Is |a| = b - c ?

Question

Is |a| = b - c ?

(1) a + c 
eq{b} 
(2) a > 0

Source: Jeff Sackman

Although the question is correctly copied from the source in which statement II is a<0, teh OA is wrong and accordingly statement II has been modified

Princ · Answer

add  Is |a| = b - c?  in question stem

longranger25 · Answer

Yes. Just made the edit.

mitrakaushi · Answer

Can't agree here.

a = -2 b=5 c =3 s1 & s2 compliant. Answer is yes.

a = -3 b=5 c=3 s1 & s2 compliant. Answer is no.

Thus answer cannot be c, as it gives 2 different answers even when taken together.

chetan2u · Answer

Pl recheck the question In present state it is E.. Either Statement I is a+b eq{c} Or Statement II would be a>0 Is |a|=b-c? If a>0, a=b-c If a<0, a=c-b 1) a+c eq{b}............a eq{b-c} But a can be equal to c-b Insufficient 2) a<0.. So from above a could be equal to c-b Insufficient Combined. If a=c-b... Yes otherwise No Insufficient E But had statement II been a>0 Combined.. a>0, so only possibility of yes is if a=b-c But statement I gives a eq{b-c} So Ans is always NO Sufficient Then C

longranger25 · Answer

I double checked the question. It is correctly copied.

I myself could not get the twisted logic behind the official explanation and hence posted the question here.

This is what the official explanation is:

Explanation: There are two ways for the equation in the question to be
true. If a is positive, then it is true if a = b - c. If a is negative, then it is true
if -a = b - c, or put another way, a = c - b. To answer the question, we need
to know whether a is positive or negative, and if the corresponding equation is
true.

Statement (1) is insufficient. a+c  
eq{b}  is the same as a  
eq{b}  - c, which means
that, if a is positive, the answer is "no." However, it doesn’t tell us what the
answer is if a is negative.
Statement (2) is also insufficient: it gives us the sign of a, but nothing about
how it relates to b and c.

Taken together, the statements are sufficient. Since we know a is negative,
we know the question asks, "Is a = c - b ?" (1) tells us that that is not true,
so the answer is "no." Choice (C) is correct.

elPatron434 · Answer

Hey  chetan2u , why can't the answer be D?,
Statement I says  a
eq{b-c}  which means it leaves us with only a+b=c, so shouldn't A be correct?
Statement ii says a>0 which leaves us with a=b-c with which we can say B is sufficient.
Are we saying C because we dont know the values of a,b and c?

Thanks in advance

chetan2u · Answer

The question will give a YES under two circumstances
1) a=b-c
2) a=c-b
Any other equation would give an answer NO
So the third case
So statement 1 says it is not (1), but it can still be (2), then YES OR third case then NO
Both no and yes possible.. insufficient
Statement II a>0 so case (1) or third case possible
Insufficient

Combined only third case possible, so C

Izzyjolly · Answer

Is |a| = b - c ? --> Is |a|+c =b ?

(1) a + c  
eq{b}

If a > 0 --> |a| = a --> a + c = |a| + c
--> |a| + c  
eq{b}  --> NO

If a < 0 --> -|a| = a --> a + c = -|a| + c
--> -|a| + c  
eq{b}  . Since we need to compare |a| + c and  b , this statement is not sufficient.
(We can test by plugging in numbers. If a=-1, b=2, c=4 --> NO, If a=-1, b=3, c=2 --> YES => Not Sufficient)

(2) a > 0 
Nothing related to b, c --> not sufficient.

Combine both statements --> we can eliminate the 2nd case in the 1st statement --> Sufficient.

Answer C.

Is |a| = b - c ?

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Is |a| = b - c ?

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