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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

The symbol ⊙ represents one of the operations: addition, subtraction, multiplication, and division. Is 2⊙2=4？

1) 1⊙1=1
2) (-1) ⊙ (-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, and then recheck the question.
Since only 2 + 2 = 4 and 2 * 2 = 4, the question asks if ⊙ is addition or multiplication.
Condition 1)
Since 1 * 1 = 1 and 1 / 1 = 1, ⊙ is multiplication or division.
Condition 1) is not sufficient.
Condition 2)
Since (-1) – (-1) = 0, ⊙ is subtraction. The answer is “no”.
CMT1 states that “no” is also an answer.
Condition 2) is sufficient.

Therefore, the answer is B.
Answer: B
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Working alone at its constant rate, machine A can produce 240 pins in x hours. Working alone at its constant rate, machine B can produce 240 pins in y hours. How many hours will it take machines A and B to produce 240 pins, when working together at their respective constant rates?

1) xy/(x+y)=4
2) x=20

=>
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, and then recheck the question.

We have 1/t = 1/x + 1/y = (x+y)/xy or t = xy/(x+y), where t is the time that machines A and B take to produce 240 pins, when working together. The question asks for xy / (x+y).

Thus, only condition 1) is sufficient. Condition 2) is not sufficient as it only gives us information about x.
Therefore, the answer is A.
Answer: A
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

The cost, c and the revenue, r are related via the equation c =ar+b. By how much is the cost increased if the revenue is increased by \$10?

1) a=0.5
2) b=5

=>

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

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

The equation c = ar + b tells us that the cost is increases by \$a when the revenue is increases by \$1.
It follows that the cost is increases by \$10a when the revenue is increases by \$10. So, the question is asking for the value of a.

The answer is A.
Answer: A
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If x and y are integers greater than 1 and x>y, what is the value of x?

1) x+y=10
2) xy=21

=>
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) and 2) together first.

Conditions 1) and 2):
y = 10 – x and xy= x(10-x) = 21
⇔ -x^2 + 10x = 21
⇔ x^2 - 10x + 21 = 0
⇔ (x-3)(x-7) = 0
⇔ x = 3 and y = 7, or x = 7 and y = 3.
Since x > y, we must have x = 7 and y = 3.
Thus x = 7, and conditions 1) and 2) are sufficient, when taken together.

Since this is an integer question (one of the key question areas), we should also consider choices A and B by CMT 4(A).
Condition 1)
There are two possible solutions: x = 6 and y = 4, and x = 7 and y = 3.
Since the solution is not unique, condition 1) is not sufficient.
Condition 2):
Either x = 3 and y = 7, or x = 7 and y = 3.
Since x > y, x = 7 and y = 3.

Thus, we have the unique solution, x = 7.
Therefore, condition 2) is sufficient.

Therefore, B is the answer.

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.

Answer: B
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is x^3-x^2+x<0?

1) x < 0
2) x^5+x<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, and then recheck the question.

Modifying the question:
x^3-x^2+x<0
⇔ x(x^2-x+1)<0
⇔ x<0 since x^2-x+1>0 always.
So, the question becomes, ‘is x<0?’.

Condition 1) is certainly sufficient.

Condition 2), x^5+x<0, is equivalent to x(x^4+1)<0 or x < 0, since x^4+1 > 0 is always true. So, condition 2) is also sufficient.

Therefore, D is the answer.
Answer: D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If x>y>0, is y<2?

1) 1/x = 1/2
2) (1/x)+(1/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 1 equation ( x > y ), D is most likely to be the answer.

Condition 1)
1/x = 1/2 implies that x = 2. Since x > y, we must have y < 2.
Condition 1) is sufficient.

Condition 2)
The original condition x > y > 0 implies that 1/x < 1/y.
Using 1/x + 1/y = 1 and 1/x < 1/y together, we can see that 1/y > 1/2.
Thus, 0 < y < 2.
Condition 2) is sufficient.

Therefore, the answer is D.
Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can’t figure out condition 2), you should choose D as the answer.

Answer: D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If x>y, is x^2>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, and then recheck the question.

Modifying the question:
x^2>xy
⇔ x^2-xy > 0
⇔ x(x-y) > 0
⇔ x > 0 since x > y (which implies that x – y > 0).
So, the question is equivalent to asking ‘is x > 0?’.

Since condition 1) is same as the modified question, it is sufficient.

