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Math Revolution GMAT Instructor
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25 Jan 2019, 02:29
[ Math Revolution GMAT math practice question] (exponents) \(m+n=?\) \(1) (4^m)(2^n)=16\) \(2) (2^{2m})(4^n)=64\)
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27 Jan 2019, 18:23
MathRevolution wrote: [ Math Revolution GMAT math practice question] If \(x\) and \(y\) are nonzero numbers and \(x≠±y\), then \(\frac{( x^2 + y^2 )}{( x^2  y^2 )}=?\) \(1) \frac{x}{y}=\frac{1}{3}\) \(2) y=3x\) => 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. The question asks for the value of \(\frac{( x^2 + y^2 )}{( x^2  y^2 )}= ( (\frac{x}{y})^2 + 1 ) / (\frac{x}{y})^2 – 1 ).\) 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. Condition 1) Since \(\frac{x}{y}=\frac{1}{3}, \frac{x}{y} = ±(\frac{1}{3})\), and \(\frac{( x^2 + y^2 )}{( x^2  y^2 )}= ( (\frac{x}{y})^2 + 1 ) / ( (\frac{x}{y})^2 – 1 ) = ( (\frac{1}{3})^2 + 1 ) / ( (\frac{1}{3})^2 – 1) = (\frac{1}{9} + 1)/(\frac{1}{9}1) = (\frac{10}{9})/(\frac{8}{9}) = \frac{10}{8} = \frac{5}{4}.\) Condition 1) is sufficient since it gives a unique solution. Condition 2) Since \(y = 3x, \frac{x}{y} = \frac{1}{3}\), and \(\frac{( x^2 + y^2 )}{( x^2  y^2 )}= ( (\frac{x}{y})^2 + 1 ) / ( (\frac{x}{y})^2 – 1 ) = ( (\frac{1}{3})^2 + 1 ) / ( (\frac{1}{3})^2 – 1) = (\frac{1}{9} + 1)/(\frac{1}{9}1) = (\frac{10}{9})/(\frac{8}{9}) = \frac{10}{8} = \frac{5}{4}.\) Condition 2) is sufficient since it gives a unique solution. Therefore, the answer is D. 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.
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27 Jan 2019, 18:25
MathRevolution wrote: [ Math Revolution GMAT math practice question] (exponents) \(m+n=?\) \(1) (4^m)(2^n)=16\) \(2) (2^{2m})(4^n)=64\) => 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. Condition 2) is equivalent to \(m + n = 3\) as shown below: \((2^{2m})(4^n)=64\) \(=> (2^{2m})(2^{2n})=2^6\) \(=> 2^{2m+2n}=2^6\) \(=> 2m+2n = 6\) \(=> m + n = 3\) Condition 2) is sufficient. Condition 1) \((4^m)(2^n)=16\) \(=> (2^{2m})(2^n)=2^4\) \(=> 2^{2m+n}=2^4\) \(=> 2m+n = 4\) If \(m = 1\) and \(n =2\), then \(m + n = 3\). If \(m = 0\) and \(n = 4,\) then \(m + n = 4.\) Since it does not yield a unique solution, condition 1) is not sufficient. Therefore, the answer is B. Answer: B
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28 Jan 2019, 01:37
[GMAT math practice question] (number properties) If \(n\) is positive integer, is \(4^n+n^2+1\) divisible by \(2\)? 1) \(n\) is a multiple of \(4\) 2) \(n\) is a multiple of \(6\)
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29 Jan 2019, 01:00
[GMAT math practice question] (function) If operation \(#\) represents one of addition, subtraction, multiplication, and division, what is the value of \(0#1\)? \(1) 2#1 = 2\) \(2) 4#2 = 2\)
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Updated on: 29 Jan 2019, 06:13
MathRevolution wrote: [GMAT math practice question]
(function) If operation \(#\) represents one of addition, subtraction, multiplication, and division, what is the value of \(0#1\)?
\(1) 2#1 = 2\) \(2) 4#2 = 2\) #1 2#1=2 # can be multiplication or division so sufficient as doing both operations we would get answer as 0 for \(0#1\) #2 4#2 =2 # can be subtraction of division; in sufficient IMO A
Originally posted by Archit3110 on 29 Jan 2019, 03:07.
