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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
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[GMAT math practice question]

Which of the following is equal to x!/(x+1)! + (x+1)!/(x+2)!?

A. 1+1/x
B. 1+1/(x+1)
C. (2x+3)/(x+1)(x+2)
D. 1/{ x(x+1) }
E. (2x-1)/{(x+1)(x+2)}

=>
x! / ( x + 1 )! + ( x + 1 )! / ( x + 2 )!
= x! / {x! * (x+1)} + (x+1)! / { (x+1)! * (x+2) }
= 1/(x+1) + 1/(x+2) = (2x+3)/(x+1)(x+2)

Therefore, C is the answer.
_________________
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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

Is the total of the sales prices of 3 products greater than \$23?

1) The price of the cheapest of the 3 products is at least \$8
2) The price of the second cheapest of the 3 products is at least \$12.

=>

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.

If a question includes the expression “greater than”, we should determine the smallest possible value, since all other possibilities are greater than the minimum. Each of the conditions includes the expression “at least”, so this gives us some minimum values.

Condition 1)
Since the cheapest of the three products costs at least \$8, the minimum total cost of the three products is
\$8 + \$8 + \$8 = \$24 > \$23.
Thus, condition 1) is sufficient.

Condition 2)
Since the second cheapest of the three products costs at least \$12, the minimum total cost of the three products is
\$0 + \$12 + \$12 = \$24 > \$23.
Thus, condition 2) is sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

Each of three consecutive positive integers is less than 100. Their sum of is a multiple of 10. What is the smallest of the three integers?

1) Their median is a multiple of 9
2) Two of the integers 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.

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

Let the integers be x – 1, x and x + 1 where x is a positive integer. Since their sum, x – 1 + x + x + 1 = 3x is a multiple of 10, x must be a multiple of 10.

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)
The median, x, of the three integers is a multiple of 9 and a multiple of 10.
Since x < 100, we must have x = 90.
Therefore, the smallest of the integers is x – 1 = 89.
Thus, condition 1) is sufficient.

Condition 2)
If x = 30, the integers are 29, 30, 31 and the smallest integer is 29.
If x = 90, the integers are 89, 90, 91 and the smallest integer is 89.
Since we do not obtain a unique answer, condition 2) is not sufficient.

Therefore, the answer is A.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

Is x>0?

1) x^3+x^2+x = 1
2) x^2 – 4x - 5 > 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.

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

Condition 1):
x^3+x^2+x = 1
=> x(x^2+x+1) = 1
=> x = 1 / (x^2+x+1)
=> x = 1 / (x^2+x+1) > 0 since x^2+x+1 > 0.

Thus, condition 1) is sufficient.

Condition 2):
x^2 – 4x -5 > 0
=> (x+1)(x-5) > 0
=> x < 1 or x > 5

Since the solution set of the inequality, x > 0, from the question does not include the solution set of the inequality from condition 2), x < 1 or x > 5, condition 2) is not sufficient.

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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

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

1) x+3y is even
2) (x-1)(y-1) 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.

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)
Since both conditions are satisfied only when x is even and y is even, x + y must be an even number.
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 two ways in which x + 3y can be even.
If x and y are both even, then x + y is even.
If x and y are both odd, then x + y is even too.
Thus, condition 1) is sufficient.

Condition 2)
Since (x-1)(y-1) is odd, both x -1 and y – 1 must be odd.
So, x and y must both be even.
It follows that x + y is even.
Thus, condition 2) is sufficient too.

Therefore, D 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

Alice makes 2-digit codes using the 26 letters of the alphabet. Letters may be used repeatedly, and at least one vowel must be used. How many possible codes can she make?

A. 235
B. 256
C. 360
D. 625
E. 676

=>

The number of vowels is 5 (a,e,i,o,u). So, the number of codes is equal to the number of 2-digit codes with no restrictions minus the number of codes that contain no vowels. This is given by

26*26 – 21*21 = (26 + 21)(26 – 21) = 47*5 = 235.

Therefore, the answer is A.
_________________
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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

What is the difference between the average (arithmetic mean) of the first 9 positive integers and the average (arithmetic mean) of the second 9 non-negative integers?

A. 0
B. 1
C. 2
D. 3
E. 4

=>

The first 9 positive integers are 1, 2, 3, …, 9. Their average is 5.
The second 9 non-negative integers are 1, 2, 3, …, 9, since the first 9 non-negative integers are 0, 1, 2, …, 8. Their average is 5 too.

Thus the difference between those averages is 0.

Therefore, A is the answer.

