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# Math Revolution Approach (DS)

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
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03 Aug 2018, 01:05
[Math Revolution GMAT math practice question]

Is 0 between x and y?

1) x-y>0
2) x^2-y^2>0

=>

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

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

If we modify the question, it asks if xy < 0. Since the two conditions do not give us enough information to determine the sign of xy, both conditions together are not sufficient, and the answer is E.

Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Conditions 1) & 2)
If x = 2 and y = -1, then 0 is between x and y.
If x = 2 and y = 1, then 0 is not between x and y.
Since we don’t have a unique solution, both conditions together 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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
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GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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05 Aug 2018, 18:04
[Math Revolution GMAT math practice question]

If the average (arithmetic mean) height of Bob, John and Tom is 180 cm, what is their median height?

1) Bob’s height is 175cm.
2) John’s height is 180cm.

=>

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.

When we have 3 numbers, if one of them is equal to their average, then it is also equal to their median.

Thus, condition 2) is sufficient.

_________________
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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05 Aug 2018, 18:05
[Math Revolution GMAT math practice question]

When a positive integer n is divided by 3, what is the remainder?

1) When n is divided by 5, the remainder is 2
2) When n is divided by 6, the remainder is 2

=>

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

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

Since the divisor (6) of condition 2) is a multiple of the divisor (3) of the question, condition 2) is sufficient.

When we encounter questions related to remainders, plugging in numbers is suggested.

Condition 1)
If n = 2, then the remainder when n is divided by 3 is 2.
If n = 7, then the remainder when n is divided by 3 is 1.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
The possible values of n are
n = 2, 8, 14, 20, …
All of these values have a remainder of 2 when they are divided by 3.
Thus, condition 2) is sufficient.

_________________
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Math Revolution GMAT Instructor
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GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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08 Aug 2018, 01:09
[Math Revolution GMAT math practice question]

a, b, c, d, e and f are integers. Is their median greater than their average (arithmetic mean)?

1) a<b<c<d<e<f
2) b-a=d-c=f-e

=>

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

Since we have 6 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.

If a = 1, b = 2, c =5, d = 6, e = 7, f = 8, we have a median of 5.5 and an average of 29/6. The median is greater than the average, and the answer is “yes”.

If a = 1, b = 2, c =3, d = 4, e = 5, f = 6, we have a median of 3.5 and an average of 3.5. The median is not greater than the average, and the answer is “no”.

Since we don’t have a unique solution, both conditions are not sufficient, when considered 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.
_________________
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Math Revolution GMAT Instructor
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GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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09 Aug 2018, 00:29
[Math Revolution GMAT math practice question]

If n is a 2-digit positive integer and its tens digit is 4 times its units digit, what is the value of n?

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit 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 = 10a + b and a = 4b
The possible pairs ( a, b ) are ( 4, 1 ) and ( 8, 2 ) by the original condition.
Thus, n = 41 or n = 82.

Since we have 3 variables and 2 equations, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Condition 1)
Since a = 8, we must have n = 82.
Thus, condition 1) is sufficient.

Condition 2)
Since 4 + 1 = 5 is not a 2-digit integer and 8 + 2 = 10 is a 2-digit integer, n = 82.
Thus, 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.
_________________
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
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GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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13 Aug 2018, 05:22
[Math Revolution GMAT math practice question]

If a, b, and c are consecutive 2-digit positive integers in that order, and a+b+c is a multiple of 10, what is the value of c?

1) a is a prime number
2) c is a prime number

=>

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 a = b – 1 and c = b + 1, we have a + b + c = ( b – 1 ) + b + ( b + 1 ) = 3b is a multiple of 10 and b is a multiple of 10. Thus, the possible triples ( a, b, c ) are ( 19, 20, 21 ), ( 29, 30, 31 ), ( 39, 40, 41 ), ( 49, 50, 51 ), ( 59, 60, 61 ), ( 69, 70, 71 ), ( 79, 80, 81 ) and ( 89, 90, 91 ). Since we have 3 variables and 2 equations ( a = b – 1, c = b + 1), D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
The triples in which a is a prime number are
( 19, 20, 21 ), ( 29, 30, 31 ), ( 59, 60, 61 ), ( 79, 80, 81 ) and ( 89, 90, 91 ).
Thus, c could be 21, 31, 61, 81 or 91.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
The triples in which c is a prime number are

( 29, 30, 31 ), ( 39, 40, 41 ), ( 59, 60, 61 ), ( 69, 70, 71 ) and ( 89, 90, 91 ).
Thus, c could be 31, 41, 61, 71 or 91.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2):
The triples in which both a and c are prime numbers are:
( 29, 30, 31 ), ( 59, 60, 61 ) and ( 89, 90, 91 ).
Thus, c could be 31, 61 or 91.
Since we don’t have a unique solution, both conditions are not sufficient, when considered 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.
_________________
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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS)  [#permalink]

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13 Aug 2018, 05:25
[Math Revolution GMAT math practice question]

x ≠ 0. Is x^2>x^4?

