Is 0 ab?

Question

Tough and Tricky questions: Inequalities.

Is 0 > ab?

(1) 0 > b

(2) a = b – 6

Kudos for a correct  solution .

littlewarthog · Answer

Answer C.

ab are smaller than 0, exactly when one of them is positive and the other is negative. With that in mind, we can analyse the statements:

Statement 1: This doesn't tell us anything about a, so this is certainly not enough.

Statement 2: This is also not enough, since we can't tell if one of a and b is smaller than 0 and the other greather than 0. They could be 4 and 10 or -3 and 3, so this is also not sufficient.

If we combine the two statements, we can tell that ab must be greather than 0, so the information is sufficient. If b is smaller than 0 (statement 1) and a is even smaller (statement 2), we know that both are negative and ab >0.

Answer C.

beattheheat · Answer

Is 0 > ab?

(1) 0 > b
b is negative, a can be positive or negative making ab negative or positive respectively.. Insufficient

(2) a = b – 6
b can be positive integer less than 6, making a negative and ab negative
b can be positive integer greater than 6, making a positive and ab positive -- Insufficient

Combining 1&2:
b is negative and a is b - 6 ==> negative, making ab positive -- Sufficient

Konstantin1983 · Answer

Statement 1. b<0. If a>0 then ab<0. But if a<0 then ab>0. Hence not sufficient
Statement 2. a=b-6 ==> b(b-6)<0? If b=1 then answer is Yes. But if b=10 then answer is No. Hence not sufficient.
Take both statements together. We know that b<0 ==> b(b-6)>0. Sufficient

qw1981 · Answer

From S1 b>0 we do not know anything about a and hence ab can be both positive or negative. Thus not sufficient.

From S2 a=b-6 --> a+6=b This does not tell us anything about a & b exact values. Hence this is not sufficient.

Combining we know that b is positive and a is 6 grater than b. Hence a also is positive and thus ab will always be positive. Thus answer is C.

sahil7389 · Answer

IMO -C
from statement 1- we dont the value of a so ab> or < 0 we dont know-- insufficient
From statement 2 a=b-6 - we dont know the sign of A and B --in sufficient
Combining both b<0 and A is b-6 so both negative hence we can conclude ab>0

veergmat · Answer

Is 0 > ab?

1) b<0 , Insufficient , because no info about 'a' +/- . ab >0,=0,<0 if a<0,=0,>0
2) a=b-6 , b*(b-6)= b^2- 6b ,insufficient more info about b is required.

Combining 1) and 2)
'b^2' always positive and if b<0,then' -6b' will always be +ve. So, b*(b-6) will be +ve.

sunaimshadmani · Answer

Statment (1): If a<0, then ab>0 and answer to the question is NO.
If a>0, then ab<0 and answer to the question is YES.
Insufficient.

Statement (2) If b=2, answer to the question is YES.
If b=-2, answer to the question is NO.
Insufficent.

Combining both we know that both a and b are -ve and ab>0.
Answer is C.

CCMBA · Answer

Is ab negative?

OR, Do a and b have opposite signs?

(1) b < 0

Tells us nothing about A. NOT sufficient. Strike A/D.

(2) a = b - 6

b > a

Both may be negative or positive, OR one may be 0. NOT sufficient. Strike B.

(1/2)

b is negative, so a must also be negative. ab > 0, so we can definitively answer "No."

The answer is C.

Bunuel · Answer

OFFICIAL SOLUTION:

The easiest way to answer this question is to use the rules for positive/negative number properties. We know that the product of two numbers is only negative when one of the numbers is positive and the other is negative. If the numbers have the same sign, the product is always positive.

From Statement (1), we know that b is negative. Without knowing the sign on a, it is impossible to determine whether ab is negative. So Statement (1) is insufficient.

If we translate Statement (2) into English, we get a is 6 less than b. Since this does not tell us the sign on either a or b, we cannot answer the question. This statement is also insufficient.

Now, we combine the statements. If b is negative and a is 6 less than b, then a must also be negative, since it is less than b. This is sufficient to answer the question.Since the statements are insufficient individually, but sufficient when combined, the correct answer is choice (C).

Alternate Method (Picking Numbers):

Statement (1) tells us that b is negative, so we can let b = -2. If a = 3, then ab = -6, which answers the original question affirmatively. However, if a = -3, then ab = 6. So Statement (1) is insufficient because the answer to the question could be either yes or no.

Statement (2) is also insufficient because we could substitute in two positive values for the variables, such as a = 20 and b = 26, which would make ab positive, or we could substitute in a negative and a positive value, such as a = -4 and b = 2, which would make ab negative.

However, when we combine the statements, b is negative, and any negative number minus 6 will yield another negative number, so a and b are both negative. So ab is positive, which answers the original question. Again, we see that the correct answer is choice (C).

jasimuddin · Answer

0>ab 
or, ab is negative?
or, one between a and b is negative and another is positive.

stat-1: 0>b says b is negative but nothing about a....insufficient.
stat-2 : a=b-6 says "both positive "or" both negative" but must not" one negative and another positive".....insufficient
combining 1&2 we can say if b is negative a must not be positive.....so ab is not less than 0.......sufficient

ans: C

HKD1710 · Answer

is the multiple of a & b negative? that means do a & b have different signs??

stmt-1:  b is negative and what about a? insuff.

stmt-2:  a - b = -6, this does not tell whether a was positive or negative because we can get -6 with a=-8, b=-2 and a=-4, b=2.

together :
a=-8, b=-2 valid
and a=-4, b=2. (according to stmt-1 b cannot be +ve). so invalid case.

if b is negative then negative sign before b in (a-b) would make it +ve and hence to get (a-b) equal -6, a has to be negative.

now both a & b are negative, hence ab has to be +ve. so answer to the question is NO. sufficient.  Answer is thus C.

Is 0 > ab?

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Is 0 > ab?

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