Hey, I have been using a preparatory manual by a guy named Jeff Sackmann called Total GMAT Math. I am having a little trouble solving a data sufficiency problem. Perhaps someone can help me out. Here is the problem:

As Z increases from 98 to 99, which of the following must increase?

I. 4 - 3z II. 4 - 3/z III. 4 / (3- z^2)

If someone can help me out, it will be greatly appreciated.

As Z increases from 98 to 99, which of the following must increase?

I. 4 - 3z II. 4 - 3/z III. 4 / (3- z^2)

Hello Tony,

Thanks for posting your question. I will do my best to answer it. There are essentially, two rules that are at play here.

The first rule is: for a fixed positive numerator of a ratio, as the denominator increases in size, the ratio decreases in size. For example, lets fix the numerator, say 3. Then, 3/5 < 3/4 < 3/2< 3/1. You see, as the denominator increases the value of the fraction decreases.

The second rule is: when the ratio is negative, the first rule goes in the opposite direction. In other words -3/5 > - 3/4 > -3/2 > -3/1.

Now, lets try and use these two rules to solve this problem. (I) 4- 3z : This is certainly not increasing since 3z is getting larger as z increases. Therefore, we are subtracting a larger quantity from 4 as z increases. The value of 4 - 3z is getting smaller. For example, 4 - 3(98.5) = -291.5, and 4 - 3(98.8) = -292.4. Of course there is no need to do any time consuming numerical values for this. Just know that as z gets bigger 4 - 3z gets smaller. Its simple enough.

Lets look at (II). 4 - 3/z. Clearly, according to our rules, as z gets bigger 3/z will get smaller. So as we go up the number line we are subtracting increasingly smaller numbers from 4. so 4 - 3/z is increasing.

Finally, lets look at (III). Again, we will use our above mentioned rules 4 / 3- z^2. Lets focus on the denominator since our numerator is positive and fixed. Our denominator is clearly negative since any value of z between 98 and 99 will be much larger than 3 when squared. So we have the ratio of 4 to an increasingly more negative denominator. If the denominator is becoming a larger negative number as we move up the number line. Normally, a larger positive denominator would make the ratio smaller, however, because its negative, the second rule tells us that the fraction is actually increasing. Lets look at a small numerical illustration 4/ 3 - (98.5^2) = -0.000412 where as 4 / 3 -(98.8^2) = -0.00410 . Clearly, the numbers are increasing.

Users browsing this forum: No registered users and 1 guest

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum

GMAT(TM) and GMAT CAT (TM) are registered trademarks of the Graduate Management Admission Council(TM). The Graduate Management Admission Council(TM) does not endorse, nor is affiliated in any way with the owner or any content of this site.