12 Days of Christmas GMAT Competition - Day 11: If a*b 0, is (a + 5)

If \(a∗b≠0\), is \(\frac{a+5}{b}>\frac{a}{b}\) ?

\(\frac{a+5}{b}>\frac{a}{b} ?\)
\(\frac{a+5}{b}-\frac{a}{b}>0 ?\)
\(\frac{a+5-a}{b}>0 ?\)
\(\frac{5}{b}>0 ?\)

(1) \(a<0\)
Knowing the value of a is not required as we need to know only the value of b
Insufficient
(2) \(b<0\)
Knowing this will tell us that \(\frac{5}{b}<0 \)
Sufficient

Ans : B

If \(a*b ≠ 0\), is \(\frac{a + 5}{b} > \frac{a}{b}\) ?

(1) \(a < 0\)

Then , let a = - 1 , -4b >-b This will be true only if b>0 otherwise it will be false .

So, Option 1 dont give us unique answer to our question .

Not sufficient

(2) \(b < 0\)

let b= - 1 , -a - 5 > -a

-5 > 0 This is false .

Answer to our question ,is \(\frac{a + 5}{b} > \frac{a}{b}\) ? is

unique No

Suffcient

Answer B

If a∗b≠0, is \(\frac{a+5}{b}>\frac{a}{b}\)?
First, simplify the given expression \(\frac{a+5}{b} -\frac{ a}{b}>0 --> \frac{a+5-a}{b}>0 --> \frac{5}{b}>0\). Now it is obvious that information about b is enough to find the answer.

(1) a<0 does not have info about b NOT SUFFICIENT

(2) b<0 From this statement we can tell that \(\frac{5}{b}\)<0 or that the original expression \(\frac{a+5}{b}<\frac{a}{b}\). SUFFICIENT

Answer B

OA) B
If a∗b≠0 is a+5/b>a/b?

(1) a<0
(2) b<0

statement I) a<0
case (1) a<0,b>0

b is positive so , \(b(\frac{a+5}{b})\) > \(b(\frac{a}{b})\)
so a+5 > a , so 5>0 which is always true s
so \(\frac{a+5}{b}\) > \(\frac{a}{b}\)

case(2) a<0,b<0
here a/b>0 , if -5>a then a+5/b<0 then , \(\frac{a+5}{b}\) < \(\frac{a}{b}\)
and if 0>a>-5 then a+5/b>0 but still , \(\frac{a+5}{b}\) < \(\frac{a}{b}\)

in both cases 1 and 2 answers are different so, the statement I alone is not sufficient

statement II) b<0
case(1) b<0,a<0
for this condition already checked before here \(\frac{a+5}{b}\) < \(\frac{a}{b}\)
case(2) b<0,a>0
here a>0 so a+5>a but b<0
so a+5/b will be more negative than a/b
so here also \(\frac{a+5}{b}\) < \(\frac{a}{b}\)
from both cases answers are the same, so statement II is alone sufficient to answer the question

(a+5)/b > a/b

subtracting a/b from both sides we have
5/b>0

a) Not sufficient
b) since b<0, then 5/b will always be less than 0, hence the answer to the question is NO. Sufficient

Correct Answer B

If \(a*b ≠ 0\), is \(\frac{a + 5}{b} > \frac{a}{b}\) ?

\(\frac{a + 5}{b} - \frac{a}{b} > 0\)

\(\frac{a + 5 - a }{b}> 0\)

\(\frac{5}{b}> 0\)

(1) \(a < 0\) - Insufficient
(2) \(b < 0\) - Sufficient

Ans: B

If a∗b≠0, is a+5/b>a/b?----i

(1) a<0
Let a=-1 b=1 put these values in equ i
4>-1,Yes

Let a =-1 b=-1

-4>1 no

st1 alone is not sufficient


(2) b<0
a=1 , b =-1
-6>-1 , no

now let a=-1,b=-1
-4>1 , no
st2 alone is sufficient

oa: b

Statement 1 : a<0. Let's say a=-10 and b=5. We get the answer as Yes. Then let's assume a=-10 and b=-5, we see that the answer is No. Therefore, since there is no fixed answer, the statement is insufficient.

Statement 2 : b<0. Let's say a=-10 and b=-5. We get the answer No. Then let's assume a=10 and b=-5. We see the answer is No. Therefore statement 2 is sufficient.

The answer is (B).

If a∗b≠0a∗b≠0, is (a+5)/b>a/b ?
simplifying the question b<5

(1) a<0 - not sufficient
(2) b<0 - sufficient
ans B

given

\(a*b ≠ 0\)
is \(\frac{a + 5}{b} > \frac{a}{b}\)
#1
a<0
we get both yes & no to this statement
as value of b can be either +ve or -ve
insufficient
#2
b<0
same as #1
insufficient

from 1 &2
we can have a=b ; a>b ; a<b
RHS would always be +ve
where as for all values of a,b ; the LHS will always be -ve for cases when a>b
for cases when b>a also RHS value would be > than LHS as its Nr is reducing by 5

OPTION C is correct

lets take below scenarios

1. when both a and b are negative

a/b will be positive and a+5/b will be positive for a<-5 and
a+5 < a (as a is negative)
a+5/b < a/b

2. when a is positive and b is negative
a+5 > a
since b is negative
a+5/b and a/b will be negative, and
a+5/b < a/b because a+5/b will be greater in value.

3. when both is positive
then a+5/b > a/b

now if only b is negative we know for sure that a+5/b > a/b

Kudos!!

(a+5)/b>a/b
ab+5b>ab
b(a+5)>ab
a+5>a
We need only the value of a to solve.

Statement 1: a<0
-2+5<-2
3<-2(False) One unique answer, Sufficient

Statement 2: b<0
Not needed one, Insufficient


Answer: A

Answer is E
(1) a<0 No info about b. Insufficient
(2) b<0 no info about a. Insufficient
(1) + (2) Insufficient.

The Answer is E. Neither is sufficient.

If a∗b≠0, is (a+5)/b>a/b ?

Is a/b+5/b >a/b??
We have to find the Sign of a/b and 5/b to evaluate further

Hence we need the signs of a & b both

for a<0 & b<0 the equation a/b+5/b> a/b is not true

Hence option C is correct