1) x^2<1
2) x^2<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.

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

x^2>x^4
=> x^4 - x^2 < 0
=> x^2 ( x^2 – 1 ) < 0
=> ( x^2 – 1 ) < 0
=> ( x + 1 )( x – 1 ) < 0
=> -1 < x < 1

This is equivalent to condition 1).
Thus, condition 1) is sufficient.

Condition 2)
x^2<2x
=> x^2 - 2x < 0
=> x(x – 2) < 0
=> 0 < x < 2

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
However, the solution set of the question -1 < x < 1 does not include the solution set of the condition, 0 < x < 2. Thus, condition 2) is not sufficient.

_________________
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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15 Aug 2018, 06:45
[Math Revolution GMAT math practice question]

If the average (arithmetic mean) of 3 integers x, y, z is 10, what is the value of z?

1) x=1
2) x=5-y

=>

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

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

The original condition gives ( x + y + z ) / 3 = 10 or x + y + z = 30. Rearranging yields z = 30 – ( x + y ). Condition 2) gives x + y = 5, so condition 2) is sufficient .

Condition 1) is not sufficient since it gives no information about the value of y.

_________________
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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16 Aug 2018, 07:49
[Math Revolution GMAT math practice question]

Is ab>bc?

1) abc=0
2) a>c

=>

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.

When we modify the question, ab > bc is equivalent to ab – bc > 0 or b(a-c) > 0. Even though we know a – c > 0 from condition 2), we don’t know if b is positive or negative. Thus, both conditions together are not sufficient.

Conditions 1) & 2):
If a = 1, b =1 and c = 0, then ab > bc and the answer is ‘yes’.
If a = 1, b =-1 and c = 0, then ab < bc and the answer is ‘no’.
Since we don’t have a unique solution, both conditions together are not sufficient.

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

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17 Aug 2018, 01:27
[Math Revolution GMAT math practice question]

What is the remainder when 2^n is divided by 10?

1) n is a positive multiple of 2
2) n is a positive multiple of 4

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

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

The remainder when 2^n is divided by 10 is the units digit of 2^n.

Now, 2^1 = 2, 2^2 = 4, 2^3 = 8, 2^4 = 16, and 2^5 = 32.
So, the units digits of 2^n have period 4:
They form the cycle 2 -> 4 -> 8 -> 6.
Thus, 2^n has the units digit of 6 when n is a multiple of 4.
Condition 2) is sufficient.

Condition 1)
If n = 4, then 2^n = 2^4 = 16 has the units digit of 6.
If n = 2, then 2^n = 2^2 = 4 has the units digit of 4.
Since we don’t have a unique solution, condition 1) is not sufficient.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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19 Aug 2018, 17:42
[Math Revolution GMAT math practice question]

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

1) y=x+1 and z=x+3
2) x, y, and z are prime 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.

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 y = x + 1, z = x + 3 and x, y, z are prime numbers, the only possibility is that x = 2, y = 3, and z = 5 because if x is an odd number, then y and z are two different even numbers, which cannot both be prime numbers.
Thus, 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)
There are many different possible values for x, y and z, including x = 1, y = 2, z = 4 and x = 2, y = 3, z = 5. Therefore, we don’t have a unique solution, and condition 1) is not sufficient.

Condition 2)
There are many different possibly values for x, y and z, including x = 2, y = 3 and z = 5, and x = 3, y = 5 and z = 7. So, we don’t have a unique solution, and condition 2) is 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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GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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19 Aug 2018, 17:44
[Math Revolution GMAT math practice question]

Is n an integer?

1) 3n is an integer
2) 4n 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.

Condition 1)
If n = 1, the answer is ‘yes’.
If n = 1/3, the answer is ‘no’.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
If n = 1, the answer is ‘yes’.
If n = 1/4, the answer is ‘no’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
Since n = 4n – 3n is a difference of two integers, n is also an integer.
Conditions 1) and 2) are sufficient, when considered 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.
_________________
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Re: Math Revolution Approach (DS)  [#permalink]

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22 Aug 2018, 00:43
[Math Revolution GMAT math practice question]

If (|x|-2)(x-1)=0, then x=?

1) x>0
2) -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.

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

Original condition:
(|x|-2)(x-1)=0
=> |x| = 2 or x = 1
=> x = 2, x = -2 or x = 1

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)
By condition 1) (x > 0), the possible solutions are x = 1 and x = 2.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
By condition 2) (-1≤x≤1), the only possible solution is x = 1.
Since we have a unique solution, condition 2) is sufficient.

