Data Sufficiency

Is q > t ?

(1) qp2 < tp2

(2) qp3 > tp3


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

MGMAT ( 500-600)

(A) alone is sufficient .

sumanr84 wrote:Is q > t ?

(1) qp2 < tp2

(2) qp3 > tp3


MGMAT ( 500-600)

p2>0

1) qp^2 <tp^2 - sufficient to conclude q<t

we cannot be sure about the sign of p^3

2) insufficient

Hence A

IMO E

@Ajith,

(1) may fail for negative numbers of Q that greater than negative numbers of t.

Pl z chk it out..

gmatmachoman wrote:IMO E

@Ajith,

(1) may fail for negative numbers of Q that greater than negative numbers of t.

Pl z chk it out..

Lets take some values

p= -4 and t = -5 q = -6


tp^2 = -5*16 = -80
qp^2 = -6*16 = -96


qp^2 < tp^2 in this case
and

q<p

Now lets consider

p= -4 and q = 5 and t =6


qp^2 = 5*16 = 80
tp^2 = 6*16 = 96

qp^2< tp^2

and q<p

In both cases it does work

Hey Ajith,

man I have totally misunderstood that query....

When it read qp2...I read it has Q raised to the power 2..Now only I recognised its not power but a variable P...


happens rite???

I just forgot the function of (^)...

gmatmachoman wrote:Hey Ajith,

man I have totally misunderstood that query....

When it read qp2...I read it has Q raised to the power 2..Now only I recognised its not power but a variable P...


happens rite???

I just forgot the function of (^)...

He he , yeah it happens, believe me, I have had my bad days too. In your defense, even the original poster did not use the (^) symbol for power. In GMAT they will never do this to you, don't worry, cheer up

MGMAT Soln,

Both of these statements give us information about the relationship of q to t, but that relationship is muddled by the presence of p in the expressions. Generally, it is not a good idea to divide an equation or inequality by a variable since dividing by zero is illegal, and a variable might be equal to zero. However, note that p cannot be zero here, since if it were, the expressions in the statements would all be zero and thus equal. Therefore, p is definitely not zero, and we are free to divide each statement by p to simplify.

(1) SUFFICIENT: Since p2 must always be positive (it has an even exponent), we can divide both sides by p2, certain that the inequality sign will not flip, and determine that q < t. We can definitively answer the question of whether q is greater than t: "no."

Remember, on data sufficiency GMAT questions, a definite "no" answer is sufficient, just as a definite "yes" answer is sufficient. A statement will be insufficient only when the answer is "maybe" or "it cannot be determined."

(2) INSUFFICIENT: Since p3 can be positive or negative (it has an odd exponent), we cannot determine which way the inequality sign will face when we divide both sides by p3. If p3 is positive, then the inequality sign will not flip. If p3 is negative, then the inequality sign will flip.

The correct answer is A.

I may have missed something, but where does it say that p and q are integers. What if q is 1/5 and t is 1/25, assuming p^2 as 5^2, So in this case the answer would be that we do not know if q is greater than or less than t. In that case statement 1 is not sufficient.

alisha18a wrote:I may have missed something, but where does it say that p and q are integers. What if q is 1/5 and t is 1/25, assuming p^2 as 5^2, So in this case the answer would be that we do not know if q is greater than or less than t. In that case statement 1 is not sufficient.

How does it matter whether p and q are integers or not?

You have p^2 on both sides.