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02 Dec 2018, 19:03
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[Math Revolution GMAT math practice question]
If m and n are positive integers, what is the greatest common divisor of m and n?
1) m=n+1
2) m*n 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 two consecutive integers are always relatively prime, the greatest common divisor of m and n is 1. Thus, condition 1) is sufficient.
Condition 2)
If m = 2 and n = 3, then the greatest common divisor of m and n is 1.
If m = 2 and n = 4, then the greatest common divisor of m and n is 2.
Thus, condition 2) is not sufficient since it does not yield a unique solution.
Therefore, the correct answer is A.
Answer: A
If m and n are positive integers, what is the greatest common divisor of m and n?
1) m=n+1
2) m*n 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 two consecutive integers are always relatively prime, the greatest common divisor of m and n is 1. Thus, condition 1) is sufficient.
Condition 2)
If m = 2 and n = 3, then the greatest common divisor of m and n is 1.
If m = 2 and n = 4, then the greatest common divisor of m and n is 2.
Thus, condition 2) is not sufficient since it does not yield a unique solution.
Therefore, the correct answer is A.
Answer: A
04 Dec 2018, 18:21
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[Math Revolution GMAT math practice question]
If n is a positive integer, is √17n an integer?
1) 68n is the square of an integer.
2) n/68 is the square of an 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.
Modifying the question:
The question asks if √17n = a for some integer a. This is equivalent to asking if 17n = a2 for some integer a.
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 68n is the square of an integer and 68 = 4*17, we must have 68n = 4*17*17*k^2 for some integer k, and n = 17*k^2 or 17n = 17^2*k^2 = (17*k)^2.
Thus, 17n is the square of the integer 17k, and condition 1) is sufficient.
Condition 2)
Since n/68 is a square of an integer and 68 = 4*17, we have n/68 = m^2 for some integer m, and n = 17*4*m^2 or 17n = 17^2*2^2*m^2 = (34m)^2.
Thus, 17n is the square of the integer 17k, and condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
If n is a positive integer, is √17n an integer?
1) 68n is the square of an integer.
2) n/68 is the square of an 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.
Modifying the question:
The question asks if √17n = a for some integer a. This is equivalent to asking if 17n = a2 for some integer a.
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 68n is the square of an integer and 68 = 4*17, we must have 68n = 4*17*17*k^2 for some integer k, and n = 17*k^2 or 17n = 17^2*k^2 = (17*k)^2.
Thus, 17n is the square of the integer 17k, and condition 1) is sufficient.
Condition 2)
Since n/68 is a square of an integer and 68 = 4*17, we have n/68 = m^2 for some integer m, and n = 17*4*m^2 or 17n = 17^2*2^2*m^2 = (34m)^2.
Thus, 17n is the square of the integer 17k, and condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
05 Dec 2018, 18:21
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[Math Revolution GMAT math practice question]
If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2+2^2+... +2^7?
A. 3
B. 5
C. 13
D. 17
E. 19
=>
1+2+2^2+... +2^7 = 2^8 – 1 = (2^4+1)(2^4-1) = (2^4+1)(2^2+1)(2^2-1) = (2^4+1)(2^2+1)(2+1)(2-1) = 17*5*3.
17 is the largest prime factor of 1+2+2^2+... +2^7.
Therefore, D is the answer.
Answer: D
If 1+2+2^2+... +2^n=2^{n+1}-1, what is the largest prime factor of 1+2+2^2+... +2^7?
A. 3
B. 5
C. 13
D. 17
E. 19
=>
1+2+2^2+... +2^7 = 2^8 – 1 = (2^4+1)(2^4-1) = (2^4+1)(2^2+1)(2^2-1) = (2^4+1)(2^2+1)(2+1)(2-1) = 17*5*3.
17 is the largest prime factor of 1+2+2^2+... +2^7.
Therefore, D is the answer.
Answer: D
10 Dec 2018, 18:16
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[Math Revolution GMAT math practice question]
x is a positive number. What is the median of x, √x and x^2?
1) x^2=x
2) x^2+x+1=3x
=>
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 >1, then √x < x < x^2 and x is their median.
If 0 < x <1, then √x > x > x^2 and x is their median.
If x = 1, then √x = x = x^2 and x is their median.
Thus, the question asks for the value of x.
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^2=x
=> x^2-x=0
=> x(x-1)=0
=> x = 0 or x = 1
Since x is positive, x = 1.
Condition 1) is sufficient.
Condition 2)
x^2+x+1=3x
=> x^2-2x+1=0
=> (x-1)^2=0
=> x = 1.
Condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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.
x is a positive number. What is the median of x, √x and x^2?
1) x^2=x
2) x^2+x+1=3x
=>
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 >1, then √x < x < x^2 and x is their median.
If 0 < x <1, then √x > x > x^2 and x is their median.
If x = 1, then √x = x = x^2 and x is their median.
Thus, the question asks for the value of x.
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^2=x
=> x^2-x=0
=> x(x-1)=0
=> x = 0 or x = 1
Since x is positive, x = 1.
Condition 1) is sufficient.
Condition 2)
x^2+x+1=3x
=> x^2-2x+1=0
=> (x-1)^2=0
=> x = 1.
Condition 2) is sufficient.
Therefore, D is the answer.
Answer: D
FYI, Tip 1) of the VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.
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.
