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Math Revolution Approach (DS)

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New post 02 Sep 2018, 18:46
[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.

Therefore, E is the answer.
Answer: E

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: Math Revolution Approach (DS)  [#permalink]

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New post 02 Sep 2018, 18:48
[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
9.3.png [ 11.02 KiB | Viewed 122 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.

Therefore, E is the answer.

Answer: E

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: Math Revolution Approach (DS)  [#permalink]

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New post 05 Sep 2018, 02:20
[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.

Therefore, A is the answer.

Answer: A

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: Math Revolution Approach (DS)  [#permalink]

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New post 06 Sep 2018, 01:32
[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.

Therefore, E is the answer.

Answer: E
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.
_________________

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]

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New post 07 Sep 2018, 01:17
[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.

Therefore, D is the answer.
Answer: D
_________________

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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]

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New post 09 Sep 2018, 18:24
[Math Revolution GMAT math practice question]

Attachment:
9.8.png
9.8.png [ 2.42 KiB | Viewed 82 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
9.10.png [ 13.33 KiB | Viewed 81 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.

Therefore, E is the answer.
Answer: E

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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
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Math Revolution GMAT Instructor
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Re: Math Revolution Approach (DS)  [#permalink]

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New post 09 Sep 2018, 18:26
[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.
Therefore, D is the answer.

Answer: D


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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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"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
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Joined: 16 Aug 2015
Posts: 6205
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: Math Revolution Approach (DS)  [#permalink]

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New post 12 Sep 2018, 02:39
[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

Therefore, A is the answer.
Answer: A
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
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Posts: 6205
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Re: Math Revolution Approach (DS)  [#permalink]

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New post 13 Sep 2018, 01:35
[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.

Therefore, C is the answer.
Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
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"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 6205
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Re: Math Revolution Approach (DS)  [#permalink]

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New post 14 Sep 2018, 00:38
[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.

Therefore, D is the answer.
Answer: D

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.
_________________

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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"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6205
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: Math Revolution Approach (DS)  [#permalink]

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New post 16 Sep 2018, 18:29
[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.

Therefore, D is the answer.

Answer: D

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).
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6205
GMAT 1: 760 Q51 V42
GPA: 3.82
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Re: Math Revolution Approach (DS)  [#permalink]

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New post 16 Sep 2018, 18:30
[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.

Therefore, B is the answer.

Answer: B

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.
_________________

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) &nbs [#permalink] 16 Sep 2018, 18:30

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