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23 Dec 2018, 11:01
MathRevolution wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] (number property) If \(n\) is an integer greater than \(1\), what is the value of \(n\)? 1) \(n\) is a prime number 2) \(\frac{(n+2)}{n}\) is 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. 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 there are many prime numbers, condition 1) is not sufficient. Condition 2) If \(n = 1\), then \(\frac{(n+2)}{n} = 3\) is an integer.If \(n = 2,\) then \(\frac{(n+2)}{n} = 2\) is an integer. Since we don’t have a unique solution, condition 2) is not sufficient. Conditions 1) & 2) If \(n = 2\), then \(\frac{(n+2)}{n} = 2\) is an integer. If \(n = 3\), then \(\frac{(n+2)}{n} = \frac{5}{2}\) is not integer. If \(n\) is a prime number bigger than \(2\), \(\frac{(n+2)}{n}\) is not an integer. Thus \(n = 2\) is the unique solution and 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. Please check the OA, Highlighted text is wrong. Stem alreay mention n as > 1. Regards
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Re: Math Revolution DS Expert  Ask Me Anything about GMAT DS
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23 Dec 2018, 19:18
MathRevolution wrote: [ Math Revolution GMAT math practice question] (absolute value) Is \(mn=mn\) ? \(1) mn = 0\) \(2) n = 0\) => 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. Squaring both sides of \(m – n = m  n\) yields \(mn^2=(mn)^2\) \(=> (mn)^2=(mn)^2\) \(=> m^2+n^22mn=m^2+n^22mn\) \(=> m^2+n^22mn=m^2+n^22mn\) \(=> 2mn=2mn\) \(=> mn=mn\) \(=> mn ≥ 0\) Condition 1): \(m – n = 0\) implies that \(m = n.\) So \(mn = n^2 ≥ 0\) for all values of \(n\). Condition 1) is sufficient. Condition 2): If \(n = 0\), then \(0 = mn ≥ 0.\) Condition 2) is sufficient. Therefore, the correct answer is D. Answer: D
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Re: Math Revolution DS Expert  Ask Me Anything about GMAT DS
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23 Dec 2018, 19:20
MathRevolution wrote: [ Math Revolution GMAT math practice question] (integer) \(n\) is a positive integer. Is \(\frac{n(n+1)(n+2)}{4}\) an even integer? 1) \(n\) is an even integer 2) \(1238 ≤ n ≤ 1240\) => 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. Asking for \(\frac{n(n+1)(n+2)}{4}\) to be an even integer is equivalent to asking for \(n(n+1)(n+2)\) to be a multiple of \(8\). If \(n\) is an even integer, \(n\) and \(n+2\) are consecutive even integers and a product of two consecutive even integers is a multiple of \(8\). Thus, condition 1) is sufficient. Condition 2) If \(n = 1238, n(n+1)(n+2)=1238*1239*1240\) is a multiple of \(8\) since \(1240\) is a multiple of \(8\). If \(n = 1239, n(n+1)(n+2)=1239*1240*1241\) is a multiple of \(8\) since \(1240\) is a multiple of \(8\). If \(n = 1240, n(n+1)(n+2)=1240*1241*1242\) is a multiple of \(8\) since \(1240\) is a multiple of \(8\). Thus, condition 2) is sufficient. Therefore, the answer is D. Answer: D Note: This question is a CMT4(B) question. Condition 1) is easy to understand and condition 2) is hard. When one condition is easy to understand, and the other is hard, D is most likely to be the answer.
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24 Dec 2018, 01:01
[ Math Revolution GMAT math practice question] (number property) \(f(x)\) is the greatest prime factor of \(x\). If \(n\) is a positive integer less than \(10\), what is the value of \(n\)? \(1) f(n) = f(1000)\) \(2) f(n) = 5\)
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Re: Math Revolution DS Expert  Ask Me Anything about GMAT DS
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24 Dec 2018, 11:17
ShankSouljaBoi wrote: MathRevolution wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] (number property) If \(n\) is an integer greater than \(1\), what is the value of \(n\)? 1) \(n\) is a prime number 2) \(\frac{(n+2)}{n}\) is 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. 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 there are many prime numbers, condition 1) is not sufficient. Condition 2) If \(n = 1\), then \(\frac{(n+2)}{n} = 3\) is an integer.If \(n = 2,\) then \(\frac{(n+2)}{n} = 2\) is an integer. Since we don’t have a unique solution, condition 2) is not sufficient. Conditions 1) & 2) If \(n = 2\), then \(\frac{(n+2)}{n} = 2\) is an integer. If \(n = 3\), then \(\frac{(n+2)}{n} = \frac{5}{2}\) is not integer. If \(n\) is a prime number bigger than \(2\), \(\frac{(n+2)}{n}\) is not an integer. Thus \(n = 2\) is the unique solution and 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. Please check the OA, Highlighted text is wrong. Stem alreay mention n as > 1. Regards You are right. The question should be changed to the followings. If \(n\) is a positive integer, what is the value of \(n\)? Thank you for your comments.