Condition 2):
Since x > y, condition 2) (y > 0) implies that x > 0.
Condition 2) is also sufficient.

Therefore, the answer is D.

Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can’t figure out condition 2), you should choose D as the answer.
Answer: D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If w^2x^3y^4z^5<0, is xyz>0?

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, and then recheck the question.

Modifying the original condition and question:
The original condition w^2x^3y^4z^5<0 is equivalent to xz<0 since we can ignore terms with even exponents in this type of inequality (they are always positive).

Under the modified condition xz < 0, the question, ‘is xyz > 0?’ is equivalent to ‘is y < 0?’, which is the same as condition 2).

Since condition 1) tells us nothing about the sign of y, the answer is B.

Therefore, the answer is B.
Answer: B
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If xy≠0, is |x|>|y|？

1) x=-4y
2) x=y3

=>

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) and 2) together first.

Conditions 1) and 2):
Since x = -4y and x = y^3, |x| = |-4y| = 4|y| and |x| = |y^3| = |y|^3.
It follows that 4|y| = |y|^3.
Now,
4|y| = |y|^3 ⇔ |y|^3 – 4|y| = 0
⇔ |y|(|y|^2- 4) = 0
⇔ |y|(|y|+2)(|y|-2) = 0.
Since |y| ≠0 and |y| ≠-2, this implies that |y| = 2.
It follows that |x| = 4*2 = 8.
So, |x| > |y|, and both conditions together are sufficient.

Since this is an absolute value 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)
Since |x| = |-4y| = 4|y| and xy≠0, |x| = 4|y| > |y|.
Condition 1) is sufficient.

Condition 2)
If x = 8, then y = 2, and the answer is ‘yes’.
If x = 1, then y = 1, and the answer is ‘no’.
Since we have obtained two different answers, condition 2) is not sufficient by CMT 2.

Therefore, A is the answer.

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.
Answer: A
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If xy>0, is x^3y^4>0?

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, and then recheck the question.

Modifying the question:
x^3y^4>0
⇔ x>0
since y^4>0 is always true. We can ignore even exponents in inequalities that have 0 on one side.
So, the question becomes, ‘is x>0?’.

Condition 1) is certainly sufficient.

Condition 2):
x > 0 since y > 0 and xy > 0. Thus, condition 2) is also sufficient.

Therefore, D is the answer.

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).

Answer: D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

When a≠0, how many solutions does the equation a(x+b)^2+c=0 have?

1) bc=0
2) |b|+|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, and then recheck the question.

There are three cases to consider:
Case 1: a > 0, c > 0 or a < 0, c < 0
The equation has no roots.

Case 2: c = 0.
The equation has only one root.

Case 3: a > 0, c < 0 or a < 0, c > 0
The equation has two roots.

Condition 1):
If bc = 0, then when
a = 1, b = 0, c = -1, the equation has two roots, and when
a = 1, b = 0, c = 0, the equation has one root.
As the question does not have a unique answer, condition 1) is not sufficient.

Condition 2)
|b| + |c| = 0 ⇔ b = c = 0.
Since c = 0, the equation has only one root.
Condition 2) is sufficient.

Therefore, the answer is B.

Answer: B

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is x|y|=xz?

1) x, y, and z are positive
2) y^2=z^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, and then recheck the question.

Modifying the question:
x|y| = xz
⇔ x(|y|-z) = 0
⇔ x = 0 or |y| = z
⇔ x = 0 or y = z or y = -z

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.

Conditions 1) & 2):

Condition 2) tells us that y = z or y = -z.
Since condition 1) states that x, y, z > 0, we can only have y = z.
Thus, both conditions are sufficient, when taken together.

Therefore, the answer is C.

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.
Answer: C
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is the positive integer x an even number?

1) The smallest prime factor of x is 3.
2) The greatest prime factor of x is 17.

=>

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 first consider each condition on its own.

Condition 1)
Since all prime factors of x are greater than or equal to 3, 2 is not a prime factor of x, and x is not an even number.
The answer is ‘no’.
This condition is sufficient by CMT (Common Mistake Type) 1, which tells us that the unique answer ‘no’ also means that the condition is sufficient.

Condition 2)

If x = 2*17 = 34, then the answer is ‘yes’.
If x = 17, then the answer is ‘no’.
Since we do not have a unique answer, condition 2) is not sufficient.

