Is |2a b|

Question

Is  |2a – b| < 7 ?
 
(1)  2a – b < 7 
(2)  a = b + 3

Bunuel · Accepted Answer

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.

Answer: E.

Hope it helps.

bobfirth · Answer

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

PathFinder007 · Answer

Hi Bunnel,

Could you please provide your comments on this. I am using following logic

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

smit29may · Answer

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?

Please help

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Bunuel · Answer

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.

EMPOWERgmatRichC · Answer

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

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

BillyZ · Answer

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.
 
The correct answer is E.

JS99 · Answer

Bunuel

Statement 1 would be sufficient only if we know 2a - b is positive or 0. For all the values 2a - b is negative, the information becomes insufficient.
Statement 2 would be insufficient on its own because the range of the expression cannot be determined. However, doesn't statement 2 tell us that a is greater than b because a is 3 more than b? If a is greater than b, 2a - b will be greater than 0,
Using this conclusion, can we not support statement 1?

Statement 2 tells 2a-b is positive, and with this condition, statement 1 should be able to justify the given problem statement.

Please help me with examples to understand where am I wrong.

Bunuel · Answer

I have provided a detailed explanation with examples for this question  here . Please go through it, and let me know if there's anything that still seems unclear.

Is |2a b| < 7? (1) 2a b < 7 (2) a = b + 3

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