Is |a| + |b| |a+b| ?

Question

GMATBusters’ Quant Quiz Question -3

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Is |a| + |b| > |a + b| ?

(1) |ab| = -ab
(2) |a|b <0

chetan2u · Accepted Answer

Is |a| + |b| > |a+b| ?
There can be 3 cases..
(I) Both a and b have SAME sign......|a|+|b|=|a+b|......so answer is NO.
(II) Both a and b have DIFFERENT sign......|a|+|b|>|a+b|......so answer is YES.
(III) Both a and b or any one is 0......|a|+|b|=|a+b|......so answer is NO.

So if we can say that a and b have different signs, YES, otherwise NO.

1) |ab| = -ab
So \(ab\leq{0}\)...Case (II) and (III) possible.
Insuff

2)|a|b<0
So b<0, but what about a..
If a<0....Yes, otherwise NO.
But |a|b<0, surely tells us that none of a or b is 0.
Insuff

Combined..
Statement 1 tells us that either ab is 0, or both and b have different sign, but statement 2 tells us that \(ab\neq{0}\), so a and b have different signs.
Sufficient

C

techwave · Answer

Is |a| + |b| > |a+b| ?
1) |ab| = -ab
2)|a|b<0

|a| + |b| > |a+b| will only be true when a and b are of opposite signs.

1) |ab| = -ab
a=b=0 ans is NO.
a=2 b=-1 ans is yes
INSUFF.

2)|a|b<0
a=2 b=-1 ans is yes
a=-2 b=-1 ans is NO
INSUFF.

1+2
Now we know (from statement 2 ) that a and b cannot be zero.
and from (1) we know that ab = -ve hence a and b are of different signs. Hence we can answer a definite YES to the statement.
SUFF.

Ans- C

Hope it's clear.

Raxit85 · Answer

Is |a| + |b| > |a+b| ?
1) |ab| = -ab
ab can be - ve only. So, a and b both are positive or both are negative.
This condition gives only signs and question is asking quantity comparison (less or greater than).
So insufficient.

2)|a|b<0
a can be -ve/+ve and b must be -ve.
Again, this condition gives only signs and question is asking quantity comparison (less or greater than).
So insufficient.
1) + 2) 
Both conditions gives only signs related information. So insufficient.

Ans E.

Kinshook · Answer

Asked: Is |a| + |b| > |a+b| ?
If a & b are of same sign; |a| + |b| = |a+b|
But if a & b are of opposite sign; |a| + |b| > |a+b|

1) |ab| = -ab
States that a & b are of opposite signs and one of them or both may also be 0.
If a & b are of opposite signs - > |a| + |b| > |a+b|
But if a=0 or b=0 or both are 0; |a| + |b| = |a+b|
NOT SUFFICIENT

2)|a|b<0
b<0 and |a|>0
If a>0; |a| + |b| > |a+b|
But if a<0; |a| + |b| = |a+b|
NOT SUFFICIENT

(1) + (2)
1) |ab| = -ab
States that a & b are of opposite signs and one of them or both may also be 0.
2)|a|b<0
b<0 and a is NOT equal to 0
Since a & b are of opposite signs and none of them is 0;
b<0 and a>0
|a| + |b| > |a+b|
SUFFICIENT
 IMO C

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Archit3110 · Answer

Is |a| + |b| > |a+b| ?
1) |ab| = -ab
2)|a|b<0

|a| + |b| > |a+b| will only be true when a and b are of opposite signs.

1) |ab| = -ab
a=b=0 ans is NO.
a=2 b=-1 ans is yes
INSUFF.

2)|a|b<0
a=2 b=-1 ans is yes
a=-2 b=-1 ans is NO
INSUFF.

1+2
Now we know (from statement 2 ) that a and b cannot be zero.
and from (1) we know that ab = -ve hence a and b are of different signs. Hence we can answer a definite YES to the statement.
SUFF.

Ans- C

Hope it's clear.

uc26 · Answer

Is |a| + |b| > |a+b|? To answer this question, we need to know the signs of a and b. If a and b have the same signs i.e both are positive or both are negative, then the answer to the question will be NO since |a| + |b|= |a+b|. If a and b have opposite signs, then the answer to the question will be YES. This can be confirmed using easy examples. The question basically asks us if a and b have opposite signs.

(1) |ab|= -ab. We know that when ab<0, |ab|= -ab. This means a and b have opposite signs and the answer to the original question is YES. Sufficient.

(2) |a|*b<0. We know that |a| will always be greater than or equal to zero. Hence, b has to be negative. We,however, do not know the sign of A. So, the answer can be a YES or a NO depending on the positive or negative nature of a. Not sufficient.

