Indians love Math

Test Preparation SAT Preparation
1

<p>Now that I have your attention, help on this official SAT problem please!</p>

<ol>
<li>How many positive integers less than 1,001 are
divisible by either 2 or 5 or both?
(A) 400
(B) 500
(C) 540
(D) 600
(E) 700</li>
</ol>

<p>I was sure it was 800, but it's obviously not a choice.
How I arrived at 800:</p>

<p>1001/2 is 500.5, so there are 500 integers divisible by 2.
1001/5 is 200.2, so there are 200 integers divisible by 5.
1001/10 is 100, so there are 100 integers divisible by 10.</p>

<p>500+200+100=800</p>

<p>The right answer is (D)</p>

2

<p>If it’s divisible the number is divisible by both 2 and 5, you would have accounted for all multiples of ten twice with the 1000/2 and the 1000/5. Which is why you subtract 1000/10.</p>

3

<p>500 + 200 - 100 = 600 D)</p>

<p>You were on the right track but you don’t add what’s already there, you subtract it.</p>

4

<p>1,2,3,4,5,6,7,8,9,10 break it down like this</p>

<p>2,4,6,8,10 -----multiples of 2</p>

<p>5,10 ------multiples of 5</p>

<p>Notice the overlap of 10 in both sets.</p>

<p>So you need to divide 200 in half and add them together</p>

<p>So you should get 500 + 100 = 600</p>

5

<p>So then what is the difference with this question? (This is, by the way, not a real SAT question):
2. For the first 1000 positive integers, how many integers are multiples of 3 or 4?</p>

<p>(A) 470
(B) 480
(C) 500
(D) 520
(E) 550</p>

<p>I get this one.
1000/3 is 333 integers.
1000/4 is 250 integers.
1000/12 is 83 integers.</p>

<p>333 + 250 - 83 = 500 (C)</p>

<p>This EXCLUDES both, but the first question INCLUDES both. D:</p>

6

<p>Exact same thing, just different numbers. Look at your original post. Your only problem was that you added the 100 instead of subtracting it.</p>

7

<p>The or both is irrelevant to the question. You could take it out and it would have no impact on the answer or how I would end up finding it if this was on a test.</p>

8

<p>The first question is a trick question. Notice how the answer does not change if you leave out the part of the sentence “or both”.</p>

9

<p>Okay thanks I have to remember to subtract the both regardless of what it really says.</p>

10

<p>No! That’s not it!! You have to understand “why”.</p>

<p>Perhaps working with smaller numbers will aid your understanding.</p>

<p>How many positive integers less than 11 are divisible by either 2 or 5 or both?</p>

<p>Divisible by 2: 2, 4, 6, 8, 10 —> 5
Divisible by 5: 5, 10 —> 2
Divisible by both: 10 —> 1</p>

<p>Since 10 is repeated in both sets, 1 is subtracted from 5+2.
5 + 2 - 1 = 6</p>

<p>Likewise, if the question read:
How many positive integers less than 101 are divisible by either 2 or 5 or both?
Divisible by 2 → 50
Divisible by 5 → 20
Divisible by both → multiples of 10 → 10.</p>

<p>50 + 20 - 10 = 60</p>