shahdevine

parallelism. the subject of this clause is "resulting increase" and so the "threaten" has to agree with "will endanger" because its connected by the conjunction "and"

2. Given: P=.75R P=.9G Step 1: Set equations equal and find ratio of R to G .75R=.9G 90/75=R/G R/G=1.2/1 .2 equals excess that R is greater than G --> 20% B

Let's say x=14 ---> which retranslates to 14/1 LCD(Lowest Common Denominator) means the lowest common denominator that both fractions share or go into. Lowest Common Denominator is not lowest common multiple(LCM). So for 14/1 and 1/7 the lowest common denominator would be 7. so 14/1 would change to 98/7 and 1/7 would stay as is. By finding the LCD you can now add these two numbers. Does this make sense? LCD for 1/7 and any random positive integer is always going to be 7 because 7 is the lowest number for a denominator that any positive integer will be able to multiply into. Remember any positive integer will have 1 as their denominator.

This is actually pretty brilliant. First what is a LCD? LCD is lowest denominator number that two or more numbers in question can go into. If it was 1/3 and 1/6 the lowest common denominator would be 6. In this case for statement 1, where it says " r is the least common denominator of 1/7 and positive integer x", the lowest common denominator has to be 7 because any positive integer has a denominator of 1. 7 shares the factors of 1 and 7. Thus R has to be 7 and we can solve 7/55 to get the hundredhs digit. Sufficient.

There's an even faster way... Step 1. Essentially write out the problem. .7A + .5B= 6.3 Step 2. Multipy both sides by 10 7A + 5B = 63 Step 3. Look at both coefficients, 7 and 5. 7 goes nicely into 63, so you isolate the equation in terms of A. 7A = 63 - 5B A= 9 - 5B/7 Step 4. Looking at this equation you know B, which is bananas has to be a multiple of 7. So B could equal 7, 14, 21, etc. But when you look at the answer choices, none of them are greater than 14 and if B = 14 that means A would have to equal 0 (again based on answers given, which would be impossible.) So therefore B has to equal 7 which means A equals 4 and so A + B equals 11. Answer B

rephrase question: what is greatest integer k which makes 30!/3k an integer? 3 gets quickly canceled in 30! which leaves k. Check answers to see highest value whose factors would get canceled when divided into 30x29x28x27....x4. 18 has factors 2 x 3 x 3 which would get canceled. Ans E.

set up your ratios: # of 2nd graders/# of 4th graders=8/5 # of 1st graders/# of 2nd graders=3/4 # of 3rd graders/# of 4th graders=3/2 # of 1st graders/# of 3rd graders=? Trick is to find common denominators for # of students in same grades...for example... # of 2nd graders/# of 4th graders also = 16/10 and # of 3rd graders/# of 4th graders also = 15/10. Since the denominator is same for both of these ratios we can extract # of 3rd graders/# of 2nd graders = 15/16. We do again... # of 1st graders/# of 2nd graders also = 12/16. Since the denominator is common for both # of 1st graders/# of 2nd graders and # of 3rd graders/# of 2nd graders we can extract # of 1st graders / # of 3rd graders = 12/15 = 4/5. Ans E.

First step: rephrase the question by manipulating the info given. z So the question is really asking, is t=-3/4? A) insuff. it only deals with z B) insuff. also inconclusive

Krovidy, great explanation. however i don't get why the probability set up isn't: Times coin lands on head(1/2^3) X coin does not land on heads(1-1/4) => 1/8 * 3/4 = 3/32 Pls explain. Thx.