<p>1)in an art class,there was just enough staplers,rulers and glue bottles.if every 2 student share a stapler,every 3 student share a ruler and every 4 students share a glue bottle and the total number of staplers,rulers and glue bottles were 65 then how many student was there?
answer: 60</p>
<p>2)how many positive integers less than 1000 are multiples of 5 and are equal to 3 times an even integer?
answer: 33</p>
<p>3)if a and b are positive integers and a+b<1000 and a/b=0.625 then what is the biggest value of b can be?
answer: 608</p>
<p>4) if q and r are positive integers, what percent of (q+1) is r?
answer: (100r)/(q+1)%</p>
<p>good luck.......i was lucky to solve them quickly.....but these are hard....god forbid,if this type of ques come up in the october,i am a goner</p>
<p>For #1.... it's multiple choice right? You just find the answer choice that can be divided by 2,3,4?</p>
<p>Is there a fast way to do #2?...Also what's the reasoning behind it?</p>
<p>For #3 I understand the 5/8=.625... but why add 5+8 and then do 1000/13? What's the reasoning for that? Another thing.. how come if 1000/13=76.923, then you round down to 76? </p>
<p>Thanks for helping ! These are definitely concepts I need clearing up on</p>
<p>Because there are 5 portions of a to every 8 portions of b, which is 13 portions total. 5/8 is a ratio more so than a fraction. You would round down because if you round up, a+b would be 1001 which is more than 1000.</p>
<p>For number 1:
s + r + g = 65
total students = 2s = 3r = 4g
Just do some basic arithmetic and you get:
s = 2 g
r = 4/3 g
So 2g + 4/3 g + g = 65
g = 15
total students = 4 g = 4*15 = 60</p>
<p>For number 2:
For a number to be 3 times an even number, it must be a multiple of 6 because 3<em>2=6. If a number is both a multiple of 5 and a multiple of 6, it must also be a multiple of 30 since 5</em>6=30. Just divide 1000 by 30 and you get the answer.</p>
<p>So you just divide 1000/15, because obviously 3 is not a factor of 5, and not the other way around either. You would get 66.6</p>
<p>However! You must notice it says "even". Then you must also take into the account 2. Clearly, only half multiples of 15 are even. (15...30...45...60...etc.), so you divide 66.6 by 2</p>
<p>And then you get 33. That took me around 9 seconds (haha, I was nerdy enough to time myself). I hope you call that "fast".</p>
<p>2 is basically saying how many multiples of 5 and 6 are there between 1 and 1000. and if its multiples of both of them, it has to be multiple of 30. so there is 30 between 1 and 900, and then 3 more for total of 33. </p>
<ol>
<li><p>I dont get this one. help please</p></li>
<li><p>whatever</p></li>
</ol>
<p>Question: if a and b are positive integers and a+b<1000 and a/b=0.625 then what is the biggest value of b can be?
Answer: 608</p>
<p>Ivy's Reasons:
It's first important to note that a and b are integers, and that a/b is exactly 0.625.
If you simply divide 1000/1.625 in hopes of finding b, you would find instead that b is not an integer. In this case, most students (me at first try, as well), attempted to round down. However! This presents a problem, as the number down (615) cannot produce an integer when multiplied by 0.625.</p>
<p>So we keep going down the track of finding a number who could satisfy the equation, a/b = 0.625, and we reach 608.</p>
<p>This is a pretty slow guess+check method. A faster way would just be to stop guessing and to start plugging in answers that they give you for multiple choice. If it's not multiple choice, unfortunatley guess+check is the best thing I can come up with O_o</p>
<p>One thing everyone should keep in mind is that when you see problems like 3 and 2, the quotient(if not an integer), must be rounded to a integerthat is smaller than that number. If 1000/13 = 76.999, its 76. Same with number 2.
1000/30 = 33.3333 = 33. If it was 33.9999, its still 33.</p>
<p>1: s = staplers, r = rulers, g = glue bottles, t = total
given:
s + r + g = 65
t = 2s = 3r = 4g
solve:
s = 2g
r = (4/3)g
s + r + g = 2g + (4/3)g + g
2g + (4/3)g + g = 65
(13/3)g = 65
g = 15
t = 4g
4g = 60</p>
<p>2: Multiples of any two numbers are also multiples of the product of those two numbers.
In other words, multiples of x that are multiples of y are also multiples of xy.
A multiple of 3 times an even integer is a multiple of 6, since all even integers are multiples of 2, and (3)(2) = 6.
A multiple of 6 that is also a multiple of 5 is also a multiple of (6)(5) or 30.
Divide 1000/30, then subtract the decimal part of the product, and what's left is the correct number of multiples, 33.</p>
<p>3: (a/b) = 0.625 = (5/8) as a fraction, which is 5:8 as a ratio.
5:8 is the ratio of a:b, 5 parts of a whole to 8 parts of a whole.
5 parts + 8 parts = 13 parts of a whole in total.
Divide 1000 by 13, subtract the decimal part of the product.
The result (76) multiplied by 5 is a: 5(76) = 380
and the result (76) multiplied by 8 is b: 8(76) = 608.</p>
<p>Don't get caught in the trap of miscalculating algebraically like I did at first. The result of a + b must be the largest possible sum that is less than 1000, not greater than or equal to it.</p>