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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
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[GMAT math practice question]

If n is a positive integer, is 91 a factor of n?

1) 91 is a factor of n^2
2) 91 is a factor of 2n

=>

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)
Since 91 = 7*13, n^2 is a multiple of both 7 and 13. Since 7 and 13 are prime numbers, n must be a multiple of both 7 and 13.
Condition 1) is sufficient.

Condition 2)
If 91 is a factor of 2n, then 91k = 2n for some integer k. Since 91 is odd, k must be an even integer. Write k = 2a, for some integer a. Then
2n = 91*2a. It follows that n = 91*a.
Thus, n is a multiple of 91.
Condition 2) is sufficient.

This is a CMT(Common Mistake Type) 4(B) question. Condition 2) is easy to understand and condition 1) is difficult to figure out. If you are unable to figure out condition 2), you should choose D as the answer.

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: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
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[GMAT math practice question]

If x and y are integers, is 4x^2-y2 an odd number?

1) x is an odd number
2) y is an odd 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, and then recheck the question.

Modifying the question:
In order for 4x^2 – y^2 to be odd, y^2 must be odd since 4x^2 is always even. This is equivalent to y being odd. So, the question asks if y is odd. Thus, the answer is B.

Condition 1)
If y is an odd number, then both 2x + y and 2x – y are odd numbers and (2x+y)(2x-y) is an odd number.
If y is an even number, both 2x + y and 2x – y are even numbers and (2x+y)(2x-y) is an even number.
Since the question does not have a unique answer, condition 1) is not sufficient.

Therefore, the answer is B.

Answer: B

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
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, is x^2+11x+13y an even number?

1) x=11
2) y=13

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

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

Now, x^2+11x+13y = x(x+11)+13y. As x(x+11) is always an even integer (one of x and x + 11 must be even), x^2+11x+13y is even precisely when 13y is even. This is equivalent to y being even, so the question can be restated as ‘Is y an even number?’.

Condition 1)
If x = 11 and y = 1, then x^2+11x+13y = 255 is an odd integer.
If x = 11 and y = 2, then x^2+11x+13y = 268 is an even integer.
Since the question does not have a unique answer, condition 1) is not sufficient.

Condition 2)
If y = 13, then y is odd, and the answer to the question is ‘no’.
Condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
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 numbers, is xy+z > x+yz?

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 3 variables (x and y) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
xy + z > x + yz
⇔ xy – x – yz + z > 0
⇔ x(y-1)-z(y-1) > 0
⇔ (x-z)(y-1) > 0
⇔ x – z > 0 since y > 1.

If x = 2, y = 2, and z = 1, then xy + z = 5, x + yz = 4 and xy + z > x + yz. So, the answer is ‘yes’.
If x = 2, y = 2, and z = 3, then xy + z = 7, x + yz = 8 and xy + z < x + yz. So, the answer is ‘no’.
Since the question does not have a unique answer, both conditions together are not sufficient.

Therefore, E is the answer.

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: E
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is xy<15?

1) x<-3
2) y<-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 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):
Since x < -3 and y < -5, we have xy > 15, and the answer is ‘no’.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, both conditions are sufficient, when used together.

Since this is an inequality question (one of the key question areas), we should also consider choices A and B by CMT(Common Mistake Type) 4(A).

Condition 1)
This condition provides us with no information about the variable y, so it is not sufficient:
If x = -4 and y = 1, then xy = -4 < 15, and the answer is ‘yes’.
If x = -4 and y = -5, then xy = 20 > 15, and the answer is ‘no’.
Since we do not obtain a unique answer, this condition is not sufficient.

Condition 2)
This condition provides us with no information about the variable x, so it is not sufficient:

If x = 1 and y = -5, then xy = -5 < 15, and the answer is ‘yes’.
If x = -4 and y = -5, then xy = 20 > 15, and the answer is ‘no’.
Since we do not obtain a unique answer, this condition is not sufficient.

Therefore, C is the answer.

Answer: C

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: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
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[GMAT math practice question]

Events E and F are independent. Is the probability that both events E and F will occur less than 0.6?

1) The probability that event E will occur is 0.4.
2) The probability that event F will occur is 0.5.

=>

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 definition of independent events E and F is P(E∩F) = P(E)P(F).
The question asks if P(E)P(F) < 0.5.

Since we have 2 variables (P(E) and P(F)) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
P(E ∩F) = P(E)P(F) = 0.4 * 0.5 = 0.2 < 0.6.
Thus, both conditions together are sufficient.

Since this is a probability question (one of the key question areas), we should also consider choices A and B by CMT(Common Mistake Type) 4(A).

Condition 1):
Since P(E) = 0.4 and P(F) ≤ 1, P(E ∩F) = P(E)P(F) ≤ 0.4 * 1 = 0.4 < 0.6.
Condition 1) is sufficient on its own.

