Aug 22 SAT question of the day

Test Preparation SAT Preparation
1

<p>At Central High School, the math club has 15 members and the chess club has 12 members. If a total of 13 students belong to only one of the two clubs, how many students belong to both clubs?</p>

<p>a.2
b.6
c.7
d.12
e.14 </p>

<p>When it says "a total of 13 students belong to one of the 2 clubs", does it mean that a total of 13 students belong in either the math or the chess? Apparently thats what the explanation is getting at, but doesnt "one of the two clubs" mean that 13 belong in ONE of the clubs? Yo help me out.</p>

2

<p>Isn't that the same as in either math or chess? there are only 2 clubs, so being in one of the two clubs = either math or chess..</p>

3

<p>There are three possibilities for a student: In only the math club, in only the chess club, or in both clubs. Anyone in only the chess club or only the math club count as "in only one of the two clubs". Try an overlapping venn diagram. Call math club only "x", chess club only "y", and both clubs "z".</p>

<p>x+y = 13
x+z = 15
y+z = 12</p>

<p>Then solve the system of equations.</p>

<p>To solve it more intuitively, the overlap (both clubs, or variable "z" from above) is counted twice in the total of the two clubs, so 15 + 12 = 13 +2z. Therefore, z = 7.</p>

<p>Hope that helps!</p>

4

<p>He meant the ambiguity of the problem. It should be clear with the data that they gave you, but it is fairly ambiguous. You should still be able to come to the correct answer though.</p>

5

<p>wow....very interesting problem.........</p>

6

<p>That was a medium level problem too...;&lt;/p>

7

<p>Here is a way EASIER way to think of the problem</p>

<p>Imagine X as the number of people who attend both clubs</p>

<p>Logically,</p>

<p>12-X = solely chess club members
15-X = solely math club members</p>

<p>Therefore 12-x + 15-x = 13 or the number of solely club members people ( excluding the X)</p>

8

<p>^ Lol, that's the explanation collegeboard gave.</p>

9

<p>think of a venn diagram </p>

<p>there is a total of 15+12 people, but you have to subtract the overlap. call this "x". therefore, 15+12-x = Math Club only + Both Clubs + Chess club only. they tell you that Math club only + Chess club only = 13, and Both clubs is x, so your final equation is </p>

<p>15+12-x=13+x</p>

<p>solve and x=7</p>

10

<p>you have to do some tai chi, man</p>

11

<p>@ Aero</p>

<p>Really?! I don't usually read the CB explanations...maybe I should..</p>