_________________
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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

A bag contains only black and white balls. What is the probability that a ball chosen randomly from the bag is black?

1) The total number of balls in the bag is 12
2) The number of white balls is 3 times the number of black balls

=>

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 VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

We can modify the original condition and question as follows.

Assume b and w are the numbers of black and white balls, respectively.
Then b + w = 12.
The question asks for the value of b / ( b + w ).

Since we have 2 variables 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) together:
b + w = 12
w = 3b

Combining these equations yields b + 3b = 4b = 12 or b = 3.
So, w = 9.
Thus, b / ( b + w ) = 3 / 12 = 1/4
Both conditions together are sufficient.

Since this question is a probability 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) : b + w = 12
Since we can't determine the value of b, we can't determine b / ( b + w ) = b / 12.
Condition 1) is not sufficient.

Condition 2) : w = 3b
b / ( b + w ) = b / ( b + 3w ) = b / 4b = 1/4.
Condition 2) is sufficient.

Therefore, B is the answer.

When a question asks for a ratio, if one condition includes a ratio and the other condition just gives a number, the condition including the ratio is most likely to be sufficient. This tells us that B is most likely to be the answer to this question.

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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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

The students at a school took a math exam. Is the average (arithmetic mean) score for the exam higher than the median score?

1) The average (arithmetic mean) score is 75.
2) 51% of the students attained more than the average (arithmetic mean) score.

=>
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 many variables 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)
The median score is attained or exceeded by 50% of students.
Since 51% of students scored more than the average, the median is more than the average.
Both conditions together are sufficient.

Since this question is a statistics 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 we don't know the median, condition 1) is not sufficient.

Condition 2)
Since 51% of students scored more than the average, the median is more than the average.
Condition 2) is sufficient.

Therefore, B 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

Is median of a, b and c equal to their average (arithmetic mean)?

1) a≤b≤c
2) b = ( a + c ) / 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 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)
b is the median of a, b and c since a≤b≤c.
b is the average of a, b and c since b = ( a + c ) / 2.
Thus, the median and the average of a, b and c are the same.

Both conditions together are sufficient.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If a = 1, b = 2, and c = 3, the average and the median are 5.
If a = 1, b = 2, and c = 6, the average is 3 and the median is 2. The average and median are different.
Thus, condition 1) is not sufficient.

Condition 2) :
b is the median of a, b and c since b = ( a + c ) / 2 ⇔ a + c = 2b.
The average of a, b and c is ( a + b + c ) / 3 = ( 2b + b ) / 3 = 3b/3 = b.
Thus, the average and the median are the same.
Condition 2) is sufficient.

Therefore, B 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.
_________________
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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

On the number line, 0 lies between x and y. Is x>y?

1) The distance between x and 0 is 2 times the distance between y and 0
2) x+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. Since 0 lies between x and y, we must have xy < 0.

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):
Condition 1) tells us that |x| = 2|y|.
Thus x = ±2y. However, since xy < 0, x = -2y.

Condition 2) tells us that x + y = (-2y) + y = -y > 0. So, y < 0 and x > 0.
Thus, x > y.
Both conditions together are sufficient.

Since this question 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): |x| = 2|y|
If x = 2 and y = -1, the answer is “yes”.
If x = -2 and y = 1, the answer is “no”.

Condition 1) is not sufficient.

Condition 2): x + y > 0
If x = 2 and y = -1, the answer is “yes”.
If x = -1 and y = 2, the answer is “no”.

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.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

How many 5 digit numbers have at least one zero digit?

A. 30951
B. 40141
C. 47132
D. 50001
E. 50433

=>

The number of 5 digit numbers is 99999 – 10000 + 1 = 90000.
The number of 5 digit numbers which have no 0 digit is 9 * 9 * 9 * 9 * 9 = 59049.
When we encounter the words “at least” in probability questions, we should consider the complementary case and subtract the number of ways it occurs from the total number of possibilities.
The total number of 5 digit numbers with at least one zero digit is
90000 – 59049 = 30951

Therefore, A is the answer.
_________________
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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

Four values from a data set of 5 elements are 10, 10, 11, and 11. What is the fifth data value?

1) The range of the data set is 2
2) The average of the data values 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.

Since we have 1 variable, x which is the fifth data value 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):
The fifth data value could be x = 9 or x = 12.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2):
( x + 10 + 10 + 11 + 11 ) / 5 > 10
=> x + 10 + 10 + 11 + 11 > 50
=> x + 42 > 50
=> x > 8
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2) :
Condition 1) tells us that x = 9 or x = 12, and condition 2) tells us that x > 8.
So, x = 9 or x = 12.
Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, E 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

If x and y are positive integers, what is the remainder when x+y is divided by 2?

