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Math Revolution GMAT Instructor
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20 Mar 2019, 01:52
MathRevolution wrote: [GMAT math practice question]
(number properties) Is \(\sqrt{15n}\) an integer?
1) \(n\) is a multiple of \(3\) 2) \(n\) 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. 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) If \(n = 15\), then \(\sqrt{15n} = \sqrt{15^2} = 15\) is an integer and the answer is “yes”. If \(n = 3\), then \(\sqrt{15n} = \sqrt{45} = 3\sqrt{5}\) is not an integer and the answer is “no”. Thus, condition 1) is not sufficient, since it does not yield a unique solution. Condition 2) We have \(n = k^2\) for some integer \(k\). So, \(\sqrt{15n} = \sqrt{15k^2}=k\sqrt{15}\) is not an integer. Since ‘no’ is also a unique answer by CMT (Common Mistake Type) 1, condition 2) is sufficient. Therefore, B is the answer. Answer: B 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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20 Mar 2019, 01:53
[GMAT math practice question] (number properties) Is \(n\) an odd number? 1) \(n\) and \(n+2\) are prime numbers 2) \(n+5\) is a multiple of \(5\)
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20 Mar 2019, 08:58
MathRevolution wrote: [GMAT math practice question]
(absolute value) \(xy=?\)
\(1) (x2)^2 = y3\) \(2) x2 + \sqrt{y3} =0\)
\(? = xy\) \(\left( 1 \right)\,\,\,{\left( {x  2} \right)^2} =  \left {y  3} \right\,\,\,\,\,\left( * \right)\) \(\left. \matrix{ {\left( {x  2} \right)^2} \ge 0 \hfill \cr  \left {y  3} \right \le 0\,\, \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left\{ \matrix{ \,x  2 = 0 \hfill \cr \,y  3 = 0 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {2,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}\) \(\left( 2 \right)\,\,\,\left {x  2} \right + \sqrt {y  3} \,\, = 0\,\,\,\,\,\,\left( {**} \right)\) \(\left. \matrix{ \left {x  2} \right \ge 0 \hfill \cr \sqrt {y  3} \ge 0\,\, \hfill \cr} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\left\{ \matrix{ \,x  2 = 0 \hfill \cr \,y  3 = 0 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {x,y} \right) = \left( {2,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}{\rm{.}}\) The correct answer is (D). We follow the notations and rationale taught in the GMATH method. Regards, Fabio.
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Math Revolution DS Expert  Ask Me Anything about GMAT DS
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Updated on: 20 Mar 2019, 09:53
MathRevolution wrote: [GMAT math practice question]
(number properties) Is \(n\) an odd number?
1) \(n\) and \(n+2\) are prime numbers 2) \(n+5\) is a multiple of \(5\) To find: n=odd? (1)n=prime and n+2=prime 2= prime but 2+2 is not prime. So this value is irrelevant.3=prime and 3+2=prime and n=odd YES 7=prime and 7+2=9 odd but not prime11=prime and 11+2=prime and n=odd YES 17=prime and 17+2=prime and n=odd YES Those values that satisfy n=prime and n+2=prime satisfies the condition, n=odd. SUFFICIENT (2) n+5 is a multiple of 5 You are doing to get various numbersboth even and odd. Different answers. INSUFFICIENT IMO Statement (1) alone is sufficient.
Originally posted by EncounterGMAT on 20 Mar 2019, 09:17.
Last edited by EncounterGMAT on 20 Mar 2019, 09:53, edited 2 times in total.



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20 Mar 2019, 09:37
MathRevolution wrote: [GMAT math practice question]
(number properties) Is \(n\) an odd number?
1) \(n\) and \(n+2\) are prime numbers 2) \(n+5\) is a multiple of \(5\) Statement 1: I know that \(n\) and \(n + 2\) are prime. So, we can discard \(n = 2\), since \(2 +2 = 4\), not prime. All other prime numbers are odd. So, sufficient. Statement 2: \(n\) could be \(0, 5, 10, 15...\). \(5\) odd, \(0\) even. Not sufficient. IMHO, correct answer is A.



