Is x < y?

[M7MBA]

Is x < y?

(1) xz < yz
(2) -3x > 6y

The OA is E.

Could someone help me? Please. I don't have an idea of how to solve this DS question. <i class="em em-cry"></i>

[Sionainn@PrincetonReview]

Where this one gets a little tricky is you need to remember with inequalities when you multiply or divide by a negative you need to flip the inequality symbol.

So for the first statement, at first it may seem that this is enough information since we can divide both sides by z and get x on the left and y on the right. The issue is we don't know if z is positive or negative. If z is positive we don't flip the sign and the result is x < y, but if z is negative we do flip the sign and x > y. Since we don't know if x >y or x <y, this is not sufficient. And we can narrow the answers to B, C, and E.


Onto the second statement, we can divide both sides by -3. Since we are dividing by a negative, we need to flip the inequality sign to get x < -2y. This isn't immediately obvious if it is or isn't sufficient, so plug in numbers that make the statement true. For example, x could be 1 and y could be 2 since 1 <-4. In this case x is less than y. But x could be -2 and y could be -3 since -2 <6. In this case x is not less than y. Since you find x can be bigger and smaller than y, this statement is also not enough info. So eliminate B.

Finally you want to see if you combine both statements if the information is sufficient. For example x = 1, y = 2 and z = 3 satisfies both statements and x <y but x = -2, y = -3 and z = -1 also satisfies both and then x >y. So both statements are also not sufficient and the answer is E.

Make sense?

[Keith@ThePrincetonReview]

Is x < y?

(1) xz < yz
(2) -3x > 6y

The OA is E.

Could someone help me? Please. I don't have an idea of how to solve this DS question. <i class="em em-cry"></i>

This Yes/No Data Sufficiency question can be answered by Plugging In.

Statement (1):
Plug In a value for z.
If z = -2, then dividing both sides of the inequality by z will flip the inequality, so that x > y. In this case, the answer is No.
If z = 2, then dividing both sides of the inequality by z yields x < y. In this case the answer is Yes.
The information in Statement (1) is insufficient to answer the question, so write down BCE.

Statement (2):
Simplify the inequality. Divide both sides by -3, so that x < -2y.
Plug In a value for y.
If y = 1, then x < -2. In this case, x < y, so the answer is Yes.
If y = -1, then x < 2. In this case, it's possible that x =1 and y = -1, in which case x > y and the answer is No.
The information in Statement (2) is insufficient to answer the question, so eliminate choice B.

Both statements together:
Statement (1) provides no information about the relative values of x and y, since x < y if z is positive, and x > y if z is negative.
In other words, any values of x and y will satisfy the first statement, so when both statements are evaluated together, Statement (1) adds no relevant information.
Thus, evaluating both statements together is tantamount to evaluating Statement (2), which has already been proved insufficient.

The correct answer is choice E.