1) xy is divisible by 4
2) y 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 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 = 4 and y = 1, x + y = 5 has remainder 1 when it is divided by 4.
If x = 2 and y = 2, x + y = 4 has remainder 0 when it is divided by 4.

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

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.

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

If x is a positive integer, is x/30 a terminating decimal?

1) x is divisible by 3
2) x is divisible by 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.

Note that 30 = 2*3*5. Therefore, for x/30 to be a terminating decimal, 3 must be a factor of x (then the 3 from the denominator will cancel out with a 3 from the numerator). So, the question is asking whether x is a multiple of 3.

As this is precisely condition 1), condition 1) is sufficient.

Note that condition 2) does not tell us whether x is a multiple of 3.

Therefore, A 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.
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

If x and y are positive integers and x>y, is x/y an integer?

1) x is a multiple of 10
2) y 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 (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 = 10 and y = 2, x / y = 5 is an integer.
If x = 10 and y = 4, x / y = 10 / 4 = 5 / 2 is not an integer.
Since we don’t have a unique solution, both conditions together are not sufficient.

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.
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[GMAT math practice question]

Working alone at its constant rate, machine A can complete a job in 24 hours. The work rate of machine B is 1/2 that of machine A. If machine A works on the job for 6 hours and machine B completes the job, how long does it take machine B to finish the job?

A. 12hrs
B. 16hrs
C. 24hrs
D. 32hrs
E. 36hrs

=>

Suppose W is the total amount of work required to do the job and that RA and RB are the work rates of machines A and B, respectively.
Then the original condition tells us that RB = (1/2)RA.

Since machine A worked on the job for 6 hours, 1/4 of the job has been done, and (3/4)W is left.
The time T that machine B takes to complete the job is T = (3/4)W / RB = (3/4)W / (1/2)RA = (6/4)W/RA = (6/4)*24 = 36.

Therefore, the answer is E.

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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
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[GMAT math practice question]

40% of the students at a school take a math class and 60% of the school’s students take a physics class. What percent of students at the school take a math class, but not a physics class?

1) 25% of students take both a math class and a physics class.
2) 25% of students take a physics class, but do not take a math class.

=>

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.

This is a typical 2 x 2 matrix question with percentages. To solve it, we need 3 percentages. The original condition provides 2 percentages, so we need only 1 more percentage. Each of the conditions provides 1 percentage, so the VA method tells us that, each condition is likely to be sufficient.

Therefore, D is the answer.
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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

abc0 is a positive, four-digit integer, where a, b and c are 1-digit positive integers. Is abc0 divisible by 4?

1) ab is an odd number
2) bc 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. We then recheck the question.

We can determine whether an integer is divisible by 4 from its final two digits.
Thus, abc0 is divisible by 4 if and only if c0 is divisible by 4.
Condition 1) tells us nothing about the value of c, so it is not sufficient.
Condition 2) tells us that both b and c are odd numbers.
If c is an odd number, then 10*c + 0 = 10*c is not a multiple of 4, and so abc0 is not a multiple of 4. The answer is ‘no’.
Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient.

Therefore, B is the answer.

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Joined: 16 Aug 2015
Posts: 8033
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The Ultimate Q51 Guide [Expert Level]  [#permalink]

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[GMAT math practice question]

What is the range of the 5 numbers x, y, 10, 15, and 20?

1) x and y lie between 10 and 20, inclusive.
2) The average (arithmetic mean) of the five 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 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):
Since we have 10 ≤ x ≤ 20 and 10 ≤ y ≤ 20 by condition 1), the maximum of the numbers is 20 and the minimum of the numbers is 10.
The range is the difference between the maximum and the minimum, which is 20 – 10 = 10.
Both conditions together are sufficient.
Since this question is a statistics 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 10 ≤ x ≤ 20 and 10 ≤ y ≤ 20 by condition 1), the maximum of the numbers is 20 and the minimum of the numbers is 10.
The range is the difference between the maximum and the minimum, which is 20 – 10 = 10.
Thus, condition 1) is sufficient.

Condition 2)
If x = 10 and y = 20, the range is 10.
If x = 9 and y = 21, the range is 12.
Since we don’t have a unique solution, condition 2) is not sufficient.

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.
_________________ Re: The Ultimate Q51 Guide [Expert Level]   [#permalink] 15 May 2018, 18:29

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