<p>Ok this is from the Kaplan SAT math workbook. Here's the problem.</p>
<p>"What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, 10?"</p>
<p>Wouldn't the answer be 7? 7/6 has a remainder 2 and that is the smallest integer greater then 1 that can be divided by 6. The problem says ANY of the integers and not ALL. I found an integer leaving a remainder dividing into 6 or ANY of the 3 given.</p>
<p>The book says that answer is 121, please tell me this is wrong. The books explanation says we are asked for the smallest remainder when divided by all the numbers (6, 8, 10) But it doesn't ask the number be divided by all it says once again ANY!!!</p>
<p>Am I stupid? What's the correct answer?</p>
<p>You translated the word "any" into something that's completely different than how it is used in mathematics. In mathematics, "any" usually is used similarly to "all", as in this case. The correct answer is 121 (that is, 2^3<em>3</em>5+1).</p>
<p>The "any" you're referring to usually comes into form as "at least one of the following" in mathematics, and I assume it is used like that on the SAT as well.</p>
<p>can you please explain this: (that is, 2^3<em>3</em>5+1)</p>
<p>how did you get that?</p>
<p>the answer is 121. the way i got it is by first finding out what number could be divided by 6, 8, and 10. if you multiply 6 8 and 10 you will get a number that is divisible by all 3. I got that by doing (3 * 5 * 8) the reason you multiply by 3 and 5 instead of 6 and 8 is because the factor of 2 is already included in the 8. anyway, so once you get 120, you add 1</p>
<p>and also, when you divide 7 by 8, you don't get a remainder of 1. the same is true when you divide 7 by 10.</p>
<p>i agree with you, bkg. "any" means "any." i'm not familiar with the convention that "any" means "all" in a mathematical context.</p>
<p>things like this are why you should only use college board questions to practice with.</p>
<p>what are you talking about? oh my god, some people...</p>
<p>when you divide 121 by 6 you get a remainder of 1. when you divide 121 by 8 you get a remainder of 1. when you divide 121 by 10 you get a remainder of 1. you are not dividing the answer by ALL of the numbers (6, 8, 10) but rather each one individually and getting a remainder of one.</p>
<p>right, but the question doesn't say that.</p>
<p>the question says to find the least integer that satisfies the requirement of leaving a remainder of 1 when divided by ANY of the three numbers. that means you can pick ANY one of the three numbers--it doesn't have to leave a remainder of 1 when divided by all three of the numbers.</p>
<p>the number 7 leaves a remainder of 1 when divided by 6. 7 is less than 121. that makes 7 the right answer.</p>
<p>the only way 7 can not be the right answer is if "any" is supposed to mean "each," which would require 7 to leave a remainder of 1 when divided by all three of the numbers 6, 8, and 10. if they meant "each" they should have said "each." "any" means you can pick ANY one of the set of numbers and satisfy the requirement only with respect to that number.</p>
<p>look it up:</p>
<p><a href="http://dictionary.reference.com/browse/any%5B/url%5D">http://dictionary.reference.com/browse/any</a></p>
<p>only one of the multiple definitions suggests that "any" is interchangeable with "all." the others all say "any" means something like "one, some, every, or all without specification."</p>
<p>the bottom line is that this issue would never arise with a cb question, which is why i recommended you only use those questions for practice.</p>
<p>Yes I do use the collegeboard's book. I went through all of the problems. I can't use their practice tests because there are no explanations. So I use Kaplan's math workbook to give me some extra help.</p>
<p>At 1st I beleived phuriku when he said "any" means "all" most of the time in math. But after reading the other responses I gather that the Kaplan book made a mistake? Now that I think about it, how could "any" possibly mean "all" in mathematics. That just doesn't make sense, math is literal the problem is what it is.</p>
<p>"Any" does not mean "all." It does mean your definition of any. However, it does not mean any that you select, it means an arbitrary any. Meaning if, at random, one of those three numbers were to be chosen to be divided into the number, the condition of a remainder of 1 would have to be satisfied - no matter which number was arbitrarily chosen.</p>
<p>If "all" had been used, it could have been inferred that it meant divisible by all three at once (as in divisible by their product) rather that one at a time.</p>
<p>So "any" and "all" are distinct, but for all intents and purposes you can see "any" to mean "all" when dealing with conditions that must be satisfied.</p>
<p>I just used me calculator program to find the lcm of 6,8 and 10. then, 120 + 1 = 121.</p>
<p>"If "all" had been used, it could have been inferred that it meant divisible by all three at once (as in divisible by their product) rather that one at a time."</p>
<p>That's silly, you are saying they implied that any meant that each of the 3 numbers had to have a remander of 1 when a number was divided by them (6,8, 10) (noticed I said each and not any because CLEARLY any used in this context with the answer 121 makes the question ambiguous)</p>
<p>Collegeboard has stated that they are not supposed to be trick questions but rather to test logical reasoning and apply mathematic skills.</p>
<p>So let me ask you what would the answer to this question be?</p>
<p>"What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by each of the integers 6, 8, 10?"</p>
<p>"the question says to find the least integer that satisfies the requirement of leaving a remainder of 1 when divided by ANY of the three numbers. that means you can pick ANY one of the three numbers--it doesn't have to leave a remainder of 1 when divided by all three of the numbers."</p>
<p>-are you kidding me? there is no SAT question that will allow you to choose which number you want to divide by. there was a question like this on the real SAT this year...</p>
<p>"What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by each of the integers 6, 8, 10?"</p>
<p>121</p>
<p>"What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by all of the integers 6, 8, 10?"</p>
<p>121 or 481 - ambiguous</p>
<p>"What is the smallest integer greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, 10?"</p>
<p>121</p>
<p><em>High Fives</em> Pkswmr76! Why does everyone make math so much more complicated than it is?</p>