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Overview of GMAT Math Question Types and Patterns on the GMAT

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 11 Jan 2018, 06:23
MathRevolution wrote:
If x and y are positive integers and y(2^x)=24, x=?

1) x 2
2) y is even

==> In the original condition, there are 2 variables (a,b), and in order to match the number of variables to the number of equations there must be 2 equations as well. Since there is 1 for con 1) and 1 for con 2) C is most likely to be the answer.
By solving con 1) and con 2), you get 24=6(2^2).

The answer is C.

I think answer should be D.
1. x=2, we will get a unique answer.
i.e. y=6.
2. y is even, only possible when x=2.


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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 14 Jan 2018, 17:55
[GMAT math practice question]

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

1) a=0.5
2) b=5

=>

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

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

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

The answer is A.
Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 18 Jan 2018, 17:39
[GMAT math practice question]

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

1) 1/x = 1/2
2) (1/x)+(1/y) =1

=>

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

Since we have 2 variables (x and y) and 1 equation ( x > y ), D is most likely to be the answer.

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

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

Therefore, the answer is D.

Note: The VA approach tells us that the answer is most likely to be D, since this is a CMT(Common Mistake Type) 4B question.
Condition 1) is easy to check, but condition 2) is more difficult to work with. If you can’t figure out condition 2), you should choose D as the answer.
Answer: D
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 21 Jan 2018, 17:44
[GMAT math practice question]

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

1) x<0
2) y<0

=>

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

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

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

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

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

Therefore, the answer is B.
Answer: B
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 28 Jan 2018, 17:49
[GMAT math practice question]

Is x|y|=xz?

1) x, y, and z are positive
2) y^2=z^2

=>

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

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

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

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

Conditions 1) & 2):

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

Therefore, the answer is C.

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

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New post 28 Jan 2018, 23:04
1
This post received
KUDOS
Hiii
That's a very nice problem, Kudo to you.
See my approach to this problem.

MathRevolution wrote:
Also, geometry questions are rising continuously. Let's take the recent question as an example.

(ex 4)
Attachment:
The attachment yin yang.jpg is no longer available


There is a yin-yang symbol shown as above figure such that its radius is 2. What is the area of the region shaded?
1) Both arc MNO and arc OCD are the same semi-circles.
2) The area of region shaded is half of the area of the circle

[Reveal] Spoiler:
Answer: B

In this case, 1) and 2) are the same, which makes D the answer. Just like the question above, slightly difficult and deriving 1)=2) questions which make D the answer are frequently given as well. This type of geometry questions are steadily on an upward tendency.

Attachments

IMG-20180129-WA0008_1517209424145.jpg
IMG-20180129-WA0008_1517209424145.jpg [ 99.84 KiB | Viewed 316 times ]


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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 29 Jan 2018, 17:33
[GMAT math practice question]

Is the positive integer x an even number?

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

=>

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

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

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

Condition 2)

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

Therefore, the answer is A.
Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 29 Jan 2018, 20:26
St1: since smallest prime factor is 3, 2 is not a factor. Hence odd. Hence sufficient.

St2: since greatest prime factors is 17, 2 can be a factor but not necessarily.

Eg. 17,34. It can be even or odd. Insufficient.

Answer is A


MathRevolution wrote:
[GMAT math practice question]

Is the positive integer x an even number?

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

=>

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

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

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

Condition 2)

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

Therefore, the answer is A.
Answer: A

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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 31 Jan 2018, 17:13
[GMAT math practice question]

If x=343y, where y is a positive integer, and x/196 is a terminating decimal, what is the smallest possible value of y?

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

=>

x/196 = (343*y)/196 = (7^3*y)/(14^2) = (7^3*y)/(2^2)(7^2) = (7y)/4
As the denominator has only 2 as a prime factor, it is a terminating decimal, regardless of the value of y.
Thus, the smallest possible value of y is 1.

Therefore, the answer is A.

Answer: A
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 05 Feb 2018, 17:37
[GMAT math practice question]

Is x^y<1?

1) x>1
2) y<1

=>

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

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

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

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

Therefore, the answer is E.

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

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New post 08 Feb 2018, 17:29
[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
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 11 Feb 2018, 17:04
[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
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 16 Feb 2018, 04:12
[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.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 18 Feb 2018, 18:26
[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
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 20 Feb 2018, 17:00
[GMAT math practice question]

How many arrangements of the letters ‘s’, ‘u’, ‘c’, ‘c’, ‘e’, ‘s’, ‘s’ in a straight line are possible?

A. 60
B. 120
C. 180
D. 240
E. 420

=>

The seven letters ‘s’, ‘u’, ‘c’, ‘c’, ‘e’, ‘s’, ‘s’ include three s’s and two c’s.
The number of permutations is 7! / (3!*2!) = 420.

Therefore, the answer is E.

Answer: E
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 20 Feb 2018, 17:00

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