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Updated on: 14 Apr 2022, 01:28
Originally posted by MathRevolution on 06 Jun 2019, 17:57.
Last edited by MathRevolution on 14 Apr 2022, 01:28, edited 2 times in total.
Last edited by MathRevolution on 14 Apr 2022, 01:28, edited 2 times in total.
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MathRevolution
=>
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 \(x = 2, y = 3, z = 5\), then \(x\) and \(z\) are relatively prime, and the answer is ‘yes’.
If \(x = 2, y = 3, z = 2,\) then \(x\) and \(z\) are not relatively prime, and the answer is ‘no’.
Both conditions together are not sufficient, since they don’t yield a unique answer.
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.
06 Jun 2019, 17:58
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[GMAT math practice question]
(number properties) We define ‘a mod n’ to be the remainder when a is divided by n. What is the value of ‘a mod 12’?
1) a mod 3=1
2) a mod 4=a mod 2
(number properties) We define ‘a mod n’ to be the remainder when a is divided by n. What is the value of ‘a mod 12’?
1) a mod 3=1
2) a mod 4=a mod 2
Updated on: 16 Feb 2021, 03:23
Originally posted by MathRevolution on 07 Jun 2019, 02:03.
Last edited by MathRevolution on 16 Feb 2021, 03:23, edited 1 time in total.
Last edited by MathRevolution on 16 Feb 2021, 03:23, edited 1 time in total.
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MathRevolution
=>
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)
Now, by condition 1),\(x < x + 2 ≤ | x + 2 | < y < z + 2,\) and \(x < y\).
By condition 2), \(|x-2|<y<z-2 < z,\) and so \(y < z\).
Thus, both conditions together are sufficient since they yield \(x < y < z\), and the unique answer is ‘yes’.
Since this question is an inequality 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 \(x = 1, y = 4\), and \(z = 7\), then the answer is ‘yes’.
If \(x = 1, y = 4,\) and \(z = 3,\) then the answer is ‘no’.
Condition 1) is not sufficient since it doesn’t yield a unique answer.
Condition 2)
If \(x = 1, y = 4,\) and \(z = 7\), then the answer is ‘yes’.
If \(x = 5, y = 4,\) and\(z = 7,\) then the answer is ‘no’.
Condition 2) is not sufficient since it doesn’t yield a unique answer.
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.
