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# Is |v - x| < 8?

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Joined: 17 Jan 2010
Posts: 23
Is |v - x| < 8?  [#permalink]

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Updated on: 27 Jul 2015, 14:41
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5% (low)

Question Stats:

86% (01:07) correct 14% (01:11) wrong based on 270 sessions

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Is |v - x| < 8?

(1) v and x are integers
(2) |v| = 4 and |x| = 6

Originally posted by rahulms on 22 Jan 2010, 05:39.
Last edited by Bunuel on 27 Jul 2015, 14:41, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Is |v - x| < 8?  [#permalink]

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22 Jan 2010, 06:54
2
1
|x-v| < 8

Solution two:
Plug in numbers. V is +4 or -4. X is +6 or -6.
Therefore, we have four combinations:
|4-6| = 2
|-4-6| = 10
Already, we can tell that |v-x| could be > OR < 8.
So, two alone cannot solve.

Now, it gets more fun:
|x-v| < 8 must be broken into two equations thanks to the inequality.
We have:
a. x-v < 8
b. -(x-v) > 8 -- note the flip in inequality*.

With these two solutions.
I. v and x are integers: this only tells us x and v are not decimal numbers. Not that useful in my opinion.
If x is 20 and v is 2, x-v is not less than 8 and -(x-v) is not greater than 8.
If x is 2 and v is 20, x-v IS less than 8 and -(x-v) IS greater than 8.
So one alone cannot work.

Well, when we tried solution two alone, we used integers anyways. Answer two essentially tells you the numbers are integers.

I would say e, neither answer alone nor together.

*Now, you really didn't need to know about the 'flip the equality' part above for this question, but I find that it is a useful thing to know when dealing with absolute numbers in equalities...
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Is |v - x| < 8?  [#permalink]

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24 Oct 2015, 04:44
In fact, this question asks whether the distance between x and v is less than 8 (modulus theory).

1) Not sufficient since provide no clue on the distance.
2) according to this condition x and v could be:
a) 4 and 6 - then distance between them is less than 8
b) -4 and 6 - then distance > 8
thus, 2) is not sufficient.

1) + 2) does not differ from 2) alone - not sufficient.
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Re: Is |v - x| < 8?  [#permalink]

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27 Oct 2015, 23:46
Forget conventional ways of solving math questions. In DS, Variable approach 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.

Is |v - x| < 8?
(1) v and x are integers
(2) |v| = 4 and |x| = 6

Looking at the original condition, there are 2 variables (v,x) and 2 equations, so there is high chance (C) will be our answer.
From the conditions, the answer to what the question asks is 'yes' for v=4, x=6, but 'no' for v=4, x=-6. So this condition is insufficient, and the answer becomes (E).

For cases where we need 2 more equation, 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, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. 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 using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Is |v - x| < 8?  [#permalink]

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18 Jul 2016, 06:03
rahulms wrote:
Is |v - x| < 8?

(1) v and x are integers
(2) |v| = 4 and |x| = 6

Is |v - x| < 8?

(1) v and x are integers
Infinite values for x and v possible
INSUFFICIENT

(2) |v| = 4 and |x| = 6
|v| = 4,-4
|x|= 6, -6
Operation of addition and subtraction will yield different values for different polarities of v and x
INSUFFICIENT

MERGEING THE TWO STATEMENTS IS NOT HELPFUL EITHER BECAUSE IT WILL FOLLOW THE LOGIC OF STATEMENT 2

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Re: Is |v - x| < 8?  [#permalink]

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06 Mar 2018, 06:06
rahulms wrote:
Is |v - x| < 8?

(1) v and x are integers
(2) |v| = 4 and |x| = 6

Question : Is |v - x| < 8

or Is -8 < v - x < 8

St 1: = v & x are integers. -7 to 7, all integers can be used. Not sufficient

St 2: |v| = 4 and |x| = 6

means v = 4 or -4 , and x = 6 or -6

Take v = 4 & x = - 6 , Answer to question, No

Take v = 4 & x = 6, Answer to question, Yes

Not Sufficient

Combining: Not Sufficient

(E)
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Re: Is |v - x| < 8?   [#permalink] 06 Mar 2018, 06:06
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