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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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[Math Revolution GMAT math practice question]

After t seconds, the height of a ball from the ground is given by the equation h =-9.8t^2+ft+g (f and g are constants). If the ball is at its maximum height, then t=?

1) f = 10
2) g = 10

=>

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

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

Y = aX^2 + bX + c has a maximum or a minimum when X = -b/2a.
Thus h =-9.8t^2+ft+g has a maximum when t = f/(2*9.8).
Condition 1) is sufficient on its own.

Condition 2) is not sufficient since it gives us no information about the value of f.

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Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
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[Math Revolution GMAT math practice question]

What is the remainder when 7^8 is divided by 100?

A. 1
B. 2
C. 3
D. 4
E. 5

=>

The remainder when 7^8 is divided by 100 is equal to the final two digits of 7^8.
Now, 7^1 = 7, 7^2 = 49, 7^3 = 343, and 7^4 = 2401.
So, the final two digits of 7^n have period 4:
The tens digits are 0 -> 4 -> 4 -> 0
and the units digits are 7 -> 9 -> 3 -> 1.
It follows that the tens and units digits of 7^8 are 0 and 1, respectively.
Therefore, the remainder when 7^8 is divided by 100 is 1.

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Joined: 16 Aug 2015
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1
[Math Revolution GMAT math practice question]

Is 0 between x and y?

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

=>

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

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

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

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

Conditions 1) & 2)
If x = 2 and y = -1, then 0 is between x and y.
If x = 2 and y = 1, then 0 is not between x and y.
Since we don’t have a unique solution, both conditions together are not sufficient.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
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[Math Revolution GMAT math practice question]

When 2 numbers are selected from the integers from 1 to 21 inclusive, what is the probability that the 2 selected numbers are prime numbers?

A. 2/15
B. 1/5
C. 1/3
D. 4/15
E. 2/5

=>

There are 8 prime numbers between 1 and 21, inclusive: 2, 3, 5, 7, 11, 13, 17 and 19.
So, there are 8C2 ways of selecting 2 numbers from these 8 prime numbers.
There are 21C2 ways of selecting 2 numbers from the 21 numbers from 1 to 21, inclusive.
Thus, the probability that the 2 selected numbers are prime numbers is 8C2 / 21C2 = ( 8*7 / 1*2) / ( 21*20 / 1*2 ) = 8*7 / 21*20 = 2/15.

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Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
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[Math Revolution GMAT math practice question]

If (n+2)!/n!=90, then n=?

A. 8
B. 9
C. 10
D. 11
E. 12

=>

(n+2)!/n!= (n+2)(n+1) = 90 = 10*9.
Thus, n + 2 = 10 or n = 8.

_________________
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Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

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

1) The tens digit of n is 8.
2) The sum of the tens digit and the units digit of n is 2-digit integer.

=>

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

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

n = 10a + b and a = 4b
The possible pairs ( a, b ) are ( 4, 1 ) and ( 8, 2 ) by the original condition.
Thus, n = 41 or n = 82.

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

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

Condition 2)
Since 4 + 1 = 5 is not a 2-digit integer and 8 + 2 = 10 is a 2-digit integer, n = 82.
Thus, condition 2) is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

Is ab>bc?

1) abc=0
2) a>c

=>

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

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

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

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

_________________
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Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

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

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

=>

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

Since we have 3 variables (x, y and z) and 0 equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since y = x + 1, z = x + 3 and x, y, z are prime numbers, the only possibility is that x = 2, y = 3, and z = 5 because if x is an odd number, then y and z are two different even numbers, which cannot both be prime numbers.
Thus, both conditions together are sufficient.

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

Condition 1)
There are many different possible values for x, y and z, including x = 1, y = 2, z = 4 and x = 2, y = 3, z = 5. Therefore, we don’t have a unique solution, and condition 1) is not sufficient.

Condition 2)
There are many different possibly values for x, y and z, including x = 2, y = 3 and z = 5, and x = 3, y = 5 and z = 7. So, we don’t have a unique solution, and condition 2) is not sufficient.

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

If (2/3)^n=(9/4)^2, what is the value of n?

A. -4
B. -2
C. 0
D. 2
E. 4

=>

(9/4)^2 = ((3/2)^2)^2 = (3/2)^4 = (2/3)^-4.
Thus, n = -4.

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Joined: 16 Aug 2015
Posts: 9146
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[Math Revolution GMAT math practice question]

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

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

=>

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

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

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

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

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

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Joined: 16 Aug 2015
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[Math Revolution GMAT math practice question]

Alice, Bob, Cindy, Dave and Eddie joined a three-person-a-side basketball tournament. In how many ways can be the three starters be chosen?