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25 Dec 2018, 02:06
[ Math Revolution GMAT math practice question] (number properties) If \(n\) is a positive integer, is \(\sqrt{n+1}\) an even integer? 1) \(n\) is the product of \(2\) consecutive odd numbers 2) \(n\) is an odd number
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26 Dec 2018, 01:42
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number property) \(f(x)\) is the greatest prime factor of \(x\). If \(n\) is a positive integer less than \(10\), what is the value of \(n\)? \(1) f(n) = f(1000)\) \(2) f(n) = 5\) => 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. Since we have \(1\) variable (\(n\)) and \(0\) equations, D is most likely to be the answer. So, we should consider each condition on its own first. Condition 1) Since \(1000 = 2^3*5^3, f(1000) = 5.\) So, \(f(n) = 5\) and \(n = 5.\) Thus, condition 1) is sufficient, since it gives a unique solution. Condition 2) Condition 2) is the same as condition 1). Thus, condition 2) is also sufficient. 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. 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.
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26 Dec 2018, 01:43
[ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number? 1) \(\frac{m}{n}\) is an even number 2) \(m\) or \(n\) is an even number
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26 Dec 2018, 02:30
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number? 1) \(\frac{m}{n}\) is an even number 2) \(m\) or \(n\) is an even number #1: m/n = even no m=6, n= 3 m/n= 2 ; m+n= 6+3= 9 sufficient m=4, n=2 ; m/n= 2 ; m+n=4+2 = 6 not sufficient #1 not sufficient #2 : m or n is an even no property of odd no in addition : even+ odd = odd no so since m & n are + integers so either of m or n being even other has to be odd integer hence we would get m+n= odd only sufficient IMO B
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26 Dec 2018, 07:19
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number? 1) \(\frac{m}{n}\) is an even number 2) \(m\) or \(n\) is an even number \(m,n\,\,\, \geqslant 1\,\,\,{\text{ints}}\,\,\,\,\left( * \right)\) \(m + n\,\,\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\boxed{\,\,\,?\,\,\,:\,\,\,\left( {m\,\,{\text{odd}}\,,\,\,n\,\,{\text{even}}} \right)\,\,\,{\text{or}}\,\,\,{\text{vice  versa}\,\,}\,\,}\) \(\left( 1 \right)\,\,\,\frac{m}{n} = {\text{even}}\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \,{\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.\) \(\left( 2 \right)\,\,\,m\,\,{\text{even}}\,\,\,{\text{or}}\,\,\,n\,\,{\text{even}}\,\,\,\,\left\{ \begin{gathered} \,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\text{E}} \right)\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. P.S.: "A or B" means "only A", "only B" or BOTH.
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26 Dec 2018, 07:21
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(n\) is a positive integer, is \(\sqrt{n+1}\) an even integer? 1) \(n\) is the product of \(2\) consecutive odd numbers 2) \(n\) is an odd number Beautiful problem, Max. Congrats (and kudos)! \(n \geqslant 1\,\,\,\operatorname{int}\) \(\sqrt {n + 1} \,\,\,\mathop = \limits^? \,\,{\text{even}}\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\boxed{\,\,n + 1\,\,\,\mathop = \limits^? \,\,\,{{\left( {{\text{even}}} \right)}^2}\,\,}\) \(\left( 1 \right)\,\,\,n = \left( {2M  1} \right)\left( {2M + 1} \right) = {\left( {2M} \right)^2}  {\left( 1 \right)^2}\,\,\,\,\,\left[ {M\,\,\operatorname{int} \,} \right]\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,n + 1 = {\left( {2M} \right)^2}\,\,\,,\,\,\,\,M\,\,\operatorname{int} \,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\) \(\left( 2 \right)\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,n = 1\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,n = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.\,\,\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio.
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26 Dec 2018, 08:21
fskilnik wrote: MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number? 1) \(\frac{m}{n}\) is an even number 2) \(m\) or \(n\) is an even number \(m,n\,\,\, \geqslant 1\,\,\,{\text{ints}}\,\,\,\,\left( * \right)\) \(m + n\,\,\,\,\mathop = \limits^? \,\,{\text{odd}}\,\,\,\,\,\mathop \Leftrightarrow \limits^{\left( * \right)} \,\,\,\,\boxed{\,\,\,?\,\,\,:\,\,\,\left( {m\,\,{\text{odd}}\,,\,\,n\,\,{\text{even}}} \right)\,\,\,{\text{or}}\,\,\,{\text{vice  versa}\,\,}\,\,}\) \(\left( 1 \right)\,\,\,\frac{m}{n} = {\text{even}}\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \,{\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.\) \(\left( 2 \right)\,\,\,m\,\,{\text{even}}\,\,\,{\text{or}}\,\,\,n\,\,{\text{even}}\,\,\,\,\left\{ \begin{gathered} \,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {2,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\ \,\left( {\operatorname{Re} } \right){\text{Take}}\,\,\left( {m,n} \right) = \left( {4,2} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\left( {\text{E}} \right)\) This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. P.S.: "A or B" means "only A", "only B" or BOTH. fskilnik#2 says m or n even ; why have you taken both as even while proving statement as insufficient?
