ADA Sample Test - Q.R. # 35

[fleur531]

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Does anybody know how to do this question?

ADA Sample Test/Quantitative Reasoning/ Q. 35

What is the maximum number of 3-inch squares (squares that are three inches on a side) that can be cut from a sheet of tin 19*23 inches?

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

The credited answer is indicated as A.

I keep getting 48 though. I've been multiplying 19*23 = 437. Then I divide this by 3*3= 9. I keep getting 48.5 and chose 48 because you can't count half a square. Not sure what I'm doing wrong. Thanks a bunch in advance!!!

 

[fleur531]

I found a previous poster's explanation.... Hope this helps anybody else that might've been stumped by this question!! Happy studying to all 🙂

SMC2UCLA2_
09-01-2005, 12:22 AM
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.

Now heres the answer:
(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.

Your answer will be 7x6=42. Please dont flame me if im wrong.

 

[Streetwolf]

Correct. You'll have leftover area, but you can't piece them together into the shape of 3x3 squares.

 

[jonkin]

this is how u do it. one dimension is 19. 3 goes into 19 a total of 6 times. So now for each column u have 6 squares and how many columns? 23 inches across, 3 goes into 23, 7 times, 7 columns. so 6x7 = 42

 

[bobu]

hi,
do not divide by area. because the need a certain shape which is 3x3. therefore, just take 19/3 =6, and 23/3=7 then 6x7=42 ( number of maximun cut you could)

 

[Streetwolf]

this is how u do it. one dimension is 19. 3 goes into 19 a total of 6 times. So now for each column u have 6 squares and how many columns? 23 inches across, 3 goes into 23, 7 times, 7 columns. so 6x7 = 42

Thank you for bumping a 2 year old post to answer a question which has already been answered twice.