GMATPrep Test Question(s)

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GMATPrep Test Question(s)

by G.K » Sat Nov 15, 2014 1:58 pm
Hi,

Lately, I have started getting uncomfortable with DS questions.
esp. questions like these:

Q1. Is m+z>0
1. m-z > 0
2. 4z-m > 0

Q2. Is xy>0
1. x-y >2
2. x-2y< -6

Please explain how to approach questions like these? and some general advice on how to conquer DS.

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by GMATGuruNY » Sat Nov 15, 2014 2:06 pm
Is m+z > 0?

1) m-3z>0
2) 4z-m >0
Statement 1: m > 3z.
It's possible that z=1 and m=4.
In this case, m+z > 0.
It's possible that z=-10 and m=4.
In this case, m+z < 0.
INSUFFICIENT.

Statement 2: m < 4z
It's possible that z=1 and m=3.
In this case, m+z > 0.
It's possible that z=1 and m=-10.
In this case, m+z < 0.
INSUFFICIENT.

Statements combined:
One approach is to LINK together the inequalities.
Since 3z < m and m < 4z, we get:
3z < m < 4z
3z < 4z
0 < z.
Since z>0 and m > 3z, m > 0.
Thus, m+z > 0.
SUFFICIENT.

The correct answer is C.
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by GMATGuruNY » Sat Nov 15, 2014 2:09 pm
Is XY > 0?

(1) X - Y > -2
(2) X - 2Y < -6
Statement 1: x > y-2
If y=2 and x= 1, is 1*2 > 0? Yes.
If y= -1 and x = 1, is 1*(-1) > 0? No.
Since the answer can both Yes and No, insufficient.

Statement 2: x < 2y-6
If y=1 and x = -10, is 1*(-10) > 0? No.
If y = 10 and x = 1, is 1*10 > 0? Yes.
Since the answer can be both No and Yes, insufficient.

Statements 1 and 2 combined:
Linking together the two statements, we get:
y-2 < x < 2y-6
y-2 < 2y-6
y > 4.
Since y > 4 and x > y-2, we know that x > 2.
Thus, x and y are both positive.
Sufficient.

The correct answer is C.
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by G.K » Sat Nov 15, 2014 2:16 pm
Thanks,

Is plugging in values the best way to get around problems like these?

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by Brent@GMATPrepNow » Sat Nov 15, 2014 3:14 pm
G.K wrote:Thanks,

Is plugging in values the best way to get around problems like these?
Plugging in numbers typically works best when you suspect that the statement is NOT SUFFICIENT. In these cases, all you need to do is find values that yield different (conflicting) answers to the target question.

Conversely, if the statement is SUFFICIENT, then plugging in values will only HINT at whether or not the statement is sufficient, but you won't be able to make any definitive conclusions.

For example, let's say we have the following target question: If n is a positive integer, is (2^n) - 1 prime?
Let's say statement 1 says: n is a prime number:

Now let's plug in some prime values of n:
If n = 2, then (2^n) - 1 = 2² - 1 = 3, and 3 IS prime
If n = 3, then case (2^n) - 1 = 2³ - 1 = 7, and 7 IS prime
If n = 5, then (2^n) - 1 = 2� - 1 = 31, and 31 IS prime
At this point, it certainly APPEARS that statement guarantees that (2^n) - 1 is prime? Let's try one more prime value of n.
If n = 7, then (2^n) - 1 = 2� - 1 = 127, and 127 IS prime

So, can we be 100% certain that statement 1 is sufficient? No. The truth of the matter is that statement 1 is NOT SUFFICIENT. To see why, let's examine the possibility that n = 11
If n = 11, then (2^n) - 1 = (2^11) - 1 = 2047, and 2047 is NOT prime


Here's a different example:
Target question: Is x > 0?
Let's say statement 1 says: 5x > 4x

Now let's plug in some values of x that satisfy the condition that 5x > 4x.
x = 3, in which case x > 0
x = 0.5, in which case x > 0
x = 15, in which case x > 0
x = 1000, in which case x > 0

Once again, it APPEARS that statement 1 provides sufficient information to answer the target question. Can we be 100% certain? No. Perhaps we didn't plug in the right numbers (as was the case in the first example). Perhaps there's a number that we could have plugged in such that x < 0

If we want to be 100% certain that a statement is SUFFICIENT, we'll need to use a technique other than plugging in.
Here, we can take 5x > 4x, and subtract 4x from both sides to get x > 0 VOILA - we can now answer the target question with absolute certainty.
So, statement 1 is SUFFICIENT.

TAKEAWAY: Plugging in numbers is best suited for situations in which you suspect that the statement is not sufficient. In these situations, plugging in values can yield results that are 100% conclusive. Conversely, in situations in which the statement is sufficient, plugging in values can STRONGLY HINT at sufficiency, but the results are not 100% conclusive.

For more on this, you can watch our free video titled "Choosing Good Numbers: https://www.gmatprepnow.com/module/gmat- ... cy?id=1102 or you can read an article I wrote for BTG about it: https://www.beatthegmat.com/mba/2013/10/ ... -in-values

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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