Last edited by Archit3110 on 29 Jan 2019, 06:13, edited 1 time in total.



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29 Jan 2019, 03:16
MathRevolution wrote: [GMAT math practice question]
(number properties) If \(n\) is positive integer, is \(4^n+n^2+1\) divisible by \(2\)?
1) \(n\) is a multiple of \(4\) 2) \(n\) is a multiple of \(6\) #1 n can be 0,4,8,12... and always the sum of \(4^n+n^2+1\) would be odd which is not divisible by 2 ; sufficient #2 n can be 0,6,12,18... and always the sum of \(4^n+n^2+1\) would be odd which is not divisible by 2 ; sufficient IMO D



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29 Jan 2019, 06:02
MathRevolution wrote: [GMAT math practice question]
(function) If operation \(#\) represents one of addition, subtraction, multiplication, and division, what is the value of \(0#1\)?
\(1) 2#1 = 2\) \(2) 4#2 = 2\)
\(?\,\, = \,\,0\# 1\,\,\,\,\,\,\left( {\# \in \left\{ { + ,  , \times , \div } \right\}} \right)\) \(\left( 1 \right)\,\,2\# 1 = 2\,\,\,\, \Rightarrow \left\{ \matrix{ \,\,\# = \times \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr \,\,{\rm{OR}} \hfill \cr \,\,\# = \div \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}\) \(\left( 2 \right)\,\,\,\,4\# 2 = 2\,\,\,\, \Rightarrow \left\{ \matrix{ \,\,\# =  \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? =  1 \hfill \cr \,\,{\rm{OR}} \hfill \cr \,\,\# = \div \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}\) The correct answer is therefore (A). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.
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30 Jan 2019, 02:20
MathRevolution wrote: [GMAT math practice question]
(number properties) If \(n\) is positive integer, is \(4^n+n^2+1\) divisible by \(2\)?
1) \(n\) is a multiple of \(4\) 2) \(n\) is a multiple of \(6\) => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. Since \(4^n\) is a multiple of \(2\), we only need to look at \(n^2+1\). If \(n\) is an odd number, \(4^n+n^2+1\) is divisible by \(2\). If \(n\) is an even number, \(4^n+n^2+1\) is not divisible by \(2\). The question asks if \(n\) is an odd number. Thus, each of conditions is sufficient. Therefore, D is the answer. Answer: D
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30 Jan 2019, 02:22
[GMAT math practice question] Five data values are \(11, 14, 16, 18\) and \(x\). What is the value of \(x\)? 1) The mode of the \(5\) data values is \(11\) 2) The average (arithmetic mean) of the \(5\) data values is \(14\)
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Updated on: 31 Jan 2019, 02:18
MathRevolution wrote: [GMAT math practice question]
(function) If operation \(#\) represents one of addition, subtraction, multiplication, and division, what is the value of \(0#1\)?
\(1) 2#1 = 2\) \(2) 4#2 = 2\) => 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 operation is considered as a variable. Since we have \(1\) variable and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) Since \(2#1 = 2\), \(#\) is one of the operations, multiplication and division. If \(#\) is the multiplication operation, then \(0#1 = 0\). If \(#\) is the division operation, then \(0#1 = 0.\) Since condition 1) yields a unique solution, it is sufficient. Condition 2) Since \(4#2 = 2, #\) is one of the operations, subtraction and division. If \(#\) is the subtraction operation, then \(0#1 = 1\). If \(#\) is the division operation, then \(0#1 = 0\). Since condition 2) doesn’t yield a unique solution, it is not sufficient. Therefore, A is the answer. Answer: A
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31 Jan 2019, 02:13
[GMAT math practice question] (number properties) Is \(3\) a factor of \(x\)? 1) \(x3\) is divisible by \(6\) 2) \(x+3\) is divisible by \(6\)
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31 Jan 2019, 02:59
MathRevolution wrote: [GMAT math practice question] Five data values are \(11, 14, 16, 18\) and \(x\). What is the value of \(x\)?
