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Updated on: 08 Aug 2024, 13:31
Originally posted by MathRevolution on 02 Oct 2017, 01:55.
Last edited by Bunuel on 08 Aug 2024, 13:31, edited 4 times in total.
Last edited by Bunuel on 08 Aug 2024, 13:31, edited 4 times in total.
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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59% (01:12) correct
41%
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If the operation # is defined by x#y = ax + by (a and b are constants), what is the value of 2#4?
(1) 1#2 = 5
(2) 1#1 = 6
(1) 1#2 = 5
(2) 1#1 = 6
02 Oct 2017, 04:34
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MathRevolution
To find the value of 24 we need the values of x, y, a and b
Statement 1: implies a+2b=5 because x=1 and y=5. From this we cannot calculate the value of a & b. Hence Insufficient
Statement 2: implies a+b=6 because x=1 and y=1. From this we cannot calculate the value of a & b. Hence Insufficient
Combining 1 & 2, solve the two equation to get a=7 and b=-1
so 24=7x-y. but we don't know the value of x & y. multiple values are possible such as x=3 & y=-3 or x=8 & y=4. Hence insufficient
Option E
Updated on: 28 Oct 2017, 12:38
Originally posted by MathRevolution on 04 Oct 2017, 01:40.
Last edited by MathRevolution on 28 Oct 2017, 12:38, edited 1 time in total.
Last edited by MathRevolution on 28 Oct 2017, 12:38, edited 1 time in total.
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Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.
The question is what the value of 2a + 4b is.
Condition 1) a + 2b = 5
2a + 4b = 2(a+2b) = 2*5 = 10
This is sufficient.
Condition 2) a + b = 6
a = 1, b = 5 ➔ 2a + 4b = 2 + 20 = 22
a = 3, b = 3 ➔ 2a + 4b = 6 + 12 = 18
This is not sufficient.
Therefore, A is the answer.
Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.
The question is what the value of 2a + 4b is.
Condition 1) a + 2b = 5
2a + 4b = 2(a+2b) = 2*5 = 10
This is sufficient.
Condition 2) a + b = 6
a = 1, b = 5 ➔ 2a + 4b = 2 + 20 = 22
a = 3, b = 3 ➔ 2a + 4b = 6 + 12 = 18
This is not sufficient.
Therefore, A is the answer.
Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
