MGMAT practice question bank

[gayathri248]

If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.


The OA C.

But my question is

Why can't I rephrase this question as follows

r^2/|r| < 1

r^2 is positive and |r| = r so there is no sign issue and r can be cancelled and the rephrase becomes whether r < 1 which is statement B. Am I missing something?


Thanks,
Gayathri

[adiagr]

see my post below.

[adiagr]

If r is not equal to 0, is r^2/|r| < 1?

(1) r > -1

(2) r < 1

A)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C)Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D)EACH statement ALONE is sufficient.
E)Statements (1) and (2) TOGETHER are NOT sufficient.


The OA C.

But my question is

Why can't I rephrase this question as follows

r^2/|r| < 1

r^2 is positive and |r| = r so there is no sign issue and r can be cancelled and the rephrase becomes whether r < 1 which is statement B. Am I missing something?


Thanks,
Gayathri

|r| = r only when r > 0, other wise it is -r.

so rephrase will be :

r<1, when r>0 (Given r not equal to zero)

r>-1, when r<0

Aditya

[gayathri248]

Isn't |r| => absolute value ?

|-r| = |r| = r

-Gayathri

[adiagr]

Isn't |r| => absolute value ?

|-r| = |r| = r

-Gayathri

say r = -8.

you say |r| = r;

is |-8| = -8?

No.

|r| = r, only when r>0

else

|r| = - r

[mschwrtz]

Aditya writes:

"|r| = r only when r > 0, other wise it is -r."

Gayathri responds:

"Isn't |r| => absolute value ?

|-r| = |r| = r"


Just to clarify, the definition of absolute value is:

If x>0, then |x|=x. If x<0, then |x|=-x.

Yes, it's counter-intuitive. But as in the example Aditya proffers, -x is actually a positive number when x<0.

The original question can be rephrased as "Is |r|<1?" Neither 1 nor 2 is sufficient to answer that question.