Condition 2):
Since P(E) ≤ 1 and P(F) = 0.5, P(E ∩F) = P(E)P(F) ≤ 1 * 0.5 = 0.5 < 0.6.
Condition 2) is sufficient on its own.

Therefore, the answer is D.

Answer: D

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: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If the average (arithmetic mean) of set A is 100 and the average (arithmetic mean) of set B is 100, what is the range of sets A and B combined?

1) The range of set A is 20.
2) The range of set B is 30.

=>

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.

There is no relationship between the average of a set and its range.
In addition, there is no way of determining the range of a set from the ranges of its subsets. Notice that “E” is in “no rElation”. Many questions about “relation” have the answer E.
Thus, E is likely to be the answer.

We can verify this by considering both conditions together:
If A = { 90, 110 } and B = { 85, 115 }, then the range of A∪B={85,90,110,115} is 30.
If A = { 90, 110 } and B = { 92, 93, 95, 98, 122 }, then the range of A∪B={ 90, 92, 93, 95, 98, 110, 122 } is 32.
Since the range of A∪B is not uniquely determined, both conditions together are not sufficient.

Therefore, the answer is E.
Answer: E
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
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[GMAT math practice question]

What is the value of the positive integer k?

1) When k is divided by 3, the remainder is 2.
2) When k is divided by 5, the remainder is 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 1 variable (k) 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):
Two possible values of k which satisfy condition 1) are 5 and 8.
Since it does not give us a unique value of k, condition 1) is not sufficient.

Condition 2):
Two possible values of k which satisfy condition 2) are 1 and 6.
Since it does not give us a unique value of k, condition 2) is not sufficient.

Conditions 1) & 2):
Two possible values of k which satisfy both conditions 1) & 2) are 11 and 26.
Since they do not give us a unique value of k, conditions 1) & 2) together are not sufficient.

Therefore, E is the answer.

Answer: E
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

Is n an even number?

1) n(n+1) is an even number
2) n(n+2) is an even 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.

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):
All integers satisfy condition 1) since n(n+1) is the product of two consecutive integers:
If n = 1, n(n+1) = 1*2 = 2 is an even number, but n is odd, so the answer is ‘no’.
If n = 2, n(n+2) = 2*3 = 6 is an even number and n is even, so the answer is ‘yes’.
Since we do not have a unique answer, condition 1) is not sufficient.

Condition 2)
The product of two integers can only be even if at least one of them is even. Since n and n+2 must both be even, or both be odd, n must be even.
Thus, 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

The lengths of two sides of a certain triangle are 3 and 9. What is the length of the 3rd side of the triangle?

1) The perimeter of the triangle is 20
2) The length of the 3rd side of the triangle 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.

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

Assume x is the length of the 3rd side of the triangle.
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.

Note:
Since (using the triangle inequality) x > 9 + 3 = 12 and x < 9 – 3 = 6, we have 6 < x < 12.

Condition 1)
x + 3 + 9 = 20
Thus x = 8.
Condition 1) is sufficient.

Condition 2)
The only integer between 6 and 12 that is a multiple of 4 is 8.
Thus, x = 8.
Condition 2) is sufficient, too.

In addition, since conditions 1) and 2) are similar, D is most likely to be the answer.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

If uv<0, is u^99v^100<0?

1) u<0
2) v>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 an inequality that has the right-hand side equal to 0, even exponents can be ignored.
Asking if u^99v1^00<0 is equivalent to asking if u < 0: simply divide both sides by u^98v^100 (> 0). We only need to consider the variables with odd exponents. Since the exponent of u is 99, which is an odd number, we must have u < 0. In addition, since uv < 0 by the original condition, u < 0 implies that v > 0. Thus, condition 1) is equivalent to condition 2), and D is most likely to be the answer by Tip 1).

Therefore, the answer is D.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

The average (arithmetic mean) of 5 numbers is 10. If 3 of the 5 numbers are removed, is the average (arithmetic mean) of the remaining 2 numbers less than 10?

1) Each of the 3 numbers removed is greater than 10
2) The average of the 3 numbers removed is greater than 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.

Let the five numbers be x1, x2, x3, x4 and x5. Then their average (arithmetic mean) is
( x1 + x2 + x3 + x4 + x5 ) / 5 = 10
⇔ x1 + x2 + x3 + x4 + x5 = 50
Assume the numbers to be removed are x1, x2, and x3.

Since we have 5 variables (x1, x2, x3, x4, x5) and 1 equation, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Condition 1) & 2):
Since x1, x2 and x3 are greater than 10 and x1 + x2 + x3 > 30, we have x4 + x5 < 20 or ( x4 + x5 ) / 2< 10.
Both conditions together are sufficient.