Therefore, the answer is A.
Answer: A
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If x, y, and z are positive integers, is x+y divisible by 2?

1) x+z is divisible by 2
2) y+z is divisible by 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.

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) and 2) together first.

Conditions 1) and 2):
There are two cases to consider.
Case 1: If x, y, and z are all even, then the answer is ‘yes’
Case 2: If x, y, and z are all odd, then the answer is also ‘yes’
Since no other cases are possible, both conditions are sufficient, when taken together.

Since this 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)
Since it tells us nothing about y, condition 1) is not sufficient.

Condition 2)
Since it tells us nothing about y, condition 2) is not sufficient.

Therefore, C is the answer.

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.

Answer: C
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is n<0?

1) n-1<0
2) |3-n| > |n+5|

=>

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

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) : n - 1 < 0 ⇔ n < 1
Since the range of the question, n < 0 does not include that of the condition 1), n < 1, the condition 1) is not sufficient.

Condition 2) :
|3-n| > |n+5|
⇔ |3-n|^2 > |n+5|^2
⇔ (3-n)^2 > (n+5)^2
⇔ n^2 -6n + 9 > n^2 +10n + 25
⇔ -16 > 16n
⇔ n < -1
Since the range of the question includes that of the condition 2), the condition 2) is sufficient.

Therefore, B is the answer.

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.

Answer: B
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is x^2-x>0?

1) x>0
2) x^3+x>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, and then recheck the question.

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

Modifying the question:
x^2-x>0
⇔ x(x-1) > 0
⇔ x < 0 or x > 1 by the “LLGG” rule.

Condition 1): x > 0
Since the solution set of the question includes the solution set of condition 1), condition 1) is sufficient.

Condition 2):
x^3+x>0
⇔ x(x^2+1)>0
⇔ x>0, since x^2+1 > 0 is always true.
Condition 2) is equivalent to the question, so it is sufficient.
Therefore, the answer is 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.

Answer: D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is xy< -(x/y)?

1) xy<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, and then recheck the question.

Modifying the question:
xy < -(x/y)
⇔ xy^3 < -xy (multiplying both sides by y^2)
⇔ xy^3 + xy < 0
⇔ xy(y^2+1) < 0
⇔ xy < 0 since y^2+1 > 0

Condition 1): xy < 0
Condition 1) is same as the question.
This condition is sufficient.

Condition 2):
Since this condition tells us nothing about x, it is not sufficient.

Therefore, the answer is 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.
Answer: A
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is x^y<1?

1) x>1
2) 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.

Conditions 1) & 2):
If x = 4 and y = -1, then xy = 1/4 < 1, and the answer is ‘yes’.
If x = 4 and y = ½, then xy = 2 > 1, and the answer is ‘no’.

Since we don’t have a unique answer, both conditions are not sufficient when taken together by CMT (Common Mistake Type) 2.

Therefore, the answer is 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.
Answer: E
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is the positive integer x divisible by 60?

1) x is divisible by 6
2) x is divisible by 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, and then recheck the question.
The question asks if x = 60t for some integer t.
x = 60t
⇔ x = 2^2*3*5*t

Conditions 1) (x = 2*3m for some integer m) and 2) (x = 2*5n for some integer n) do not tell us whether 2^2 is a factor of x. So, they are not sufficient, when taken together. For example, if
x = 60, then the answer is ‘yes’, but if
x = 30, then the answer is ‘no’.

Both conditions together are not sufficient, as the question does not have a unique answer.

Therefore, E is the answer.

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.

Answer: E
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7752
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

What is the value of (x+3y)/(3x-y)?

1) x-2y = 1
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.

When the question asks for a ratio, a fraction, a percent, a proportion or a rate, if one of conditions provides a ratio and the other condition provides a number, the condition with a ratio could be sufficient.

This question asks for a ratio.
Condition 1) provides a number and condition 2) provides the ratio, x/y = 2.
Thus, condition 2) is likely to be sufficient.

Condition 1) :
If x = 3 and y = 1, then (x+3y)/(3x-y) = 6/8 = 3/4
If x = 5 and y = 2, then (x+3y)/(3x-y) = 16/13
Since we do not obtain a unique answer, condition 1) is not sufficient.

Condition 2) :
Since x = 2y, (x+3y)/(3x-y) = 5y/5y = 1.
Condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
_________________ Re: Math Revolution Approach (DS)   [#permalink] 07 Feb 2018, 00:45

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