If ac/(db)

Question

If ac/(db) < 0, is d – b < 0 ?

(1) |a − c| = |a| − |c|
(2) d – b > d + b

deabas · Answer

If ac/(db) < 0, is d – b < 0 ?

(1) |a − c| = |a| − |c|
This statement holds only if both a and c have the same sign
-------> ac>0
-------> db<0 but not necessarily d - b < 0 [consider this case: d=5 and b=-1: db<0 but d-b >0]
Statement 1 is not sufficient (eliminate A and D)

(2) d – b > d + b
----> d - d > b + b
----> 0 > 2b
----> b < 0
Statement 2 is not sufficient alone (eliminate B)

Both statements together:
----> ac>0
----> db<0 ----> b<0 ----> d>0
the difference between any two different numbers (+ve and -ve) > 0

"C"

something123 · Answer

Could you please explain why

|a − c| = |a| − |c|
This statement holds only if both a and c have the same sign

Thanks.

chetan2u · Answer

Hi,

If both a and c are of opposite sign....
|a-c| will result in a higher value than |a|-|c|, as a-c will result in numeric value of a and c getting added up, and then MODULUS value will make it a positive value..

lets check with example..
let a = 5, and c = -10...... a-c = 5-(-10)=15 and |15| = 15....... but |a| = |5| and |c| = |-10|, so |a|-|c| = |5|--10|=5-10 =-5....

But if a and b are of same sign...
a= 5 and c=10...
 |a-c| = |5-10| = |-5| = 5........  and |a|-|c| = |5|-|10| = -5....  But  5
eq{-5} ..
  What does it tell us? 
That Not only both a and c should be of same sign BUt also numeric value of a should be mor than that of c...... Numeric value is value without sign..

target760gmat · Answer

If ac/(db) < 0, is d – b < 0 ?

(1) |a − c| = |a| − |c|
This statement holds only if both a and c have the same sign
-------> ac>0
-------> db<0 but not necessarily d - b < 0 [consider this case: d=5 and b=-1: db<0 but d-b >0]
Statement 1 is not sufficient (eliminate A and D)

(2) d – b > d + b
----> d - d > b + b
----> 0 > 2b
----> b < 0
Statement 2 is not sufficient alone (eliminate B)

Both statements together:
----> ac>0
----> db<0 ----> b<0 ----> d>0
the difference between any two different numbers (+ve and -ve) > 0

"C"

mokarios · Answer

Hi, can you kindly explain how you arrived at 'd' as >0?
That is the missing link for me to understand the solution to this problem.

Thanks!

rsrighosh · Answer

Bunuel chetan2u VeritasKarishma

Could you please help me in explaining where I am going wrong. Because I am getting answer B because of following reasons

given \(\frac{ac}{db} <0\)
This implies all 3 have same sign, only one has a different sign

(1) \(|a − c|\) = \(|a| − |c|\)
This says \(a\) and \(c\) are positive but it does not give any info on \(b\) and \(d\)

(2) \(d – b > d + b\)
This says that \(b<0\) and \(d>0.\)
Now that we see that \(b\) and \(d\) have 2 different signs, it hardly matters what is \(a\) and \(c\). \(a\) & \(c\) can be both positive or negative because \(\frac{ac}{db} <0\)
As \(b\) is -ve and \(d\) is +ve, hence b<d.

What am I missing here? Why do we also need 1st statement to find the solution?

chetan2u · Answer

d-b>d+b is equal to 2b<0 or b<0. Nothing about d as d cancels out. It could be 0, <0 or >0.

rithhinj · Answer

Why cant the answer be just B. The stem clearly says and AC/DB <0.

So there is no chance of any of the variables being = 0.

Bunuel · Answer

(2) just tells that b < 0. Hence, we know that ac/(db) < 0 and b < 0. How can you decided whether d – b < 0 from that?

If ac/(db) < 0, is d – b < 0 ?

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GMAT Data Sufficiency (DS) Questions

If ac/(db) < 0, is d – b < 0 ?

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