Is a(b+c) 0, given abc ≠ 0 ?

Question

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Is a(b + c) > 0, given abc ≠ 0 ?

(1) |a + b| = |a| + |b| 
(2) |a + c| = |a| + |c|

GMATBusters · Answer

Official Solution:  
Is a(b + c) > 0, given abc ≠ 0 ?

(1) |a + b| = |a| + |b|
This means either a and b are of the same sign or at least one of them = 0
since, abc ≠ 0 , hence none of them = 0, 
a and b are of the same sign

NOT SUFFICIENT to say whether a(b + c) > 0,

(2) |a + c| = |a| + |c|
This means either a and c are of the same sign or at least one of them = 0
since, abc ≠ 0 , hence none of them = 0, 
a and c are of the same sign

NOT SUFFICIENT to say whether a(b + c) > 0,

Combining both statements 1 & 2, a, b, c are all of same sign.
Now a(b + c) = ab+ ca = ( +ve )+ (+ve) , hence > 0 
SUFFICIENT.

Answer C

NikuHBS · Answer

According to the question "Is a*(b+c) >0", we are supposed to find the signs of "a" and "(b+c)"

Statement 1:
| a+b | = | a | + | b |
This says that both "a" and "b" are of the same signs but we don't know anything about "c".
Not Sufficient.

Statement 2:
| a+c | = | a | + | c |
This says that both "a" and "c" are of the same signs but we don't know anything about "b".
Not Sufficient.

Both Together:
We know that all the three variables a,b, and c are of the same signs.

Case 1: a,b, and c are positive.
The answer to "Is a*(b+c) >0" is YES

Case 2: a,b, and c are NEGATIVE.
The answer to "Is a*(b+c) >0" is YES

Hence,  Option C is the answer

Papist · Answer

We can rewrite the equation as  ab + ac >0 using the distributive property, which will come in handy when we evaluate the statements.

S1: The only way for this to be true is if  a  and  b  are either both positive or both negative. However, we know nothing about  c . It could have the same signage as  a  and  b  and make the statement true or be a large number with the opposite signage, making the statement false. NOT SUFFICIENT.

S2: Same as S1, except  b  is the issue this time. NOT SUFFICIENT.

S1+S2: We know that  a ,  b , and  c  are either all positive or all negative. Either way, the result will be a positive number, so the equation is definitely true. SUFFICIENT.

ANSWER: C

yashikaaggarwal · Answer

Is a(b+c) > 0, given abc ≠ 0 ?

1)| a+b | = | a | + | b |
The statement is only true if both a and b have same sign,
For ex, let a = 2 & b = 3
Case 1: | 2+3 | = | 2 | + | 3 |
=> 5 = 5(correct)

Let a =-2 & b = -3
Case 2: | a+b | = | a | + | b |
=> | -2-3 | = | -2 | + | -3 |
=> 5 = 5 (correct)

Let a =-2 & b = +3
Case 2: | a+b | = | a | + | b |
=> | -2+3 | = | -2 | + | +3 |
=> 1 ≠ 5 (incorrect)
There both a and b has to be of same sign, but we don't have any information about C
(Insufficient)

2)| a+c | = | a | + | c |
The statement is only true if both a and c have same sign,
For ex, let a = 2 & c = 3
Case 1: | 2+3 | = | 2 | + | 3 |
=> 5 = 5(correct)

Let a =-2 & c = -3
Case 2: | a+c | = | a | + | c |
=> | -2-3 | = | -2 | + | -3 |
=> 5 = 5 (correct)

Let a =-2 & c = +3
Case 2: | a+c | = | a | + | c |
=> | -2+3 | = | -2 | + | +3 |
=> 1 ≠ 5 (incorrect)
There both a and c has to be of same sign, but we don't have any information about B
(Insufficient)

Together 1&2: a(b+c)>0 
Case 1 when A,B,C all are negative
-a(-b-c) => Ab+ac > 0

Case 2 when A,B,C all are positive
+a(+b+c) => Ab+ac > 0
Hence together they are sufficient.

