The diagram shows a square quilt pattern with an area of 36 square uni

Question

https://gmatclub.com/forum/download/file.php?mode=view&id=59968 The diagram shows a square quilt pattern with an area of 36 square units. The pattern is composed of 13 colored regions, each of which has an area, in square units, that is an integer. Based on the information provided, select from each drop-down menu the option that completes the statement most accurately. Measured in square units, the mode of the areas of the 13 colored regions is exactly GRAPH_1_PLACEHOLDER than the GRAPH_2_PLACEHOLDER of those areas. 1.jpg

Sajjad1994 · Accepted Answer

Official Explanation

RO1

The diagram shows 2 regions of exactly 1 square unit, 3 regions of exactly 2 square units, 6 regions of exactly 3 square units, and 2 regions of exactly 5 square units. When listed in ascending order, the 13 areas are:

1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5.

For this list, the mode is equal to the listed area that appears most frequently, or 3; the mean is equal to the sum of the listed areas (36) divided by the number of colored regions (13), or approximately 2.8; the median is equal to the 7th greatest listed area, or 3; and the range is equal to the greatest of the listed areas (5) minus the least of the areas (1), or 4. Thus, the mode is approximately 0.2 greater than the mean, is equal to the median, and is exactly 1 less than the range.
 
  The correct answer is 1 less.  
 
 RO2

As explained in the analysis of RO1, the mode of these areas is exactly 1 square unit less than the range of these areas.
 
  The correct answer is range.

Sumi1010 · Answer

Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

Blue - 8 units. (2,3,3)
White - 9 units.(3,3,3)
Grey - 10 units (2,3,5)
Orange - 9 units (1,1,2,5)
Thus, the set for the pattern is {1,1,2,2,2,3,3,3,3,3,3,5,5}.

Mean = sum/13 = 36/13 
Median = 7th term= 3 
Mode (the number that occurs the most frequently) = 3
Range = 5-1 = 4
 
Thus, mode is one less than Range.

First blank :  A. 1 Less 
Second blank :  A. Range

Deepakjhamb · Answer

lets analyze this q :

we have 13 areas : now square is total 36 square units , so each side is 6 units and thus we have 36 squares with 1 unit sizes in this . Now lets find the areas of each different area coloured by observation : these come out to be

1,1,2,2,2,3,3,3,3,3,3,5,5 so we have mode = 3 , median = 3 , range = 5-1=4 and mean = 36/13 = 2.769

so the blanks fit in with only 2 items which is mode less than range by exactly 1

Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

First Blank

answer is A. 1 less 
 
A. 1 Less
B. 2 Less
C. 1 Greater
D. 2 Greater

Second Blank

answer is A. RANGE  
A. Range
B. Mean
C. Median

rocky620 · Answer

Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

Total regions = 13
Total Area = 36
Orange Region areas - 2, 5, 1, 1, Total=9
Blue Region areas - 3, 3, 2 Total=8
White Region areas - 3, 3, 3, Total=9
Grey Region areas - 3, 2, 5, Total=10

All Regions (arranged) = 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5

Mean =   \frac{36}{13}  ~ 2.7
 Median (7th val) =  3
 Mode (highest count) =  3
 Range (highest - lowest) =  5-1 = 4

We can see that the Mode (3) is exactly 1 less than the Range (4). So,

First Blank - A. 1 Less
Second Blank - A. Range

TarunKumar1234 · Answer

As per the figure attached, we have area of Square = 36 square units, so one side length= 6 and it is equally distributed by dots.

So,  distance between 2 dots = 1 unit

Area of 1 = 2*1 =2 square units, 
Area of 2 = 1*1 =1 square unit,
Area of 3 = 2*1 +1*1 =3 square units,
Area of 4 = 2*1 +1*1 =3 square units,
Area of 5 = 1*1 =1 square unit,
Area of 6 = 2*1 +1*1 =3 square units,
Area of 7 = 3*1 +1*1 +1*1 =5 square units,
Area of 8 = 4*1 +1*1 =5 square units,
Area of 9 = 2*1 +1*1 =3 square units,
Area of 10 = 2*1 +1*1 =3 square units,
Area of 11 = 2*1 +1*1 =3 square units,
Area of 12 = 2*1 =2 square units,
Area of 13 = 2*1 =2 square units,

Now, in areas in ascending order: 1,1,2,2,2,3,3,3,3,3,3,5,5
mode = count of the most repeated integer = 6 
Range = 5-1 = 4, Median = 3, Mean= (1+1+2+2+2+3+3+3+3+3+3+5+5)/13 = 36/13~3

Mode- Range = 6-4 = 2

Measured in square units, the mode of the areas of the 13 colored regions is exactly___________than the_____________of those areas.

1st blank: 2 units greater. D. 
  2nd blank: Range. A.

Sajjad1994 · Answer

OA has been updated now its A for both blanks. Good work Sumi1010 and Deepakjhamb I have feelings for you TarunKumar1234 you done a lot work but not in true direction

rocky620 I like it when you keep your post organized. Official explanation will be posted soon have a look at that and match your answers and reasoning. Thank you

Rohanx9 · Answer

I saved some time by taking a structured approach to counting and organising the data sets to a tree and branch format:

1: II 
2: III
3: IIIII I
4:
5: II

Therefore, mode is 3. Range is 5-4 = 4. Ans is "1 less" and "Range".

bumpbot · Answer

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The diagram shows a square quilt pattern with an area of 36 square uni

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