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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 15 May 2018, 18:31
[GMAT math practice question]

If 5m=25^{2n}, what is the value of m, in terms of n?

A. m=5^{3n-2}
B. m=25n
C. m=5^{4n-1}
D. m=5^{2n-1}
E. m=5n

=>

5m = 25^{2n}
=> 5m = (5^2)^{2n} = 5^{4n}
=> m = 5^{4n-1}

Therefore, C is the answer.

Answer C
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New post 17 May 2018, 18:20
[GMAT math practice question]


In a certain theater, the first row has 12 seats, and each row has 1 more seat than the previous row. If the last row has 50 seats, what is the total number of seats in the theater?

A. 1003
B. 1029
C. 1129
D. 1209
E. 1,339

=>

The question asks for the value of 12 + 13 + ... + 50. This is the sum of an arithmetic sequence with first term a = 12, and last term l = 50.
The sum of n terms of an arithmetic sequence may be found using the formula n/2 (a + l).
The number of rows is n = 50 – 12 + 1 = 39.
So, the number of seats in the theater is 39 * ( 12 + 50 ) / 2 = 39 * 62 / 2 = 39 * 31 = 1209.

Therefore, the answer is D.

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 May 2018, 17:11
[GMAT math practice question]

What is the remainder when a positive integer n is divided by 36?

1) The remainder when n is divided by 12 is 5.
2) The remainder when n is divided by 18 is 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)
Since the divisor (12) of condition 1) is not a multiple of the divisor (36) of the question, condition 1) is not sufficient.
For example, if n = 5, the remainder when n is divided by 36 is 5.
If n = 17, the remainder when n is divided by 36 is 17.
Since we don’t have a unique solution, condition 1) is not sufficient.
Condition 2)
Since the divisor (18) of condition 2) is not a multiple of the divisor (36) of the question, condition 2) is not sufficient.
For example, if n = 11, the remainder when n is divided by 36 is 11.
If n = 29, the remainder when n is divided by 36 is 29.
Since we don’t have a unique solution, condition 2) is not sufficient.
Conditions 1) & 2)
The first integer satisfying both conditions is 29, and the lcm of 12 and 18 is 36. Therefore, the integers satisfying both conditions are 29, 65, 101, ….
Each of these integers has a remainder of 29 when it is divided by 36.
Both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

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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New post 24 May 2018, 18:34
[GMAT math practice question]

How many 4-digit integers have the form abcd, where b is even and d >= 2b?

A. 900
B. 1200
C. 1520
D. 2400
E. 2700

=>

Suppose abcd is a 4-digit number.
There are 9 possible values for a: a = 1, 2, …, 9.
There are 10 possible values of c: c = 0,1,2,…,9.
Since b is even, b can take on the values 0,2,4,6 and 8.
However, the condition d >= 2b limits the possible values of b to 0, 2 and 4.

Case 1 : b = 0 => d = 0, 1, … , 9
The number of possible values of d is 10.
There are 10 * 9 * 10 = 900 4-digit integers with b = 0.

Case 2: b = 2 => d = 4, 5, …, 9
The number of possible values of d is 6.
There are 6 * 9 * 10 = 540 4-digit integers with b = 2.

Case 3: b = 4 => d = 8, 9
The number of possible values of d is 2.
There are 2 * 9 * 10 = 180 4-digit integers with b = 4.
In total, there are 900 + 540 + 180 = 1520 possible 4-digit integers of this form.

Therefore, the answer is C.

Answer: C
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New post 28 May 2018, 18:09
[GMAT math practice question]

The median of 5 numbers is 50, and their range is 40. If the median of the 3 smallest numbers is 40, which of the following could not be the range of the 3 largest numbers?

I. 0
II. 20
III. 40

A. I only
B. II only
C. I & II only
D.I & III only
E. I, II & III

=>

Suppose a, b, c, and d satisfy a ≤ b ≤ 50 ≤ c ≤ d. Since the median of the 3 smallest numbers is 40, we must have b = 40.

The range of the 3 largest numbers is d – 50.

Since we are told that d – a = 40, the maximum range of the 3 largest numbers occurs when a = b = 40.
Then d = 80, and the maximum range is d – 50 = 80 – 50 = 30.

The minimum range of the 3 largest numbers occurs when a = 10 and b = 40.
Then we have c = 50 and d = 50, and the range is d – 50 = 50 – 50 = 0.

The range of the 3 largest numbers lies between 0 and 30, inclusive.
Thus, 0 and 20 are the only possible values.

Therefore, the answer is C.
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 01 Jun 2018, 02:45
[GMAT math practice question]

p, q, x, and y are positive integers. If p^mq^n=72, what is the value of p+q?

1) m>n
2) mn=6

=>

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 4 variables (p, q, m and n) and 1 equation, 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):
We can write 72 = 2^33^2=1^672^1. (find the “hidden 1”)
If p = 2, q = 3, m = 3 and n = 2, then p + q = 5.
If p = 1, q = 72, m = 6 and n = 1, then p + q = 73.
Since we don’t have a unique solution, both conditions, taken together, are not sufficient.

Therefore, the answer is E.

