If the dimensions of a rectangle (in inches) is equal to a prime numbe

Question

If the dimensions of a rectangle (in inches) is equal to a prime number that lies between 55 and 65, exclusive, which of the following statements must be true?

I. There is only one other rectangle that has integral dimensions and the same area as the given rectangle
II. There is only one other rectangle that has integral dimensions and the same perimeter as the given rectangle
III. The area of the given rectangle is 3599 square inches.

A. I only
B. II only
C. III only
D. I and II only
E. None of the above

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GMATinsight · Answer

Dimensions of rectangle = two of {59, 61}

i.e there is only one such Rectangle Possible

I. There is only one other rectangle that has integral dimensions and the same area as the given rectangle -  FALSE 
II. There is only one other rectangle that has integral dimensions and the same perimeter as the given rectangle -  FALSE 
III. The area of the given rectangle is 3599 square inches. - Area = 59*61 = 60^2-1^2 = 3599    - TRUE

Answer: Option C

nick1816 · Answer

Hey  GMATinsight

I think 'I' is correct too.

Dimension of only other possible rectangle is (1, 59*61). What you say?

GMATinsight · Answer

Hey  GMATinsight

I think 'I' is correct too.

Dimension of only other possible rectangle is  (1, 59*61) . What you say?

nick1816

Dimensions can be only prime numbers so 1 is not acceptable as dimension

I called that wrong because of word  Other  in statement  "There is only one  other  rectangle..."  while my claim is that there is only 1 rectangle possible no other rectangle.

Bunuel at one of the discussions brought the understanding that Length is always greater than the width and he quoted Oxford dictionary If I am not wrong.

nick1816 · Answer

GMATinsight
i guess you misunderstood the question. (i might be wrong tho)

What I) is saying is there is only one other rectangle that has integral dimensions and the same area as the given rectangle.

That Length of that rectangle is 59*61 and breadth = 1. The dimension of this rectangle need not fell in the given range. It's area must be equal to the given rectangle and dimensions must be integers.

Anyways we can wait for the OA.

nick1816 · Answer

There are 3 rectangles possible-

Case 1-  L=59; B=59
I) There is only one other rectangle that has integral dimensions and the same area as the given rectangle; i.e L=59*59 and B=1
II) There are more thatn 1 rectangle that has integral dimensions and the same perimeter as the given rectangle. 
i) L=60; B=58
ii) L=61: B=57

III) Area of given triangle = 59*59 not equal to 3599

Case 2-  a=61; b=59
I) There is only one other rectangle that has integral dimensions and the same area as the given rectangle; i.e L=61*59 and B=1
II) There are more thatn 1 rectangle that has integral dimensions and the same perimeter as the given rectangle. 
i) L=60; B=60
ii) L=62: B=58

III) Area of given triangle = 61*59 = 3599

Case 3 - L=61; B=61
I) There is only one other rectangle that has integral dimensions and the same area as the given rectangle; i.e L=61*61 and B=1
II) There are more thatn 1 rectangle that has integral dimensions and the same perimeter as the given rectangle. 
i) L=62; B=60
ii) L=63: B=59

III) Area of given triangle = 61*61 not equal to 3599

If the dimensions of a rectangle (in inches) is equal to a prime numbe

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If the dimensions of a rectangle (in inches) is equal to a prime numbe

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