obs23 wrote:

Not sure if this type of question has been posted, but I could not find. The problem says expression \(|6-4Pi+3\sqrt{2}| + |8-6Pi+4 \sqrt{2}|\) is in the form of \(a,bPi,c \sqrt{2}\), what is \(a+b+c\)?

I do not have the answers, nor the source, however I am confused as to the action to take here. How would you recommend solving this please? I am totally confused as to how I could even start here, and the absolute values complicate this in my mind even more...Thanks much in advance.

I'm happy to help with this.

First of all, let me say --- as it stands, this question is not likely at all to appear on the GMAT. Not only is it not in the proper test-question format (multiple choice or DS), but more importantly, I have never seen the GMAT ask anything like this. This is, in essence, an estimation problem.

Basically, we have to figure out whether each expression is positive or negative.

Think about \(6-4

Pi+3\sqrt{2}\) first. Is this positive or negative? Well, pi is a little more than 3, so 4*(pi) is little more than 12. The square root of two is about 1.4 ---- this is a very handy approximation to know ---- so 3*sqrt(2) is about 4.2

Well, the positive terms, 6 + 3*sqrt(2) are around 10.2, which is less than the negative term, 4*(pi). Taking the absolute value will multiply this expression by an "opposite" sign, making it all the opposite sign

\(|6-4

Pi+3\sqrt{2}|= 4

Pi-6-3\sqrt{2}\)

Now, think about the second expression, \(8-6

Pi+4 \sqrt{2}\). Here, the only negative term, 6*(pi), is a little larger than 18. 4*sqrt(2) is around 4*1.4 = 5.6, so the sum of the positive terms, 8 + 4*sqrt(2), is around 13.6, and this is clearly less than 18. Once again, this expression is negative, so all terms get multiplied by the opposite sign.

\(|8-6

Pi+4 \sqrt{2}|=6

Pi-8-4\sqrt{2}\)

Now that these are both out of the absolute values, we can add them

Sum = \(10

Pi-14-7\sqrt{2}\)

I don't know the exact form in which the a/b/c stuff is stated, but if the sum is supposed to be in the form .....

Sum = \(a+b

Pi+c\sqrt{2}\)

Then a = -14, b = +10, and c = -7, so a+b+c = -11

Does all this make sense?

Mike

_________________

Mike McGarry

Magoosh Test Prep