Answer: A.

ashwini2k6jha · Answer

state1-sufficient
|ab|=-ab
ab<0,let putting a=4,b=-3 and a=-5,b=1 and a=-1/2,b=10 in every case |a|+|b|>|a+b|
State:2 not sufficient
|a|b<0,
b<0
Let put a=5,b=-2 in above expression|a|+|b|>|a+b| answer is yes
again put a=-5,b=-10 then 15>15 answer NO
answer A

Tommy6e · Answer

Answer is C

Is |a| + |b| > |a+b| ?
This statement will be true only if a's and b's sign will be opposite (a negative and b positive and vice versa.)

1) |ab| = -ab
Insufficent. 
Two scenarios: 
Scenario 1 - a and b have opposite signs --> the statement |a| + |b| > |a+b| would be true
Scenario 2 - at least either a or b is 0 --> the statement |a| + |b| > |a+b| wouldn't be true

2)|a|b<0
Insufficent. 
Two scenarios: 
Scenario 1 - b is negative and a is negative --> the statement |a| + |b| > |a+b| wouldn't be true
Scenario 2 - b is negative and a is positive --> the statement |a| + |b| > |a+b| would be true

Both statements:
b must be negative and a must be positive --> the statement |a| + |b| > |a+b| would be true under these conditions

1BlackDiamond1 · Answer

Is |a|+|b|>|a+b|?
1) |ab| = - ab
since the result od modulus is always positive wither a is -ve or b is -ve.
Therefore |a|+|b| is not > |a+b| (number sense)

Statement I is sufficient.

2) |a| b < 0

|a| is positive
since |a| b < 0 then b must be - ve.
Therefore |a|+|b| is not > |a+b| (number sense)
Statement II is sufficient
Answer id D

SR71Blackbird · Answer

The answer to this question is D

Statement 1: mod ab = -ab
For the statement to be true, ab = negative number, integer, so on, only then both the sides will be equally positive. 
ab = ive means either a or b is negative. 
Ex: a= 2 b = -3 ------> 2 + 3 > 1
Ex: a= 10 b=-1000 ---> 10 + 1000 > 990 vice versa is also true where a is negative and b is positive.

Statement B : |a| b < 0 This statement is telling us what we already inferred in the previous statement. A is positive, for the product to be negative, b has to be negative, then ab = -ve and same examples and cases can be applied.

zs2 · Answer

Is |a| + |b| > |a+b| ?
1) |ab| = -ab
2)|a|b<0

|a| + |b| > |a+b| will only be true when a and b are of opposite signs.

1) |ab| = -ab
a=b=0 ans is NO.
a=2 b=-1 ans is yes
INSUFF.

2)|a|b<0
a=2 b=-1 ans is yes
a=-2 b=-1 ans is NO
INSUFF.

1+2
Now we know (from statement 2 ) that a and b cannot be zero.
and from (1) we know that ab = -ve hence a and b are of different signs. Hence we can answer a definite YES to the statement.
SUFF.

Ans- C

Hope it's clear.

Amogh223 · Answer

Oa is A for this ques

Posted from my mobile device

lacktutor · Answer

Is |a| + |b| > |a+b| ?
(Statement1): |ab| = -ab

(Case1): a >0, b< 0
|4| +|—1| > |4–1|
5 > 3 (Yes)

(Case2): a <0, b> 0
|—4|+ |1| > |—4+1|
5 > 3 (Yes)

(Case3:) a= 0, b= 0
0> 0 (No)
Insufficient

(Statement2): |a|b<0

(Case1): a >0, b<0
|4| +|—1| > |4–1|
5 > 3 (Yes)

(Case2): a < 0, b< 0
|—4| + |—1| > |—4–1|
5 > 5 (No)
Insufficient

Taken together 1&2,
a > 0 and b < 0
|4| +|—1| > |4–1|
5 > 3 (Always Yes)
Only this is common for two statements
Sufficient

Answer (C)

jrk23 · Answer

i think the answer is "A".

|ab|= -ab. It means one of the variable is negative and one is positive.

therefore |a| + |b| > |a + b|

for "b" option we can't say that we are not sure whether a variable is positive or negative

stne · Answer

Is |a| + |b| > |a+b| ?
1) |ab| = -ab
2)|a|b<0

|a| + |b| > |a+b| will only be true when a and b are of opposite signs.

1) |ab| = -ab
a=b=0 ans is NO.
a=2 b=-1 ans is yes
INSUFF.

2)|a|b<0
a=2 b=-1 ans is yes
a=-2 b=-1 ans is NO
INSUFF.

1+2
Now we know (from statement 2 ) that a and b cannot be zero.
and from (1) we know that ab = -ve hence a and b are of different signs. Hence we can answer a definite YES to the statement.
SUFF.

Ans- C

Hope it's clear.

bumpbot · Answer

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Is |a| + |b| > |a+b| ?

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