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What is the value of X?

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What is the value of X?  [#permalink]

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New post 18 Jan 2019, 08:59
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A
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What is the value of X?

A. 8X+16Y+24K = 80

B. 18X+24Y+36K= 180

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Re: What is the value of X?  [#permalink]

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New post 18 Jan 2019, 10:34
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fitzpratik wrote:
What is the value of X?

A. 8X+16Y+24K = 80

B. 18X+24Y+36K= 180


Answer C

Statement A .
8X+16Y+24K = 80
Can be reduced to
X + 2Y + 3K = 10
X = 10 - 2Y - 3K ---------------(a)

2 unknowns cant do anything here, OUT

Statement B
18X+24Y+36K= 180
Can be reduced to
3X + 4Y + 6K = 30
X = (30 - 4Y - 6K)/3 -------------------(b)

2 unknowns cant do anything here, OUT

Combine C, Now we can equate for (a) & (b)
(30 - 4Y - 6K)/3 = 10 - 2Y - 3K
30 - 4Y - 6K = 30 - 6Y - 9K
-4Y + 6Y = -9K + 6K
2Y = 3K
Y = - (3K/2)

Value of Y in (a)
X = 10 + 3k - 3k
X = 10
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Re: What is the value of X?  [#permalink]

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New post 18 Jan 2019, 10:55
The answer is option C.

So better not to try and get the value of X by substituting values. Rather try to check whether they are solvable or not.

A. 8X+16Y+24K = 80

B. 18X+24Y+36K= 180

Let me write equation A in the form:- lX + mY + nZ = 80
and equation B in the form:- pX + qY + rZ = 180

So to check whether we can solve this find the value of l:m:n and p:q:r and compare both of them. (we are find the ratio of coef. here)

For equation A, we have l:m:n = 8:16:24 which is equal to 1:2:3
For equation B, we have p:q:r = 18:24:36 which is qual to 3:4:6

We can see here that the ratio of second and the third terms in this ratio are equal (which is 1:2) but the ratio of the first term is not equal with respect to any other term. So somehow if you subtitute, the value of X (the first term) can be found out and not the remaining terms.
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What is the value of X?  [#permalink]

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New post 18 Jan 2019, 11:00
We can multiply equuation 1 by 3 and equation 2 by 2 and get the value 10 easily. Is my method incorrect ?

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Re: What is the value of X?  [#permalink]

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New post 18 Jan 2019, 11:21
Laksh128 wrote:
We can multiply equuation 1 by 3 and equation 2 by 2 and get the value 10 easily. Is my method incorrect ?

Posted from my mobile device


Yes absolutely the method is correct.
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Re: What is the value of X?   [#permalink] 18 Jan 2019, 11:21
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