Kaplan--DS--2010-11 premier

[prachich1987]

Does Rectangle A have a greater perimeter than rectangle B?

1) The length of a side of rectangle A is twice the length of a side of rectangle B
2) The area of rectangle A is twice the area of rectangle B

[Anurag@Gurome]

Does Rectangle A have a greater perimeter than rectangle B?

1) The length of a side of rectangle A is twice the length of a side of rectangle B
2) The area of rectangle A is twice the area of rectangle B

Say length of the sides of rectangle A are A1 and A2.
Say length of the sides of rectangle B are B1 and B2.

Perimeter of A = 2(A1 + A2)
Perimeter of B = 2(B1 + B2)

Statement 1: A1 = 2*B1
As we don't know about the other sides the perimeter of A may or may not be greater than perimeter of B.

Not sufficient

Statement 2: (A1)*(A2) = 2*(B1)*(B2)
Consider A1 = A2 = 2, B1 = 2, B2 = 1 => (A1 + A2) > (B1 + B2)
Consider A1 = A2 = 2, B1 = 20, B2 = 0.1 => (A1 + A2) < (B1 + B2)

Not sufficient

1 & 2 Together: (A1)*(A2) = 2*(B1)*(B2)
Replacing A1 with 2*B1: 2*(B1)*(A2) = 2*(B1)*(B2) => A2 = B2
Therefore, Perimeter of A = 2(A1 + A2) = 2[2*(B1) + B2] = 4*(B1) + 2*(B2) = 2*(B1) + [2(B1 + B2)] > 2(B1 + B2) = Perimeter of B

Sufficient

The correct answer is C.

[prachich1987]

Does Rectangle A have a greater perimeter than rectangle B?

1) The length of a side of rectangle A is twice the length of a side of rectangle B
2) The area of rectangle A is twice the area of rectangle B

Say length of the sides of rectangle A are A1 and A2.
Say length of the sides of rectangle B are B1 and B2.

Perimeter of A = 2(A1 + A2)
Perimeter of B = 2(B1 + B2)

Statement 1: A1 = 2*B1
As we don't know about the other sides the perimeter of A may or may not be greater than perimeter of B.

Not sufficient

Statement 2: (A1)*(A2) = 2*(B1)*(B2)
Consider A1 = A2 = 2, B1 = 2, B2 = 1 => (A1 + A2) > (B1 + B2)
Consider A1 = A2 = 2, B1 = 20, B2 = 0.1 => (A1 + A2) < (B1 + B2)

Not sufficient

1 & 2 Together: (A1)*(A2) = 2*(B1)*(B2)
Replacing A1 with 2*B1: 2*(B1)*(A2) = 2*(B1)*(B2) => A2 = B2
Therefore, Perimeter of A = 2(A1 + A2) = 2[2*(B1) + B2] = 4*(B1) + 2*(B2) = 2*(B1) + [2(B1 + B2)] > 2(B1 + B2) = Perimeter of B

Sufficient

The correct answer is C.

Hi,

Thanks for the above explanation.
I tried to solve the problem by taking different values of lengths,widths.
But I couldn't find a single triangle where the length of one triangle is twice the length of the other triangle & still the perimeter of former is lesser than the latter.
Can you plz give such example.
Thanks!

[anshumishra]

Does Rectangle A have a greater perimeter than rectangle B?

1) The length of a side of rectangle A is twice the length of a side of rectangle B
2) The area of rectangle A is twice the area of rectangle B

Say length of the sides of rectangle A are A1 and A2.
Say length of the sides of rectangle B are B1 and B2.

Perimeter of A = 2(A1 + A2)
Perimeter of B = 2(B1 + B2)

Statement 1: A1 = 2*B1
As we don't know about the other sides the perimeter of A may or may not be greater than perimeter of B.

Not sufficient

Statement 2: (A1)*(A2) = 2*(B1)*(B2)
Consider A1 = A2 = 2, B1 = 2, B2 = 1 => (A1 + A2) > (B1 + B2)
Consider A1 = A2 = 2, B1 = 20, B2 = 0.1 => (A1 + A2) < (B1 + B2)

Not sufficient

1 & 2 Together: (A1)*(A2) = 2*(B1)*(B2)
Replacing A1 with 2*B1: 2*(B1)*(A2) = 2*(B1)*(B2) => A2 = B2
Therefore, Perimeter of A = 2(A1 + A2) = 2[2*(B1) + B2] = 4*(B1) + 2*(B2) = 2*(B1) + [2(B1 + B2)] > 2(B1 + B2) = Perimeter of B

Sufficient

The correct answer is C.

Hi,

Thanks for the above explanation.
I tried to solve the problem by taking different values of lengths,widths.
But I couldn't find a single triangle where the length of one triangle is twice the length of the other triangle & still the perimeter of former is lesser than the latter.
Can you plz give such example.
Thanks!

Here is one example : ( I guess you made a typo by mentioning "triangle" instead of "rectangle" )
I am only providing example for the two statements, not proving full solution as you have already got the solution (Instead if you need help to get the full solution, let me know ) :

Statement 1: The length of a side of rectangle A is twice the length of a side of rectangle B
If A1 = 10, A2 = 10, B1 = 5, B2 = 10 => Perimeter of rectangle A = 40 > Perimeter of rectangle B = 30
If A1 = 10, A2 = 5, B1=5, B2 = 20 => Perimeter of rectangle A = 30 < Perimeter of rectangle B = 50

INSUFFICIENT

Statement 2 : The area of rectangle A is twice the area of rectangle B
A1 = 10, A2 = 5, B1 = 5, B2 = 5 => Perimeter of rectangle A = 30 > Perimeter of rectangle B = 20
A1 = 10, A2 = 5, B1 = 25, B2 = 1 => Perimeter of rectangle A = 30 < Perimeter of rectangle B = 52

So, INSUFFICIENT

Hope that helps !




Statement 1 :