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Is |2a – b| < 7?

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Is |2a – b| < 7? [#permalink] New post 02 Dec 2011, 05:22
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (02:43) correct 27% (01:46) wrong based on 18 sessions
Is |2a – b| < 7?

(1) 2a – b < 7
(2) a = b + 3

Guyz, I can't agree with official answer. What are your thoughts on this?
[Reveal] Spoiler: OA
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Re: from online Manhattan drill [#permalink] New post 03 Dec 2011, 04:01
What was your answer, and why?

I get E.

From 1:
2a – b < 7 AND |2a – b| < 7 WHERE 2a -b > -7
2a – b < 7 BUT |2a – b| > 7 WHERE 2a -b < -7
INSUFFICIENT

to confirm this you can find values of a & b that satisfy the condition 2a – b < 7 but provide different answers for |2a – b| < 7 ?
A: a = 3, b = 0
2a - b = 6 - 0 = 6
6 < 7 and |6| < 7
B: a = -10, b = 1
2a - b = -20 - 1 = -21
-21 < 7 but |-21| > 7

From 2 you can refactor the original question:
Is |2(b + 3) - b| < 7? => is |b + 6| < 7?
This is true for -13 < b < 1 but false for value outside of this range.
Again INSUFFICIENT.

Together, we can further combine in a similar manner as above to see that
b + 6 < 7 so we find that b < 1, but we still don't know if b > -13.

So together is INSUFFICIENT.

Again, to see that this is the case, you can substitute numbers that satisfy both 1 & 2, but give different answers to the main question:

A: a = 3, b = 0
2a – b < 7 : 2a - b = 6 - 0 = 6 < 7
a = b + 3 : 3 = 0 + 3
|2a – b| < 7 ? : |6| < 7 TRUE

B: a = -20, b = -17
2a – b < 7 : 2a - b = -40 - (-17) = -23 < 7
a = b + 3 : -20 = -17 + 3
|2a – b| < 7 ? : |-23| < 7 FALSE
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Re: from online Manhattan drill [#permalink] New post 05 Dec 2011, 04:45
I ended up with C though.When you combined both statements. the statement is true
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Re: from online Manhattan drill [#permalink] New post 05 Dec 2011, 13:00
Can you see from my explanation above that when you combine both statementsiit is true for some values (a=3, b=0), but not all values (a=-20, b=-17)?

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Re: from online Manhattan drill   [#permalink] 05 Dec 2011, 13:00
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Is |2a – b| < 7?

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