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The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value

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The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value  [#permalink]

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New post 05 Sep 2018, 02:16
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[Math Revolution GMAT math practice question]

The numbers \(x, y\) and \(z\) are in the ratio \(3\) to \(4\) to \(5\). What is the value of \(x\)?

1) \(y = 16\)
2) The difference between \(y\) and \(z\) is \(4\)

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Re: The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value  [#permalink]

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New post 05 Sep 2018, 02:33
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The numbers \(x, y\) and \(z\) are in the ratio \(3\) to \(4\) to \(5\). What is the value of \(x\)?

1) \(y = 16\)
2) The difference between \(y\) and \(z\) is \(4\)



We know the ratio x:y:z=3:4:5=3a:4a:5a
So if we know any one value, we can find all

1) y=16
So 4a=16....a=4
x=3a=4*3=12
Sufficient

2) z-y=4
So 5a-4a=4....a=4
So x=3a=3*4=12...
But is it possible that 4a-5a=4...a=-4 and thus 3a=-12
NO, because generally on GMAT, the ratios are of positive quantity
So only one value 12
Sufficient

D
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value  [#permalink]

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New post 07 Sep 2018, 01:16
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method I s 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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The original condition gives the proportion \(x : y : z = 3 : 4 : 5\), so we can write \(x = 3k, y = 4k\) and \(z = 5k\). We have 4 variables and 3 equations.
Therefore, D is most likely to be the answer.

Condition 1) is sufficient since \(16 = y = 4k\), and so \(k = 4\). Then \(x = 3k = 12.\)
Condition 2) is also sufficient since \(4 = z – y = 5k – 4k = k\). So, \(x = 3k = 12.\)

Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) give similar information.

Therefore, D is the answer.
Answer: D
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Re: The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value  [#permalink]

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New post 13 Sep 2018, 10:21
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Dear moderator,

This is not a work rate problem. Please amend the tag.
Thanks
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Re: The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value  [#permalink]

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New post 13 Sep 2018, 21:09
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Re: The numbers x, y and z are in the ratio 3 to 4 to 5. What is the value &nbs [#permalink] 13 Sep 2018, 21:09
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