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# If x/3 - x/6 + x/9 - x/12 = 1 - 1/2

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If x/3 - x/6 + x/9 - x/12 = 1 - 1/2 [#permalink]  08 Jan 2019, 10:29
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If $$\frac{x}{3} - \frac{x}{6} + \frac{x}{9} - \frac{x}{12} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}$$ , then $$x =$$

A. $$3$$

B. $$1$$

C. $$\frac{1}{3}$$

D. $$-\frac{1}{3}$$

E. $$-3$$
[Reveal] Spoiler: OA

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Re: If x/3 - x/6 + x/9 - x/12 = 1 - 1/2 [#permalink]  09 Jan 2019, 04:35
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Carcass wrote:
If $$\frac{x}{3} - \frac{x}{6} + \frac{x}{9} - \frac{x}{12} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}$$ , then $$x =$$

A. $$3$$

B. $$1$$

C. $$\frac{1}{3}$$

D. $$-\frac{1}{3}$$

E. $$-3$$

Explanation::

$$\frac{x}{3} - \frac{x}{6} + \frac{x}{9} - \frac{x}{12} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}$$

$$\frac{7x}{36} = \frac{7}{12}$$

or x = 3
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Re: If x/3 - x/6 + x/9 - x/12 = 1 - 1/2 [#permalink]  09 Jan 2019, 06:29
Expert's post
Carcass wrote:
If $$\frac{x}{3} - \frac{x}{6} + \frac{x}{9} - \frac{x}{12} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}$$ , then $$x =$$

A. $$3$$

B. $$1$$

C. $$\frac{1}{3}$$

D. $$-\frac{1}{3}$$

E. $$-3$$

$$\frac{x}{3} - \frac{x}{6} + \frac{x}{9} - \frac{x}{12} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}$$ .....
We can see the formation of the terms is similar on both sides, so let us get the left hand side in terms similar to RHS, by taking out $$\frac{x}{3}$$..
$$\frac{x}{3} - \frac{x}{6} + \frac{x}{9} - \frac{x}{12} =\frac{x}{3}*1 - \frac{x}{3}*\frac{1}{2} + \frac{x}{3}*\frac{1}{3} - \frac{x}{3}*\frac{1}{4} = \frac{x}{3}(1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4})$$
This should be equal to RHS..
$$\frac{x}{3}(1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}) = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4}........\frac{x}{3}=1....x=3$$ .....

A
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: If x/3 - x/6 + x/9 - x/12 = 1 - 1/2   [#permalink] 09 Jan 2019, 06:29
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# If x/3 - x/6 + x/9 - x/12 = 1 - 1/2

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