_________________
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Re: Math Revolution Approach (DS)  [#permalink]

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23 Aug 2018, 01:10
[Math Revolution GMAT math practice question]

If x and y are prime numbers, how many factors has x^2y^2?

1) xy=10
2) x+y is odd

=>

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.

If x and y are different prime numbers, then xy has (2+1)(2+1) = 9 factors.
If x and y are the same prime number, then xy has 4+1 = 5 factors.

Condition 1)
Since x and y are prime numbers and xy = 10, either x = 2 and y = 5, or x = 5 and y = 2.
So, x and y are different prime numbers. Thus, condition 1) is sufficient.

Condition 2)
Since x and y are prime numbers and x + y is odd, one of them is even and the other one is odd.
So, x and y are different prime numbers. Thus, condition 2) is sufficient.

_________________
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Re: Math Revolution Approach (DS)  [#permalink]

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23 Aug 2018, 23:51
[Math Revolution GMAT math practice question]

If x and y are integers, is x^3+3x-y an even number?

1) x=11
2) y=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.

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

x^3+3x is always even number, regardless of the value of x. If y is even, then x^3+3x-y is an even number, and if y is odd, then x^3+3x-y is odd.

Thus, condition 2) is sufficient.

Condition 1) is not sufficient since it tells us nothing about the value of y.

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Re: Math Revolution Approach (DS)  [#permalink]

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26 Aug 2018, 17:21
[Math Revolution GMAT math practice question]

What is the length of the sides of a given cube?

1) The surface area of the cube is 150
2) The volume of the cube is 125

=>

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 a cube is uniquely determined by its side length, we have only one variable. So, we should consider each of the conditions on their own first.

Condition 1)
Let x be the side-length of the cube. Then condition 1) tells us that 6x^2 = 150. Solving this equation yields x = 5.
Condition 1) is sufficient.

Condition 2)
Let x be the side-length of the cube. Then condition 2) tells us that x^3 = 125. Solving this equation yields x = 5.
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.
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Re: Math Revolution Approach (DS)  [#permalink]

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26 Aug 2018, 17:22
[Math Revolution GMAT math practice question]

Is x|y|=|xy|?

1) x>0
2) y>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.

Modifying the question:
x|y|=|xy|
=> x|y|-|xy| = 0
=> x|y|-|x||y| = 0
=> |y|(x-|x|) = 0
=> |y|=0 or x-|x| = 0
=> y=0 or x=|x|
=> y=0 or x≥0

Condition 1) is sufficient.
Condition 2) is not sufficient since it tells us nothing about the value of x.

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Math Revolution GMAT Instructor
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Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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29 Aug 2018, 00:53
[Math Revolution GMAT math practice question]

If m and n are integers greater than 1, is m^n>500?

1) n>8
2) n>2m

=>

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.

If a question states “greater than”, then we should find the minimum value because all data are greater than the minimum. Considering condition 1), the minimum value is m^n=2^9=512>500, so the answer is ‘yes’ and condition 1) is sufficient.

Condition 2)
If m = 2, n = 100, then 2^{100} > 500 and the answer is ‘yes’.
If m = 2, n = 5, then 2^5 = 32 < 500 and the answer is ‘no’.
Thus, condition 2) is not sufficient, since we don’t have a unique solution.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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29 Aug 2018, 23:50
[Math Revolution GMAT math practice question]

Is xy>0?

1) x+y>0
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)
If x = 1/2 and y = 1/4, then xy > 0 and the answer is ‘yes’.
If x = 1/2 and y = -(1/4), then xy < 0 and the answer is ‘no’.

Since the answer is not unique, both conditions are not sufficient, when taken together.

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Math Revolution GMAT Instructor
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Posts: 8987
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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31 Aug 2018, 00:11
[Math Revolution GMAT math practice question]

Does x^2+px+q = 0 have a root?

1) p<0
2) q<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 discriminant of the equation is p^2 – 4q. If the discriminant is greater than or equal to zero, then the quadratic equation has roots.
The question asks if p^2-4q ≥ 0 or not.

Since p^2 ≥ 0, if q < 0, then p^2-4q ≥ 0. Thus, condition 2) is sufficient.

Condition 1)
If p = -1 and q = 0, then the discriminant is positive and the equation has 2 roots, which are 0 and 1. So, the answer is ‘yes’.
If p = -1 and q = 1, then the discriminant is negative and the equation has no real roots. So, the answer is ‘no’.
Since we don’t have a unique solution, condition 1) is not sufficient.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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Re: Math Revolution Approach (DS)   [#permalink] 31 Aug 2018, 00:11

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# Math Revolution Approach (DS)

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