Ramon wants to cut a rectangular board into identical square pieces.

Question

Ramon wants to cut a rectangular board into identical square pieces. If the board is 18 inches by 30 inches, what is the least number of square pieces he can cut without wasting any of the board?

(A) 4
(B) 6
(C) 9
(D) 12
(E) 15

Source -> Manhattan

AkshayKS21 · Accepted Answer

Area of Rectangle = 18 * 30 = 2*3*3 * 3*2*5 = 2^2 * 3^2 * 15
Area of individual square of side s= s^2.
Number of such squares = n
so, ns^2 = 2^2 * 3^2 * 15
s^2 can be 2^2*3^2. 15 remains on one side. This is number of squares n.

Is this logic correct?

BeingHan · Answer

Is it E . 
As 6 is the HCF for 30 and 18.amd 30x18/36 is 15.

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broall · Answer

BeingHan  is right. We find Greatest Common Factor of 18 and 30. GCF(18, 30) = 6.

18 = 6 * 3
30 = 6 * 5

Hence the least number of square pieces is: 3 * 5 = 15.

chetan2u · Answer

Hi,

One way is to find the GCD of 30 and 18...
So ans is 6..

The other way is that ....  When you divide 18*30 by the # of pieces , you will get the Area of each piece...
Since we are talking of square pieces, the area we get should be a SQUARE integer..

So divide by the choices and see what gives you square INTEGER..
If there are more than one such choices, the least will be the answer as we are looking for least number of pieces..
ONLY 18*30/15 gives square 36, which is 6^2..

Hence E

JeffTargetTestPrep · Answer

To find the least number of square pieces Ramon can cut without wasting any of the board, we need the greatest common factor (GCF) of 18 and 30, which is 6. Thus he can cut the board into 6-inch square pieces without wasting any of the board since 6 divides into both 18 and 30 and is the largest number that does so. Therefore, the number of square pieces he can cut is:

(18 x 30)/(6 x 6) = (18/6) x (30/6) = 3 x 5 = 15

Answer: E

BrentGMATPrepNow · Answer

If we aren't wasting any wood, the length and width must be divisible by one side of the square 
So, this question is a clever way of asking us what the greatest common divisor (GCD) of 18 and 30
The GCD of 18 and 30 is 6, so if we cut squares that are 6 x 6, then we won't waste any wood.

We get something like this:
 https://i.imgur.com/KLxkez2.png

So, we can cut 15 squares. 
Answer: E

Cheers,
Brent

bumpbot · Answer

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Ramon wants to cut a rectangular board into identical square pieces.

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