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21 Mar 2019, 02:31
MathRevolution wrote: [GMAT math practice question]
(absolute value) \(xy=?\)
\(1) (x2)^2 = y3\) \(2) x2 + \sqrt{y3} =0\) => 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. Condition 1) \((x2)^2 = y3\) \(=> (x2)^2 + y3 = 0\) \(=> x=2\) and \(y = 3\) Condition 1) is sufficient since it yields a unique solution. Condition 2) \(x2 + \sqrt{y3} =0\) \(=> x=2\) and \(y = 3\) Condition 2) is sufficient since it yields a unique solution. 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.
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21 Mar 2019, 02:31
[GMAT math practice question] (number properties) If \(m\) and \(n\) are positive integers, is \(m+n\) divisible by \(15\)? 1) \(m\) is divisible by \(9\) and \(n\) is divisible by \(15\). 2) \(mn\) is divisible by \(225\).
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22 Mar 2019, 00:35
MathRevolution wrote: [GMAT math practice question]
(number properties) Is \(n\) an odd number?
1) \(n\) and \(n+2\) are prime numbers 2) \(n+5\) is a multiple of \(5\) => 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. We then recheck the question. If \(n\) and \(n+2\) are prime numbers from condition 1), then both \(n\) and \(n + 2\) are odd numbers. Note that \(2\) is the only even prime number, and \(2 + 2 = 4\) is not prime. Thus, condition 1) is sufficient. Condition 2) If \(n + 5 = 10\), then \(n = 5\) is an odd number and the answer is ‘yes’. If \(n + 5 = 15\), then \(n = 10\) is an even number and the answer is ‘no’. Thus, condition 2) is not sufficient, since it does not yield a unique solution. Therefore, A is the answer. Answer: A
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22 Mar 2019, 00:36
[GMAT math practice question] (number properties) If \(m\) and \(n\) are prime numbers, what is the value of \(m+n\)? \(1) 15 ≤ m < n ≤ 20\) \(2) mn = 323\)
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24 Mar 2019, 18:23
MathRevolution wrote: [GMAT math practice question]
(number properties) If \(m\) and \(n\) are positive integers, is \(m+n\) divisible by \(15\)?
1) \(m\) is divisible by \(9\) and \(n\) is divisible by \(15\). 2) \(mn\) is divisible by \(225\). => 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) If \(m = 45\) and \(n = 45\), then \(m + n = 90\) is divisible by \(15\) and the answer is ‘yes’. If \(m = 9\) and \(n = 225\), then \(m + n = 234\) is not divisible by \(15\) and the answer is ‘no’. Thus, both conditions together are not sufficient, since they do not yield a unique solution. 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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24 Mar 2019, 18:24
MathRevolution wrote: [GMAT math practice question]
(number properties) If \(m\) and \(n\) are prime numbers, what is the value of \(m+n\)?
\(1) 15 ≤ m < n ≤ 20\) \(2) mn = 323\) => 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 1) \(15≤m<n≤20\) tells us that \(m = 17\) and \(n = 19\). So, \(m + n = 17 + 19 = 36.\) Condition 1) is sufficient since it yields a unique solution. Condition 2) \(mn=323\) tells us that \(m = 17\) and \(n = 19\), or \(m = 19\) and \(n = 17\). In both cases, \(m + n\) is \(36\). Condition 2) is sufficient since it yields a unique solution. Therefore, D is the answer. Answer: D
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25 Mar 2019, 00:32
[GMAT math practice question] (number properties) \(m, n\) and \(\frac{2}{m}+\frac{3}{n}\) are positive integers. What is the value of \(mn\)? 1) \(m\) and \(n\) are prime numbers 2) The greatest common divisor of \(m\) and \(n\) is \(1\)
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26 Mar 2019, 02:09
[GMAT math practice question] (number properties) \(p, q\), and \(r\) are different prime numbers. What is the value of \(q\)? \(1) (pq)^2=36\) \(2) (qr)^2= 225\)
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27 Mar 2019, 00:59
MathRevolution wrote: [GMAT math practice question]
(number properties) \(m, n\) and \(\frac{2}{m}+\frac{3}{n}\) are positive integers. What is the value of \(mn\)?
