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# If the operation is defined by xy=ax+by (a and b are

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Math Revolution GMAT Instructor
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If the operation is defined by xy=ax+by (a and b are  [#permalink]

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Updated on: 09 Oct 2017, 08:06
00:00

Difficulty:

45% (medium)

Question Stats:

54% (01:15) correct 46% (01:18) wrong based on 71 sessions

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[GMAT math practice question]

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

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Originally posted by MathRevolution on 02 Oct 2017, 01:55.
Last edited by chetan2u on 09 Oct 2017, 08:06, edited 3 times in total.
Corrected the Q and OA
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Re: If the operation is defined by xy=ax+by (a and b are  [#permalink]

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02 Oct 2017, 04:34
MathRevolution wrote:
[GMAT math practice question]

If the operation @ is defined by x@y=ax+by (a and b are constants), what is the value of 24?

1) 1@2=5
2) 1@1=6

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
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If the operation is defined by xy=ax+by (a and b are  [#permalink]

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Updated on: 28 Oct 2017, 12:38
1
=>

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.

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.
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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.
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Re: If the operation is defined by xy=ax+by (a and b are  [#permalink]

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04 Oct 2017, 06:46
MathRevolution wrote:
=>

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.

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.

Ans: E

Hi MathRevolution

Both the question and your response are ambiguous. What is the question exactly asking? is it to calculate the value of 24 or is it to calculate 2a+4b?
In you post at one point you are saying the answer is A and at the end you have mentioned E and the OA provided is also E, So what exactly is the correct Option?
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Posts: 8006
Re: If the operation is defined by xy=ax+by (a and b are  [#permalink]

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09 Oct 2017, 08:09
1
MathRevolution wrote:
[GMAT math practice question]

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

x#y=ax+by..
so 2#4=2a+4b...

lets see the statements

1) 1#2=5
a+2b=5..
so 2a+4b=5*2=10
suff

2) 1#1=6
a+b=6
insuff

A
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Re: If the operation is defined by xy=ax+by (a and b are  [#permalink]

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28 Mar 2019, 18:15
Hi,

What does it mean by "a and b are constants"? Are a and b constant integers like 1 and 2, 3 and 4, and so on?
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Posts: 8006
Re: If the operation is defined by xy=ax+by (a and b are  [#permalink]

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28 Mar 2019, 20:32
1
JS1290 wrote:
Hi,

What does it mean by "a and b are constants"? Are a and b constant integers like 1 and 2, 3 and 4, and so on?

Yes, a and b as constant means that it cannot have more than one value.
say a line is y=mx+c..
Here the line is formed by taking different values of (x,y), m is the slope and will always remain the same . Even c is a constant here, that is it will not vary with x and y.
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Re: If the operation is defined by xy=ax+by (a and b are   [#permalink] 28 Mar 2019, 20:32
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