1) The mode of the \(5\) data values is \(11\) 2) The average (arithmetic mean) of the \(5\) data values is \(14\) #1 mode of set is 11 so x=11 mode most repeated no in a set sufficient #2 avg of set = 14 sum of digits = 59+x = 70 x=11 sufficient IMO D



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31 Jan 2019, 03:02
MathRevolution wrote: [GMAT math practice question]
(number properties) Is \(3\) a factor of \(x\)?
1) \(x3\) is divisible by \(6\) 2) \(x+3\) is divisible by \(6\) #1 sufficient x= 9,15,21 x3 divisible by 6 and x a factor of 3 #2 sufficient x+3 divisible by 6 x=3,9,15,18 sufficient IMO D



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01 Feb 2019, 02:48
MathRevolution wrote: [GMAT math practice question] Five data values are \(11, 14, 16, 18\) and \(x\). What is the value of \(x\)?
1) The mode of the \(5\) data values is \(11\) 2) The average (arithmetic mean) of the \(5\) data values is \(14\) => 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) The data values include four different values and \(x\). Since the mode of the five data values is \(11, x\) must equal \(11\). Condition 1) is sufficient. Condition 2) Calculating the mean of the five data values yields \(\frac{( 11 + 14 + 16 + 18 + x )}{5} = 14.\) Solving for \(x\) gives \(11 + 14 + 16 + 18 + x = 70\) \(59 + x = 70\) \(x = 11\) Condition 2) is also sufficient. Therefore, D is the answer. Answer: D
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01 Feb 2019, 02:49
[GMAT math practice question] (exponent) If \(p, x,\) and \(y\) are integers, \(\frac{x^p}{x^q}\)=? \(1) p=q+4\) \(2) x^q=16\)
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01 Feb 2019, 06:08
MathRevolution wrote: [GMAT math practice question]
(exponent) If \(p, x,\) and \(q\) are integers, \(\frac{x^p}{x^q}\)=?
\(1) p=q+4\) \(2) x^q=16\)
\(p,x,q\,\,{\rm{ints}}\) \(?\,\, = \,\,{{{x^p}} \over {{x^q}}}\) \(\left( {1 + 2} \right)\,\,\,\left\{ \matrix{ \,p = q + 4 \hfill \cr \,{x^q} = 16 \hfill \cr} \right.\,\,\,\,\,\,::\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {x,q,p} \right) = \left( {16,1,5} \right)\,\,\,\, \Rightarrow \,\,\,? = {16^4} \hfill \cr \,{\rm{Take}}\,\,\left( {x,q,p} \right) = \left( {2,4,8} \right)\,\,\,\, \Rightarrow \,\,\,? = {2^4} \hfill \cr} \right.\) The correct answer is therefore (E). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.
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04 Feb 2019, 05:30
MathRevolution wrote: [GMAT math practice question]
(number properties) Is \(3\) a factor of \(x\)?
1) \(x3\) is divisible by \(6\) 2) \(x+3\) is divisible by \(6\) => 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 1 variable (x) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first. To solve remainder questions, plugging in numbers is recommended. Condition 1) If we plug in x = 9, then x – 3 = 6 is divisible by 6 and x is a multiple of 3. Condition 1) is sufficient. Condition 2) If we plug in x = 9, then x + 3 = 12 is divisible by 6 and x is a multiple of 3. Condition 2) is sufficient. Therefore, the answer is D. Answer: D
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04 Feb 2019, 05:36
MathRevolution wrote: [GMAT math practice question]
(exponent) If \(p, x,\) and \(y\) are integers, \(\frac{x^p}{x^q}\)=?
\(1) p=q+4\) \(2) x^q=16\) => 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) If \(x = 2, p = 8\) and \(q = 4\), then \(\frac{x^p}{x^q} = x^{pq} = x^4 = 2^4 = 16.\) If \(x = 16, p = 5\) and \(q = 1\), then \(\frac{x^p}{x^q} = x^{pq} = x^4 = 16^4 = 2^{16} = 65536.\) Since they do not yield a unique solution, both conditions are not sufficient, when considered together. Therefore, the answer is E. Answer: E Note: This question is related to finding a hidden 1. 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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04 Feb 2019, 05:38
[GMAT math practice question] (number properties) If \(x, y\) are integers, is \((xy)(x+y)(x^2+y^2)\) an odd number? 1) \(x\) is an odd number 2) \(xy\) is an odd number
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