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26 Dec 2018, 09:35
Archit3110 wrote: #2 says m or n even ; why have you taken both as even while proving statement as insufficient? Hi Archit3110 , Thank you for your interest in my solution. As I explained in my post scriptum (PS), the word "OR" has not the everyday common use of "exclusive or". In other words, when it is given that "m is even or n is even", there are three possibilities available: (i) m is even and n is not even (ii) m is not even and n is even (iii) m is even and n is also evenRegards and success in your studies, Fabio.
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27 Dec 2018, 02:14
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(n\) is a positive integer, is \(\sqrt{n+1}\) an even integer? 1) \(n\) is the product of \(2\) consecutive odd numbers 2) \(n\) is an odd number => 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 is equivalent to asking if \(\sqrt{n+1} = 2k\) for some positive integer \(k\). \(\sqrt{n+1} = 2k\) \(=> n+1 = 4k^2\) \(=> n = 4k^21\) \(=> n = (2k1)(2k+1)\) \(n\) is a product of two consecutive odd integers. Thus, condition 1) is sufficient. Condition 2) If \(n = 3\), then \(\sqrt{3+1} = \sqrt{4}=2\) and the answer is ‘yes’. If \(n = 1\), then \(\sqrt{1+1} = 2\) is not an integer and the answer is ‘no’. Condition 2) is not sufficient. Therefore, A is the answer. Answer: A
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27 Dec 2018, 02:15
[ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(3^{4m+2}+n\) divisible by \(5\)? \(1) m=3\) \(2) n=1\)
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28 Dec 2018, 03:17
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(m + n\) an odd number? 1) \(\frac{m}{n}\) is an even number 2) \(m\) or \(n\) is an even number => 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 (\(m\) and \(n\)) 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) Since \(\frac{m}{n}\) is even, \(\frac{m}{n} = 2k\) and \(m = (2k)n\) for some positive integer \(k\). If \(m = 2\) and \(n = 1\), then \(m + n = 3\), is an odd integer and the answer is ‘yes’. If \(m = 4\) and \(n = 2\), then \(m + n = 6\) is an even integer and the answer is ‘no’. Since we do not obtain a unique answer, conditions 1) & 2) are not sufficient when considered together. Therefore, E is the answer. 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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28 Dec 2018, 03:18
[ Math Revolution GMAT math practice question] (function) In the \(xy\)coordinate plane, does \(y=a(xh)^2+k\) intersect the \(x\)axis? \(1) h=1\) \(2) k=2\)
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30 Dec 2018, 18:28
MathRevolution wrote: [ Math Revolution GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(3^{4m+2}+n\) divisible by \(5\)? \(1) m=3\) \(2) n=1\) => 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The units digits of \(3^k\) have period \(4\) as they form the cycle \(3 > 9 > 7 > 1.\) \(3^{4m+2}\) has \(9\) as its units digit if \(3^{4m+2}\) has units digit \(9\), regardless of the value of \(m\). Thus, the divisibility of \(3^{4m+2}+n\) by \(5\) relies on the variable n only. Therefore, the correct answer is B. Answer: B
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Re: Math Revolution DS Expert  Ask Me Anything about GMAT DS
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30 Dec 2018, 18:30
MathRevolution wrote: [ Math Revolution GMAT math practice question] (function) In the \(xy\)coordinate plane, does \(y=a(xh)^2+k\) intersect the \(x\)axis? \(1) h=1\) \(2) k=2\) => 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 (\(a, h\) and \(k\)) 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 \(a = 1\), then the graph doesn’t intersect the \(x\)axis shown as below. Attachment:
1231.png [ 5.04 KiB  Viewed 145 times ]
If \(a = 1\), then the graph intersects the \(x\)axis shown as below. Attachment:
12311.png [ 5.23 KiB  Viewed 145 times ]
Since neither condition gives us information about the value of \(a\), conditions 1) & 2) are not sufficient, when considered together. 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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



Math Revolution GMAT Instructor
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Posts: 7367
GPA: 3.82

Re: Math Revolution DS Expert  Ask Me Anything about GMAT DS
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31 Dec 2018, 02:23
[ Math Revolution GMAT math practice question] (absolute value) Is \(\sqrt{(x+1)^2}=x+1\) ? \(1) x(x2) = 0\) \(2) x(x+2) = 0\)
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MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"




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