Since this is a statistics problem (one of the key question areas), we should also consider choices A and B by CMT (Common Mistake Type) 4(A).

Condition 1)
Since x1, x2 and x3 are greater than 10, we have x1 + x2 + x3 > 30. So, x4 + x5 < 20 or ( x4 + x5 ) / 2< 10.
Condition 1) is sufficient.

Condition 2)
Since ( x1 + x2 + x3 ) / 3 > 10, we have x1 + x2 + x3 > 30, and x4 + x5 < 20 or ( x4 + x5 ) / 2< 10.
Condition 2) is sufficient, too. In addition, since condition 1) is equivalent to condition 2), D is most likely to be the answer by Tip 1).

Therefore, the answer is D.

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: D
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

A data set contains 5 values: 11, 13, 15, 19, and x. What is the value of x?

1) The median of the 5 values is 15
2) The range of the data set is 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.

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.

Note: if the question doesn’t include the phrase, “in increasing order”, then x could be any number. In particular, it could be greater than or less than 19.

Attachment: 2.23.png [ 810 Bytes | Viewed 302 times ]

Condition 1):
Since the median is 15, we only know that x ≥ 15.
Condition 1) is not sufficient.

Condition 2):
Since the range of the values is 8, we have 11 ≤ x ≤ 19.
Condition 2) is not sufficient.

Conditions 1) & 2):
Both conditions 1) & 2) together yield 15 ≤ x ≤ 19. But this does not tell us the exact value of x. We do not have a unique solution.
Thus, both conditions together are not sufficient.

Therefore, E is the answer.

Answer: E
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
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 7?

1) x+z is divisible by 7
2) y+z is divisible by 7

=>

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.

Conditions 1) & 2):
If x = 7, y = 7, and z = 7, the answer is ‘yes’, since x + y = 14 is divisible by 7.
If x = 1, y = 1, and z = 6, the answer is ‘no’, since x + y = 2 is not divisible by 7.
Thus, conditions 1) and 2) together are not sufficient.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

For positive integer m and n, is 2m/3n an integer?

1) m is a multiple of 3
2) n is a multiple of 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 2 variables (m and n) 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):
m = 3, n = 2: 2m/3n = 6/6 = 1 is an integer.
m = 3, n= 4: 2m/3n = 6/12 = 1/2 is not an integer.

Since we don’t have a unique solution, both conditions together are not sufficient.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
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 number of factors of a positive integer n?

1) n is a multiple of 7
2) n 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.

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 = 7 : The number of factors of n is 2.
n = 14 : The number of factors of n is 4.
Since the answer is not unique, condition 1) is not sufficient.

Condition 2)
n = p^1, where p is a prime number.
The number of factors on n is 1 + 1 = 2.
Thus, condition 2) is sufficient.

Therefore, the answer is B.

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.
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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
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+y?

1) x+y is between 50 and 60
2) x and y 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 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 = 23, y = 29 : x + y = 52
x = 23, y = 31 : x + y = 54

Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, the answer is E.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

When n is divided by 5, what is the remainder?

1) When n is divided by 3, the remainder is 2
2) When n+1 is divided by 5, the remainder is 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.

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.
It is suggested we plug in numbers for the remainder questions.

Condition 1): n=3p+2=2,5,8……..
n = 2 : The remainder of n is 2 when it is divided by 5.
n = 5 : The remainder of n is 0 when it is divided by 5.

Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2):
We have n + 1 = 5q + 3 for some integer, since n + 1 has the remainder 3 when it is divided by 5.
It is equivalent to n = 5q + 2=2,7,12,17,….
The remainder is 2 when n is divided by 5.
Thus 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Math Revolution Approach (DS)  [#permalink]

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[GMAT math practice question]

For the integers x and y, if xy is a multiple of 25, is y a multiple of 5?

1) x-y is a multiple of 5
2) x is a multiple of 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.

Since xy = 25 =5^2, x is a multiple of 5 or y is a multiple of 5. If x is a multiple of 5, y = x – 5 is also a multiple of 5. Thus the condition 1) is sufficient.

Condition 2)
Since we don’t have any information from the condition 2), it is not sufficient.

Therefore, A is the answer.

Answer: A
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7728
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 <0?
1) x is positive
2) y 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.

Question:
x^y <0
⇔ x < 0 and y is an odd integer.

Condition 1)
Since x > 0, x^y > 0, regardless of the value of y.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
If x = -1 and y = 3, x^y = (-1)^3 = -1 < 0, and the answer is ‘yes’.
If x = -1 and y = 2, x^y = (-1)^2 = 1 > 0, and the answer is ‘no’.
Condition 2) is not sufficient since the question does not have a unique answer.

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.
_________________ Re: Math Revolution Approach (DS)   [#permalink] 07 Mar 2018, 03:37

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