A. 5
B. 6
C. 8
D. 9
E. 10

=>

The number of ways of choosing the three starters is the number of ways of choosing three people from a set of five people, where order does not matter and repetition is not allowed.
The number of possible selections of three starters is:
5C3 = 5C2 = (5*4)/(1*2) = 10.

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Joined: 16 Aug 2015
Posts: 9146
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[Math Revolution GMAT math practice question]

Is xy>0?

1) x+y>0
2) |x|+|y|<1

=>

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

Since we have 2 variables (x and y) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

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

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

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Please tell me the pattern most which is most recently applied in Gmat.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9146
GMAT 1: 760 Q51 V42
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[Math Revolution GMAT math practice question] 7

What is the units digit of (3^101)(7^103)?

A. 1
B. 3
C. 5
D. 7
E. 9

=>

The units digit is the remainder when (3^101)(7^103) is divided by 10.

The remainders when powers of 3 are divided by 10 are
3^1: 3,
3^2: 9,
3^3: 7,
3^4: 1,
3^5: 3,

So, the units digits of 3^n have period 4:
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, 3^n has the units digit of 3 if n has a remainder of 1 when it is divided by 4.
The remainder when 101 is divided by 4 is 1, so the units digit of 3^101 is 3.

The remainders when powers of 7 are divided by 10 are
7^1: 7,
7^2: 9,
7^3: 3,
7^4: 1,
7^5: 7,

So, the units digits of 7^n have period 4:
They form the cycle 7 -> 9 -> 3 -> 1.
Thus, 7^n has the units digit of 3 if n has a remainder of 3 when it is divided by 4.
The remainder when 103 is divided by 4 is 3, so the units digit of 7^103 is 3.

Thus, the units digit of (3^101)(7^103) is 3*3 = 9.

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[Math Revolution GMAT math practice question]

Is n an odd number?

1) n is the sum of 2 prime numbers
2) n is a multiple of 11

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

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If n = 2 + 3, then n = 5 is odd and the answer is ‘yes’.
If n = 3 + 5, then n = 8 is even and the answer is ‘no’.
Since we don’t have a unique solution, condition 1) is not sufficient.

Condition 2)
If n = 11, then n is odd and the answer is ‘yes’.
If n = 22, then n is even and the answer is ‘no’.
Since we don’t have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
If n = 2 + 31, then n = 33 is odd and the answer is ‘yes’.
If n = 13 + 31, then n = 44 is even and the answer is ‘no’
Since we don’t have a unique solution, both conditions 1) and 2) are not sufficient, when taken together.

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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Joined: 16 Aug 2015
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[Math Revolution GMAT math practice question]

If r is a positive integer, n=^r3 and 4,14, and 27 are factors of n, which of the following must be a factor of n?

A. 16
B. 32
C. 36
D. 48
E. 64

=>

Since 4 = 2^2,14 = 2*7, 27 = 3^3 are factors of n and n is a perfect cube, the smallest possible value of n is 2^3*3^3*7^3.

When n = 2^3*3^3*7^3, 16 = 2^4, 32 = 2^5, 48=2^4*3 and 64 = 2^6 can’t be factors of n. The only answer choice that is a factor of n is 36 = 2^2*3^2.

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[Math Revolution GMAT math practice question]

x=?

1) x^3+x^2+x=0
2) x=-2x

=>

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

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

Condition 1)
x^3+x^2+x=0
=> x(x^2+x+1)=0
=> x = 0 since x^2+x+1 ≠ 0
Condition 1) is sufficient.

Condition 2)
x = -2x
=> 3x = 0
=> x = 0
Condition 2) is sufficient.

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: 9146
GMAT 1: 760 Q51 V42
GPA: 3.82
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[Math Revolution GMAT math practice question]

What is the value of 22C19?

A. 770
B. 1540
C. 3080
D. 4620
E. 6160

=>

Since nCn-r = nCr,
22C19 = 22C3 = (22*21*20)/(1*2*3) = 11*7*20 = 1540.

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Joined: 16 Aug 2015
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[Math Revolution GMAT math practice question]

If n is an integer, is n(n+2) divisible by 8?

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

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If n is an even integer, then n and n + 2 are two consecutive even integers.
Products of two consecutive even integers are multiples of 8 since one of them must be a multiple of 4, and the other a multiple of 2.
Condition 1) is sufficient.

Condition 2)
Since n is a multiple of 4, n + 2 is an even integer.
Thus, n(n+2) is a multiple of 8.
Condition 2) is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT  [#permalink]

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Are you sure that statistics is up there with the most important concepts? I have seen various books and online courses which stress upon Number Properties, Algebra and geometry as the three main areas to concentrate from. Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 27 Sep 2018, 08:21

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# Overview of GMAT Math Question Types and Patterns on the GMAT   