Jiayi is designing a game that uses a peg board that contains an 11

Question

Jiayi is designing a game that uses a peg board that contains an 11 by 11 rectangular array of peg holes. For design purposes she is modeling the positions of the peg holes on the board as the set of all points (a,b) in the standard (x,y) coordinate plane such that each of a and b is an integer between -5 and 5, inclusive. Set S consists of the rectangular array of those points in the model such that -5 ≤ a ≤ -2 and -3 ≤ b ≤ -2. Set T consists of the rectangular array of those points in the model such that 2 ≤ a ≤ 3 and -3 ≤ b ≤ 4.

Select for Least distance the least distance between a point in S and a point in T, and select for Greatest distance the greatest distance between a point in Sand a point in T. Make only two selections, one in each column.

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Select for  Least distance  the least distance between a point in S and a point in T, and select for  Greatest distance  the greatest distance between a point in S and a point in T. Make only two selections, one in each column.

https://gmatclub.com/forum/download/file.php?id=76106

Bunuel · Accepted Answer

Check the image below: https://gmatclub.com/forum/download/file.php?id=82004 The least distance between a point in S and a point in T is the length of the green line, which is 4 units. The greatest distance between a point in S and a point in T is the length of the purple line, which is \sqrt{8^2 + 7^2} = \sqrt{113} units. GMAT-Club-Forum-6dw79wir.png

byebyebye · Answer

do these type of questions really come in the exam?
I've heard from a lot of Gmat test takers that the DI question are more logic based than pure math based and even in mocks we don't see questions like these

Bunuel · Answer

Yes. This is a GMAT Prep Focus question.

tanishqgirotra · Answer

This question took me 7 minutes to solve. How the hell can the gmat expect from us to solve these type of questions in 3 minutes?

Parthsarthi · Answer

Took me 3 and a half minutes to solve and still i have heard thats bad. but these questions will comeonly when you are doing exceptionally well in the test meaning you will have somewhere around 3-4 miniutes to solve these questions.

sayan640 · Answer

KarishmaB   chetan2u   GMATinsight  Can you please explain in a simpler way ? I dint understand the logic behind the figure drawn by bunuel. Can you kindly throw some more light on this ?

KarishmaB · Answer

The figure Bunuel has shown is exactly what I would make too.  
You have an 11 *11 peg board so 11 integer co-rodinates on X axis and 11 on Y axis. Since the co-ordinates are from -5 to 5, the point at the centre of the peg board is (0, 0) as Bunuel has shown. 
Set S consists of the points lying on the red rectangle and set T consists on points lying on the Blue rectangle.

ashdank94 · Answer

I took values in the inequalities to find my answer, wasn't easy.

Least distance: I found that b2-b1 can be 0 due to -3 in both set S and T. So least value of a is 2 -(-2) = 4. Hence, distance = 4.

Greatest distance: Largest value of a2-a1 = 3-(-5) = 8 and b2-b1 = 4-(-3) = 7. Hence, distance = 64+49 = 113

egmat · Answer

Looking at this coordinate geometry problem, you'll need to identify the points in each set and then find the minimum and maximum distances between them.

Let me walk you through the key steps:

Step 1: Define the sets clearly 
Set S contains points where  -5 \leq a \leq -2  and  -3 \leq b \leq -2 
So S =  \{(-5,-3), (-5,-2), (-4,-3), (-4,-2), (-3,-3), (-3,-2), (-2,-3), (-2,-2)\}

Set T contains points where  2 \leq a \leq 3  and  -3 \leq b \leq 4 
This gives us 16 points total in T (2 x-values × 8 y-values).

Step 2: Find the minimum distance 
Since the sets are separated horizontally, the closest points will have:
- The rightmost x-coordinate in S:  a = -2 
- The leftmost x-coordinate in T:  a = 2 
- The same y-coordinate in both sets

Both sets contain  y = -3  and  y = -2 , so the closest points are  (-2,-3)  and  (2,-3) .

Distance =  \sqrt{(2-(-2))^2 + (-3-(-3))^2} = \sqrt{16 + 0} = 4

Step 3: Find the maximum distance 
The farthest points will be at opposite corners of the rectangular regions:
- Farthest point in S:  (-5,-3) 
- Farthest point in T:  (3,4)

Distance =  \sqrt{(3-(-5))^2 + (4-(-3))^2} = \sqrt{64 + 49} = \sqrt{113}

Answer:  Least distance = 4, Greatest distance =  \sqrt{113}

The key insight here is recognizing that for minimum distance, you want points with the same y-coordinate and closest x-coordinates, while for maximum distance, you need the corner points that are diagonally opposite.

You can check out the  complete framework on Neuron  to understand the systematic approach that works for all coordinate geometry distance problems. You can also practice with comprehensive solutions for  similar official questions here  to build consistent accuracy across different problem variations.

Least distance	Greatest distance
		\(4\)
		\(\sqrt{17}\)
		\(6\)
		\(\sqrt{61}\)
		\(\sqrt{98}\)
		\(\sqrt{113}\)

Jiayi is designing a game that uses a peg board that contains an 11

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Jiayi is designing a game that uses a peg board that contains an 11