# QR question

#### joooj86

##### Senior Member
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ADA question......Jill has six different books. in how many ways can jill select two different books. Answer is 30 according to ADA

i thought it was 15 "assuming the order doesnt matter" did u guys understand that order mattered in this question??

thanks

#### Kremlar

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joooj86 said:
ADA question......Jill has six different books. in how many ways can jill select two different books. Answer is 30 according to ADA

i thought it was 15 "assuming the order doesnt matter" did u guys understand that order mattered in this question??

It's 6x5 I believe.. 6 for the total possible books she can choose from, then 5 choices remaining... they want to know how many different ways she can select the books... hence if she selects book 3 first then selects book 4, it's indicating that its not the same as selecting book 4 then book 3.... eventhough she's selecting the same books, the order she takes them off the shelf lets say is different....

##### DDS 2008
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Kremlar said:
joooj86 said:
ADA question......Jill has six different books. in how many ways can jill select two different books. Answer is 30 according to ADA

i thought it was 15 "assuming the order doesnt matter" did u guys understand that order mattered in this question??

It's 6x5 I believe.. 6 for the total possible books she can choose from, then 5 choices remaining... they want to know how many different ways she can select the books... hence if she selects book 3 first then selects book 4, it's indicating that its not the same as selecting book 4 then book 3.... eventhough she's selecting the same books, the order she takes them off the shelf lets say is different....

Exactly!

#### fob12

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A Painting whis 4 feet wide and 5 feet long is surrounded by a rectangular frame 6 inches wide. What percent of the area of the picure and the frame is occupied by the frame?

A. 10.5
B. 20
C. 30
D. 33 1/3
E. 50

I have another one:

What is the maximum number of 3 inch squares (square that are 3 inches on a side) that can be cut from a sheet of tin 19X23 inches?

A. 42
B. 48
C. 49
D. 145
E. 146

##### DDS 2008
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#1.

A. Square ft of painting = 5 X 4 = 20 sqft
B. Square ft of frame = 6 X 5 = 30 sqft minus 20 sqft (painting) = 10 sqft
C. % of total picture occupied by frame = 10sqft/30sqft = 33.33%

#2.

A. Total possible area to cut from = 19 X 23 = 437 inches
B. Total # of 3 inch squares that can be cut = 437/3 = 145.6
C. Since the question only wants to know the MAX number of WHOLE squares, the answer is 145 and not 146.

#### makwendo

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you used 437/3, why 3 and not 9 (3x3).

Here's my reasoning

take for example a 9"x9" square and divide it into 9 equal parts. You get 9 squares that are 3"x3". Therefore, using these numbers to do Q#2, you have

Total area = 9X9=81"square
Max # of squares = 81/(3x3)= 9 squares

Is my reasoning off here?

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These seem really easy once you break them down, but I can't even get to that part... #### Kremlar

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makwendo said:

you used 437/3, why 3 and not 9 (3x3).

Here's my reasoning

take for example a 9"x9" square and divide it into 9 equal parts. You get 9 squares that are 3"x3". Therefore, using these numbers to do Q#2, you have

Total area = 9X9=81"square
Max # of squares = 81/(3x3)= 9 squares

Is my reasoning off here?

If im not wrong, 9"x9" square cut into 9 equal parts will give you 9 1"x1" squares... not 9 3" squares...

#### makwendo

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9"
________
|__|__|__| 3"
|__|__|__| 3" 9"
|__|__|__| 3"
3" 3" 3"

9"X9" total sides
3"x3" for each square
9 total squares

if you did it Java's way it would come out to

9"X9"=81"
81"/3=27 squares......clearly, from the diagram above, there aren't 27 squares....

but
81"/(3X3)=9=# of squares drawn above.......

#### SMC2UCLA2_

##### Senior Member
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makwendo said:
9"
________
|__|__|__| 3"
|__|__|__| 3" 9"
|__|__|__| 3"
3" 3" 3"

9"X9" total sides
3"x3" for each square
9 total squares

if you did it Java's way it would come out to

9"X9"=81"
81"/3=27 squares......clearly, from the diagram above, there aren't 27 squares....

but
81"/(3X3)=9=# of squares drawn above.......

Hmm...I get 42. If you do it Java's way it doesn't make sense to me. So lets figure this out.

Total area: 19 x 23 = 437

If you divide 437/3= 145.6, you are NOT getting the number of 3x3 inch squares. This calculation neglects the size requirement of each square which is 3x3.

Now you may think that 437/(3x3) = 48.5 or 48 squares is the right answer
...but this is another trap. Here you neglecting the requirement that each square be specifically 3x3. Instead you are finding how many "9 area units" will fit into your 19 x 23 sheet. This above calculation will give u odd shaped rectangles of 9x1 or even 4.5x2.

(19/3)= 6.33...so there will be 6 segments of length 3 on this side.
(23/3)=7.66... so there will be 7 segments of length 3 on this side.