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

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New post 02 Jun 2018, 19:04
1
chetan2u wrote:
ruhibhatia wrote:
MathRevolution , can you please explain the solution of the below question.

When both positive integers a and b are divided by 7, both have a remainder of 4. What is the remainder when ab3 is divided by 7?
A. 6
B. 5
C. 4
D. 3
E. 2

Can we assume that a and b and single digit integers, since abc3 is a three-digit integer?


Hi ruhi,
there are two things which ab3 can mean..a three digit number or a*b*3..
1)if ab3 is three digit number, as you have said a and b should be a single digits..
so a and b have to be 4, as the next number to leave a remainder of 4 would be 11, which is not a single digit number..
so our number is 443.. and remainder when 443 is divided by 7 is 6..
2)if ab3 actually meant a*b*3...
remainder will be 4*4*3=48..
48 when divided by 7 leaves a remainder 6..

Hope it helps u


Hi chetan2u,

I was wondering how did you get the remainder to be 6 when you divided 443 by 7? I am getting 2 instead. 7*63=441, which leaves us a remainder of 2. For 48 however, I am getting a remainder of 6. I am getting two different values 2 or 6. Could you please explain where I am going wrong? Would greatly appreciate it!
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New post 06 Jun 2018, 19:08
[GMAT math practice question]

When x and n are positive integers, if x^{2n}>(3x)^n, which of the following must be true?

A. x>3
B. n>1
C. x=3
D. n=3
E. x=n

=>

x^{2n}>(3x)^n
=> x^{2n} > 3^nx^n
=> x^n > 3^n
=> x > 3

Therefore, A is the answer.
Answer: A
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New post 10 Jun 2018, 18:39
[GMAT math practice question]

In the x-y plane, does the parabola y=ax^2+bx+c have x-intercepts?

1) b^2-4ac<0
2) a<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.

For y=ax^2+bx+c to have an x-intercept, we must have b^2-4ac ≥ 0.
Thus, condition 1) gives the answer of ‘no’. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 1) is sufficient.

Condition 2)
If a = -1, b = 0, c = 0, we have y = -x, which has an x-intercept of zero, so the answer is ‘yes’.
If a = -1, b = 0, c = -1, we have y = -x2 – 1, which has no x-intercept. The answer is ‘no’ in this case.
Since we don’t have a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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New post 11 Jun 2018, 18:03
[GMAT math practice question]

If the sum of the minimum and the maximum of 7 consecutive odd integers is 114, what is the average (arithmetic mean) of the seven integers?

A. 19
B. 38
C. 57
D. 76
E. 114

=>

Let the 7 consecutive odd integers be 2n-5, 2n-3, 2n-1, 2n+1, 2n+3, 2n+5, and 2n+7. Then their minimum is 2n-5 and their maximum is 2n+7. The sum of the maximum and minimum is ( 2n – 5 ) + ( 2n + 7 ) = 4n + 2 = 114 and so n = 28.
Since the average and the median of consecutive odd integers are equal, the average is 2n + 1 = 57.

Therefore, the answer is C.

Answer: C

Another way to solve this problem is to note that the average of the consecutive odd integers is equal to the average of the two end points. That is, 114 / 2 or 57.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT [#permalink]

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New post 14 Jun 2018, 18:29
[GMAT math practice question]

Is |x|+x <2?

1) x>-1
2) x<0

=>

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

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

The definition of the absolute value gives us two cases to consider when examining the question.

Case 1: x ≥ 0
|x| + x < 2
=> x + x < 2
=> 2x < 2
=> x < 1
The question asks if 0 ≤ x < 1 in this case.

Case 2: x < 0
|x| + x < 2
=> (-x) + x < 2
=> 0 < 2
As this is always true, the answer is always “yes” if x < 0.

Combining these two cases shows that the question asks if x < 1.

In inequality questions, the law “Question is King” tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient

Thus condition 1) is not sufficient, but condition 2) is sufficient since the solution set of the question includes the solution set of condition 2), but it doesn’t include that of condition 1).

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 17 Jun 2018, 18:32
[GMAT math practice question]

If x and y are prime numbers, and n is a positive integer, what is the number of factors of xnyn?

1) xy=6
2) n=2

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

Since we have 3 variables (x, y and n) 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 x and y are prime numbers and xy = 6, we must have x = 2 and y = 3, or x = 3 and y = 2.
If x = 2 and y = 3, then x^ny^n = 2^23^2 has (2+1)(2+1) = 9 factors, since x and y are different prime numbers and n = 2.
If x = 3 and y = 2, then x^ny^n = 3^22^2 has (2+1)(2+1) = 9 factors, since x and y are different prime numbers and n = 2.
Since we have a unique answer, 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)
Since it doesn’t give us any information about the variable n, condition 1) is not sufficient.

Condition 2)
Since it doesn’t give us any information about the variables x and y, condition 2) is not sufficient.

Therefore, C is the answer.

Answer: 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.
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Re: Overview of GMAT Math Question Types and Patterns on the GMAT   [#permalink] 17 Jun 2018, 18:32

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Overview of GMAT Math Question Types and Patterns on the GMAT

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