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# Is |2a – b| < 7?

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Is |2a – b| < 7? [#permalink]

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02 Dec 2011, 06:22
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Is $$|2a – b| < 7$$?

(1) $$2a – b < 7$$
(2) $$a = b + 3$$

[Reveal] Spoiler:
Guyz, I can't agree with official answer. What are your thoughts on this?
[Reveal] Spoiler: OA
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Re: Is |2a – b| < 7? [#permalink]

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03 Dec 2011, 05:01
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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: Is |2a – b| < 7? [#permalink]

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05 Dec 2011, 05:45
I ended up with C though.When you combined both statements. the statement is true
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Re: Is |2a – b| < 7? [#permalink]

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05 Dec 2011, 14:00
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: Is |2a – b| < 7? [#permalink]

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16 Apr 2014, 07:05
Is Is |2a – b| < 7?

Statement 1

Clearly insufficient we need to know if 2a>b for this to be true

Statement 2

Here we have that a=b+3

But still nothing useful up to this point

Both together

Here's were the magic happens. 2a = 2b+6

So we need to know is 2a>b, is 2b+6>b? Is b>-6? We don't have information to answer this question so clearly answer will be E

Hope this helps
Cheers!
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Re: Is |2a – b| < 7? [#permalink]

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10 Jul 2014, 03:50
Postal wrote:
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?

Hi Bunnel,

is |2a-b| <7

is -7<2a-b<7

here in st1 2a-b <7 but we dont know lower limit of 2a-b so clearly not sufficient.

in St2 a= b+3 . ( nothing new information)

I want to know how to combine both the statement and proceed further?

Thanks
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Re: Is |2a – b| < 7? [#permalink]

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10 Jul 2014, 12:55
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Expert's post
PathFinder007 wrote:
Postal wrote:
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?

Hi Bunnel,

is |2a-b| <7

is -7<2a-b<7

here in st1 2a-b <7 but we dont know lower limit of 2a-b so clearly not sufficient.

in St2 a= b+3 . ( nothing new information)

I want to know how to combine both the statement and proceed further?

Thanks

Actually this is a 30 second question.

Is |2a – b| < 7?

(1) 2a – b < 7. If 2a - b = 0, then |2a - b| = 0 < 7 but if 2a - b = -10, then |2a - b| = 10 > 7. Not sufficient.

(2) a = b + 3. Clearly insufficient.

(1)+(2) Clearly 2a - b = 0 and a = b + 3 as well as 2a - b = -10 and a = b + 3, have solutions, so both cases are still possible. Not sufficient.

Hope it helps.
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Re: Is |2a – b| < 7? [#permalink]

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10 Jul 2014, 21:57
But when we open the mod we get 2 options:

2a-b < 7 OR

2a-b > -7

When A mentions the first option, how come it's not sufficient?

Posted from GMAT ToolKit
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Re: Is |2a – b| < 7? [#permalink]

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11 Jul 2014, 05:26
smit29may wrote:
But when we open the mod we get 2 options:

2a-b < 7 OR

2a-b > -7

When A mentions the first option, how come it's not sufficient?

Posted from GMAT ToolKit

See there lies your fallacy.. Both can be possible so it is NOT possible ( SUFFICIENT) to answer conclusively. Had there been some other condition outlining that 2a-b is always greater than 0 , then it would have been SUFFICIENT. Right now as it is stands , it is ambiguous.

Hope this helps
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Re: Is |2a – b| < 7? [#permalink]

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11 Jul 2014, 11:42
Expert's post
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smit29may wrote:
But when we open the mod we get 2 options:

2a-b < 7 OR

2a-b > -7

When A mentions the first option, how come it's not sufficient?

Posted from GMAT ToolKit

That's not true. The question asks: is |2a - b| < 7? --> is -7 < 2a - b < 7.

(1) says 2a - b < 7. Do we know whether -7 < 2a - b? No. Thus this statement is NOT sufficient.

Check complete solution here: is-2a-b-124076.html#p1381900

Hope it helps.
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Re: Is |2a – b| < 7? [#permalink]

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12 Jan 2015, 15:08
Is |2 a – b| < 7?

(1) 2 a – b < 7
(2) a = b + 3
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Re: Is |2a – b| < 7? [#permalink]

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12 Jan 2015, 15:52
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Expert's post
Hi viktorija,

We can answer this DS question by TESTing VALUES. We just have to make sure to be thorough with what we're TESTing:

We're asked if |2A - B| < 7. This is a YES/NO question.

Fact 1: 2A - B < 7

IF...
A = 0
B = 1
|0 - 1| = |-1| = 1 and the answer to the question is YES

IF...
A = 0
B = 10
|0 - 10| = |-10| = 10 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: A = B + 3

IF...
B = 0
A = 3
|6 - 0| = |6| = 6 and the answer to the question is YES

IF....
B = 1
A = 4
|8 - 1| = | 7| = 7 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we know:
2A - B < 7
A = B + 3

We can substitute in the value of A and get...
2(B+3) - B < 7
2B + 6 - B < 7
B < 1

So whatever we TEST for B, it MUST be < 1

IF....
B = 0
A = 3
|6 - 0| = |6| = 6 and the answer to the question is YES

B can be ANY negative number though, so what happens if we take B to an 'extreme'....?

IF....
B = -100
A = -97
|-194 - (-100)| = |-94| = 94 and the answer to the question is NO
Combined, INSUFFICIENT

[Reveal] Spoiler:
E

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Re: Is |2a – b| < 7? [#permalink]

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12 Jan 2015, 17:55
viktorija wrote:
Is |2 a – b| < 7?

(1) 2 a – b < 7
(2) a = b + 3

Merging topics. Please refer to the discussion above.
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Re: Is |2a – b| < 7? [#permalink]

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16 Feb 2016, 20:01
Postal wrote:
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?

went with E.

1. 2a-b< 7
suppose 2a-b=4 - in this case, both answers are yes.
but if 2a-b=-20? 1 is satisfied, but the answer to the question is no.
not sufficient.

2. we can rewrite |b+6|<7?
if b for ex is -2 -> b+6=4 and the answer is yes.
if b=-20 -> then we have -14 and 14>7 and the answer is no.

1+2
b+6<7
b=-2 - yes
b=-20 - no

E
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Re: Is |2a – b| < 7? [#permalink]

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23 Mar 2017, 17:09
Postal wrote:
Is $$|2a – b| < 7$$ ?

(1) $$2a – b < 7$$
(2) $$a = b + 3$$

OFFICIAL SOLUTION

Absolute value can be understood as distance from zero on the number line. The quantity 2 a – b has an absolute value less than 7 if (and only if) that quantity is less than 7 units away from 0 on a number line.

(1) INSUFFICIENT: This statement tells us that 2 a – b is less than 7, but this does not tell us whether it is less than 7 units away from 0. For instance, 2 a – b could be equal to –20.

(2) INSUFFICIENT: We can manipulate the equation a = b + 3 so that it tells us the value of 2 a – b:

a = b + 3
2 a = 2 b + 6
2 a – b = b + 6

Since there is no restriction on the value of b, b + 6 can be anywhere on the number line. This implies that 2 a – b can be anywhere on the number line, making both “yes” and “no” answers possible.

(1) & (2) INSUFFICIENT: Statement (2) does not restrict the value of 2 a – b at all, so combining it with statement (1) yields the same result as for statement (1) alone. In a sense, the catch in this problem is that there is no catch: we should be suitably suspicious when a problem seems easier than it ought to be, but we should then trust our analysis and choose confidently.

Re: Is |2a – b| < 7?   [#permalink] 23 Mar 2017, 17:09
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