IMO C

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KG04 · Answer

For S1 to be true either both a>0 and b>0 or both a<0 and b<0 but no information about c => insufficient
For S2 to be true either both a>0 and c>0 or both a<0 and c<0 but no information about b => insufficient
S1 + S2
if a>0 => b>0 and c>0 => a(b+c) > 0
if a<0 => b<0 and c<0 => a(b+c) > 0
=> Sufficent (C)

urshi · Answer

Answer : Option C

ashwini2k6jha · Answer

ANSWER:C
a(b+c)>0 ?
STATE:1 NOT SUFFICIENT
|a+b|=|a|+|b|
Now let a=3,b=3 and c=3 then a(b+c)>0 yes
let a=3,b=3 and c=-4,then a(b+c)>0 NO
State:2,Not sufficient
Now let a=3,b=3 and c=3 then a(b+c)>0 yes
let a=3,b=-4 and c=3,then a(b+c)>0 NO
now 1+2: either a,b and c must be >0 or <0
In this case a(b+c)>0 true sufficient

vtexcelgmat · Answer

ANSWER IS C

Is a(b+c) > 0 ??
YES - If  a  &  (b+c)  are on same side of zero on number line.
NO - If  a  &  (b+c)  are on different sides of zero on number line.

Each statement confirms that  a  &  b  or  c  are on same side of zero on number line.

Both statements are required.

MayankSingh · Answer

IMO C

Ques: Is a(b+c) > 0 ?
Given abc ≠ 0 ?
0r, a=0, b=0, c=0 is not possible...

1)| a+b | = | a | + | b |
Above is only possible when a & b are of same sign.
eg. | 3+4 | = |3| +|4|
|(-3) + (-4)| = |-3|+|-4|
But , |-3+4| isn't equal = |-3|+|4|
So,
Case I: a>0 & b>0
Case II: a<0 & b<0
* But we don't know value of c with respect to b to ascertain sign of (b+c)

Not Sufficient

2)| a+c | = | a | + | c |
Above is only possible when a & c are of same sign.
Case I: a>0 & c>0
Case II: a<0 & c<0
* But we don't know value of c with respect to b to ascertain sign of (b+c)

Not Sufficient

Together Statement 1 & 2
Case I : a>0 & c>0 , b>0 , so a(b+c) > 0
Case II: a<0 & c<0 , b<0 , so a(b+c) > 0

Sufficient

firas92 · Answer

Is a(b+c) > 0, given abc ≠ 0 ?

1)| a+b | = | a | + | b |

From our property, we can see that a and b have the same sign.

But we have no info about c

1 is not sufficient

2)| a+c | = | a | + | c |

From our property, we can see that a and c have the same sign.

But we have no info about b

2 is not sufficient

(1)+(2)

a, b and c are of the same sign

So a(b+c) =  negative*negative  or  positive*positive  which are both always positive

(1)+(2) is sufficient

Answer is  (C)

Kinshook · Answer

Asked: Is a(b + c) > 0, given abc ≠ 0 ?

(1) |a + b| = |a| + |b| 
a & b have same sign
a(b+c) = ab + ac
ab>0 but nothing is known about c
NOT SUFFICIENT

(2) |a + c| = |a| + |c| 
a & c have same sign
a(b+c) = ab + ac
ac>0 but nothing is known about b
NOT SUFFICIENT

(1) + (2) 
(1) |a + b| = |a| + |b| 
a & b have same sign
(2) |a + c| = |a| + |c| 
a & c have same sign
a(b+c) = ab + ac 
ab>0 & ac>0
a(b+c) > 0
SUFFICIENT

IMO C

Archit3110 · Answer

Is a(b + c) > 0, given abc ≠ 0 ?

(1) |a + b| = |a| + |b|
(2) |a + c| = |a| + |c|

#1
|a + b| = |a| + |b|
possible when a& b are both +ve 
but c is not know insufficient
#2
 |a + c| = |a| + |c|
possible when both a & c are +ve but b is not know
insufficient
from 1 &2 
a,,b,c are all +ve so a(b + c) > 0 ; sufficient
OPTION C

SatvikVedala · Answer

Considering Statement (1)

|a+b| = |a|+|b|

Squaring on both sides

=> a2+ b2 +2ab = a2+b2+2|a||b|
=> ab = |a||b|
=> ab = |ab| -- (1)
from (1) ab is +ve, but we don't have any information on value of C --> Not sufficient

Considering Statement (2)
|a+c| = |a|+|c|

=> a2+ c2 +2ac = a2+c2+2|a||c|
=> ac = |a||c|
=> ac = |ac| -- (2)
from (2) ac is +ve but we don't have any information on value of B --> Not sufficient

combining (1) & (2)
ab is +ve, ac is +ve, which implies ab+ac>0

Therefore Option C

Is a(b+c) > 0, given abc ≠ 0 ?

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Is a(b+c) > 0, given abc ≠ 0 ?

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