82 is the only one of these integers that is even.
Condition 2) is also sufficient, since 82 the only one of these integers with a units digit that is greater than 1.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Is xy>0?

1) x^3y>0
2) x^2y>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.

Since even powers are always non-negative, we can ignore the even exponents.
Condition 1)
x^3y > 0 is equivalent to xy > 0, which is the question itself. Therefore, condition 1) is sufficient.
Condition 2)
x^2y>0 is equivalent to y > 0.
It is not sufficient

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Does y=ax^2+bx+c intersect the x-axis?

1) a<0
2) c>0

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

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

Since we are asked about a quadratic polynomial, the question asks if the discriminant b^2-4ac is positive. Neither condition 1) nor condition 2) on its own is sufficient to determine this.

Considering both conditions 1) & 2) together yields b^2-4ac > 0 since b^2 ≥ 0 and ac < 0.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

x=?

1) x^3+x^2+x=0
2) x=-2x

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
x^3+x^2+x=0
=> x(x^2+x+1)=0
=> x = 0 since x^2+x+1 ≠ 0
Condition 1) is sufficient.

Condition 2)
x = -2x
=> 3x = 0
=> x = 0
Condition 2) is 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

If n is an integer, is (n+1)^2 an even integer?

1) n-1 is an even integer
2) (n-1)^2 is an even 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.

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

(n+1)^2 is an even integer
=> n+1 is an even integer
=> n is an odd integer

Condition 1)
Since “n-1 is an even integer” is equivalent to “n is an odd integer”, condition 1) is sufficient.

Condition 2)
“(n-1)^2 is an even integer” is equivalent to “n-1 is an even integer”, which is condition 1).
Condition 2) is also 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).
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Is x<0?

1) |x|=-x
2) |x|>x

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
|x| = -x
=> x ≤ 0
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.
Since the solution set “x<0” of the question doesn’t include the solution set “x ≤ 0” of the condition 1), condition 1) is not sufficient.

Condition 2)
|x|>x
=> x < 0
Since condition 2) is equivalent to the question, condition 2) is 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

2^p/2^q=?

1) p = q + 2
2) pq=8

=>

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.

Modifying the question:
What is the value of 2^p/2^q = 2^{p-q}?
So, we need to be able to find the value of p-q.

Thus, condition 1), which is equivalent to p – q = 2, is sufficient.

Condition 2):
If p =4 and q = 2, then 2^p/2^q = 2^{p-q} = 2^2 = 4.
If p =8 and q = 1, then 2^p/2^q= 2^{p-q} = 2^7 = 128.
Since we don’t have a unique solution, condition 2) is not sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

a and b are positive numbers. What is the value of (a-b)/(a+b)?

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

=>

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.

When a question asks for a ratio, 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.

Condition 1)
a = 2b is equivalent to a/b = 2.
So, (a-b)/(a+b) = { (a/b) – 1 } / { (a/b) + 1 } = ( 2 – 1 ) / ( 2 + 1 ) = 1/3.
Condition 1) is sufficient.

Condition 2)
(a^2-b^2) / (a+b)^2 =1/3
=> (a-b)(a+b)/(a+b)^2 =1/3
=> (a-b)/(a+b) =1/3
Condition 2) is sufficient.

FYI, Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

If n is an integer, is n(n+2) divisible by 8?

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.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If n is an even integer, then n and n + 2 are two consecutive even integers.
Products of two consecutive even integers are multiples of 8 since one of them must be a multiple of 4, and the other a multiple of 2.
Condition 1) is sufficient.

Condition 2)
Since n is a multiple of 4, n + 2 is an even integer.
Thus, n(n+2) is a multiple of 8.
Condition 2) is 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

What is the perimeter of a rectangle?

1) The square of the diagonal is 52.
2) The area of the rectangle is 24.

=>

Forget conventional ways of solving math qAnswer: CAnswer: Cuestions. 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.

When we apply VA method to geometry, we need to count the number of variables. For a rectangle, we have two variables for the length and the width of the rectangle. Let x and y be the length of the width of the rectangle, respectively.

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
We have x^2+y^2 = 52 by Pythagoras’ theorem, and Area = xy = 24.
So, (x+y)^2 = x^2+2xy + y^2 = (x^2+y^2) +2xy = 52 + 48 = 100.
Therefore, x+y = 10 and we can calculate the perimeter.
Both conditions (together) are sufficient.

_________________
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Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

If x, y, z are integers, is xyz a multiple of 6?

1) x+y+z is a multiple of 6
2) x, y, and z are consecutive integers

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since x and y are two consecutive integers, one of them, x or y is an even integer, and xy is a multiple of 2.
Since x, y and z are three consecutive integers, one of them, x, y or z is a multiple of 3, and xyz is a multiple of 3.
Therefore, xyz is a multiple of 6.
Both conditions (together) 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)
If x = 1, y = 2 and z = 3, then xyz = 6 is not a multiple of 6.
If x = 2, y = 2 and z = 2, then xyz = 8 is a multiple of 8.
Since we do not have a unique answer, condition 1) is not sufficient.

Condition 2)
Using the same argument as the one given for both conditions together, condition 2) 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.
_________________
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Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

For an integer n greater than 1, the set Sn={ kn | k is an integer greater than or equal to 1} is defined. What is the value of n?

1) 2 is contained in the set Sn.
2) 4 is contained in the set Sn.

=>

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.

Condition 1)
Only S2 = { 2, 4, 6, … } includes 2.
Therefore, n = 2.
Condition 1) is sufficient.

Condition 2)
Two sets,
S2 = { 2, 4, 6, … }
S4 = { 4, 8, 12, … }
contain 4. So, n could be 2 or 4.
Since we don’t have a unique solution, condition 2) 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
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Re: Math Revolution Approach (DS)  [#permalink]

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[Math Revolution GMAT math practice question]

Is x>x/y?

1) y>1
2) xy>0

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

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

The question x>x/y is equivalent to xy(y-1) > 0 as shown below:
x>x/y
=> xy^2 > xy since y^2 > 0
=> xy^2 – xy > 0
=> xy(y – 1) > 0

Condition 1) tells us that y – 1 > 0, and condition 2) tells us that xy > 0. Thus, both conditions together are sufficient.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8456
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[Math Revolution GMAT math practice question]

When f(x)=ax^2+bx+c (a≠0), is x+1 a factor of f(x)?

1) f(1)=0
2) f(-1)=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.

x+1 is a factor of f(x) precisely when f(x) = (x+1)(ax+b) for some numbers a and b. This occurs when f(-1) = 0, but not necessarily when f(1) = 0.

Thus, only condition 2) is 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.
_________________ Re: Math Revolution Approach (DS)   [#permalink] 28 Sep 2018, 00:38

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# Math Revolution Approach (DS)

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