Odd

Discus: SAT/ACT Tests and Test Preparation: October 2003 Archive: Odd
 By Student9 (Student9) on Thursday, October 09, 2003 - 05:39 pm: Edit

If m and k are positive integers and the ratio of m to k is the same as the ratio of m+5 to k+5, which of the following must be true?

I. m=k
II. m=5
m=5k

cross multiplying:

mk +m5 = mk + k5, if m is equal to k, then they are equal.

What if m=5?

5k + k5 = 5k + k5, so isn't m also equal to 5?

The answer is supposed to be I only, but why not II. also?

One more question:

Grape drink contains 25% grape juice by volume. Which of the following expressions represents the percentage of grape juice by volume in a mixture of g gallons of Grape drink and w gallons of water?

25g/(g+w) %

Is anyone here smart enough to prove this?

 By Akaflex (Akaflex) on Thursday, October 09, 2003 - 05:47 pm: Edit

For the first question read it "MUST NOT COULD" now m = k is a must bc once u divide 5 in both sides it will be m=k u cant get m=5 and u cant prove that, this is not a "could" question

The grape question uw ant to know how much grape juice is in total. well If 25% grape juice usually takes a volume it has to be .25 x g to see how much grape is in there. Now once u figure that out u put it over the total to see the percent of grape juice inside mixed with water. I probably didnt explain this well hopefully u get it. U can also pick numbers and it will prove wut i mean

 By Nhlgoalie (Nhlgoalie) on Thursday, October 09, 2003 - 05:50 pm: Edit

II states that m must equal 5. Therefore any example that works where m is not 5 disproves conclusively statement II.

"the ratio of m to k is the same as the ratio of m+5 to k+5"

Any value other than 5 will work for m, as long as k is the same value

For example, say m=10 and k=10

ratio of m to k = 10/10 = 1
ratio of m+5 to k+5 = 15/15 = 1

The grape juice question is simply a matter of units and is very easy to prove. Email me or post here is you really need a written out proof, cause I should go study for SATs a bit.

 By Xiggi (Xiggi) on Thursday, October 09, 2003 - 06:12 pm: Edit

If m and k are positive integers and the ratio of m to k is the same as the ratio of m+5 to k+5, which of the following must be true?

m can equal 5 but only when k also equals 5. As such is satisfies condition I. However, as long as m = k, m can have any value. It can be 1, 2, 3, etc. For that reason, it does NOT have to be 5 but could be 5. Not the same difference

As far as the 5 and volume, simply imagine a mixture of grape drink and water. Let's say, it is 20 gallons each. The amount of grape juice is still 25% of the 20 gallons of grape drink. However, to calculate the new percentage in the new drink, you need to change the volume of total drink

25% of of g is now x% of (g+w) or 25% of 20 /(20+20) or 5 gallons of juice for 40 gallons of "satorade".

You can also express the 5 as 25% of 20. In this case, 20 is g and 20 is also w, so 5/(100+100) is 25%g/(g+w)

Kinda long to explain, but much simpler with a piece of paper.

 By Xiggi (Xiggi) on Thursday, October 09, 2003 - 06:14 pm: Edit

LOL - forgot to refresh

 By Student9 (Student9) on Thursday, October 09, 2003 - 06:38 pm: Edit

Thanks everyone.

I appreciate it.