1) \(m\) and \(n\) are prime numbers 2) The greatest common divisor of \(m\) and \(n\) 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The possible pairs \((m,n)\) are \((1,1),(1,3),(2,1),(2,3)\) and \((5,5)\). 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) There is a unique pair of integers which satisfies both conditions. This is \(m = 2\) and \(n = 3\). So, \(mn = 6\). Conditions 1) & 2) are sufficient, when applied together. 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) If \(m = 2\) and \(n = 3\), then \(mn = 6\). If \(m = 5\) and \(n = 5\), then \(mn = 25\). Condition 1) is not sufficient since it does not yield a unique solution. Condition 2) If \(m = 2\) and \(n = 3\), then \(mn = 6\). If \(m = 1\) and \(n = 1\), then \(mn = 1\). Condition 2) is not sufficient since it does not yield a unique solution. Therefore, C is the answer. Answer: C 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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27 Mar 2019, 01:00
[GMAT math practice question] (number properties) Is the fourdigit positive integer \(a,bc6\) divisible by \(4\)? 1) \(ac\) is an odd number 2) \(bc\) is an even number
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28 Mar 2019, 01:39
MathRevolution wrote: [GMAT math practice question]
(number properties) \(p, q\), and \(r\) are different prime numbers. What is the value of \(q\)?
\(1) (pq)^2=36\) \(2) (qr)^2= 225\) => 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 (\(p, q\) and \(r\)) 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 \(p^2q^2=2^2^32\) and \(q^2r^2 = 3^25^2\), we have \(p = 2, q = 3\) and \(r = 5\). Conditions 1) & 2) are sufficient, when applied together. 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 \(p^2q^2=2^23^2\), we must have \(p = 2, q = 3\) or \(p = 3, q = 2.\) Condition 1) is not sufficient since it does not yield a unique solution. Condition 2) Since \(q^2r^2=3^25^2\), we have \(q = 3, r = 5\) or \(q = 5, r = 3.\) Condition 2) is not sufficient since it does not yield a unique solution. 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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28 Mar 2019, 01:40
[GMAT math practice question] (statistics) What is the median of the three numbers \(a, b\) and \(24\)? \(1) a – 24 = 24  b\) \(2) (a24)(b24) < 0\)
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29 Mar 2019, 00:14
MathRevolution wrote: [GMAT math practice question]
(number properties) Is the fourdigit positive integer \(a,bc6\) divisible by \(4\)?
1) \(ac\) is an odd number 2) \(bc\) 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. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. The number \(a,bc6\) is divisible by \(4\) precisely when \(c\) is an odd number. Condition 1) tells us that both \(a\) and \(c\) are odd numbers. Thus, condition 1) is sufficient. Condition 2) If \(a = 1, b = 2, c = 1\), then \(1216\) is divisible by \(4\) and the answer is ‘yes’. If \(a = 1, b = 1, c = 2\), then \(1126\) is not divisible by \(4\) and the answer is ‘no’. Thus, condition 2) is not sufficient, since it does not yield a unique solution. Therefore, A is the answer. Answer: A
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29 Mar 2019, 00:15
[GMAT math practice question] The diagram below contains four right triangles with legs a and b. What is the area of the larger square? Attachment:
3.29.png [ 8.7 KiB  Viewed 207 times ]
1) a = 12 2) b = 9
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31 Mar 2019, 18:36
MathRevolution wrote: [GMAT math practice question]
(statistics) What is the median of the three numbers \(a, b\) and \(24\)?
\(1) a – 24 = 24  b\) \(2) (a24)(b24) < 0\) => 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. Condition 1) means the average of \(a, b\) and \(24\) is \(\frac{(a + b + 24 )}{3} = 24\) since it implies that \(\frac{( a + b )}{2} = 24\). Since one of the three data points is their average, it is also their median. Condition 1) is sufficient. Condition 2) If \(a > 24\) and \(b < 24\), the median of \(a, b\) and \(24\) is \(24\). If \(a < 24\) and \(b > 24\), the median of \(a, b\) and \(24\) is \(24\). Thus, we have a unique value for the median, and condition 2) is sufficient. Therefore, D is the answer. Answer: D Note: Condition 1) is easy to understand and condition 2) is hard to understand. Thus, this question is a CMT4(B) question. When one condition is easy to understand, and the other is hard to understand, D is most likely to be the answer.
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