harsh.champ wrote:Is the length of a side of equilateral triangle E less than the length of a side of square F?

1. The perimeter of E and the perimeter of F are equal.
2. The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.

Be x the side of the triangle and y the side of the square.

(1) P_t = 3*x and P_s = 4*y. Given that 3x=4y => x>y. SUFF.

(2) We have the ratio between the height and the diagonal but we cannot say anythng about the length of the sides. INSUFF.

For me, the answer is A.

cunazza wrote:

harsh.champ wrote:Is the length of a side of equilateral triangle E less than the length of a side of square F?

1. The perimeter of E and the perimeter of F are equal.
2. The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.

Be x the side of the triangle and y the side of the square.

(1) P_t = 3*x and P_s = 4*y. Given that 3x=4y => x>y. SUFF.

(2) We have the ratio between the height and the diagonal but we cannot say anythng about the length of the sides. INSUFF.

For me, the answer is A.

St.1: If perimeter is same surely lengthofside of square will be less than triangle.... simply think of wire being molded in form of square and a triangle wire being of same lengh.
suff
St.2 height of T is known but we don't know abt sides. and many triangles could be formed with sameheight and perimeter
from diagnal of square we can calculate its side..so insuff due totriangle

Ans A[spoiler][/spoiler]

harsh.champ wrote:Is the length of a side of equilateral triangle E less than the length of a side of square F?

1. The perimeter of E and the perimeter of F are equal.
2. The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.

1 is enough and thats clear.

2. Height of an equilateral triangle = (sqrt(3) / 2 ) * T ( where T is one side of a triangle )
Length of diagonal of sq = sqrt(2) * S ( where S is the side of a square )


[ (sqrt(3) / 2 ) * T ] / [ sqrt(2) * S ] = 2√3 / 3√2

=> 3T = 4S ( Hence, Sufficient )


IMO : C ( BOTH)

Pls correct me if wrong

sumanr84 wrote:

harsh.champ wrote:Is the length of a side of equilateral triangle E less than the length of a side of square F?

1. The perimeter of E and the perimeter of F are equal.
2. The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.

1 is enough and thats clear.

2. Height of an equilateral triangle = (sqrt(3) / 2 ) * T ( where T is one side of a triangle )
Length of diagonal of sq = sqrt(2) * S ( where S is the side of a square )


[ (sqrt(3) / 2 ) * T ] / [ sqrt(2) * S ] = 2√3 / 3√2

=> 3T = 4S ( Hence, Sufficient )


IMO : C ( BOTH)

Pls correct me if wrong

yeah suman u r correct ..I just missed the equilateral triangle while solving the problems.. I just thought of many triangles but I missed that there can be only single equilateral triangle with that particular height...

surely for eq triangle if we know height we can easily calculate out the sides (which are all equal).
So correct ans would be C

Thanks shashank..

I really enjoy your solutions along with harsh.champ and ajith..you guys really rock the Quanty part..great

I missed 2 names, I like thephoneix and sanju09 solutions too.

Is the length of a side of equilateral triangle E less than the length of a side of square F?

1. The perimeter of E and the perimeter of F are equal.
2. The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.


1. If the perimeter of E and F are similar then definitely E has longer side. Infact the ratio of their sides are 4 : 3. Sufficient.

2. Let us suppose E and F have side = 2 units. The ratio of height : diagonal will be √3 :2 √2.
So the ratio of height : diagonal defines the length of the sides of E and F. Sufficient

IMO C.

P.S. I did try to spend time working out the respective lengths , only to realize its not necessary. Just the fact that the fact given in eitheer choice has a bearing on the length is sufficient.

kstv wrote:Is the length of a side of equilateral triangle E less than the length of a side of square F?

1. The perimeter of E and the perimeter of F are equal.
2. The ratio of the height of triangle E to the diagonal of square F is 2√3 : 3√2.


1. If the perimeter of E and F are similar then definitely E has longer side. Infact the ratio of their sides are 4 : 3. Sufficient.

2. Let us suppose E and F have side = 2 units. The ratio of height : diagonal will be √3 :2 √2.
So the ratio of height : diagonal defines the length of the sides of E and F. Sufficient

IMO C.

P.S. I did try to spend time working out the respective lengths , only to realize its not necessary. Just the fact that the fact given in eitheer choice has a bearing on the length is sufficient.

Hey kstv,
It is very important to realise that in Data Sufficiency,you don't actually solve the question.It is found that Data Sufficiency is the portion where test-takers can save time which can be invested in Problem-Solving.
It happens to many people that at the end of the time-limit,they couldn't attempt 4-5 questions.
One of the major reasons can be that they actually try to solve the question completely rather than only checking the sufficiency of the 2 statements.

Ofcourse,there are some trap questions in which you actually need to solve the question completely but they are very few hence for the rest of the question ,we can adopt the technique of just forming the equations,looking at what the question is asking.

Why is the answer not D ???????????????


Let e be the sides of equilateral triangle and s be the sides of square

statement 1: 3e=4s => e=(4/3)s ................sufficient

statement 2: h/d = 2√3 / 3√2

for equilateral triangle h=(√3/2)e
for square d=s√2

on solving we get e=(4/3)s ...............sufficient

So each statement alone is sufficient, answer D

Mom4MBA wrote:Why is the answer not D ???????????????


Let e be the sides of equilateral triangle and s be the sides of square

statement 1: 3e=4s => e=(4/3)s ................sufficient

statement 2: h/d = 2√3 / 3√2

for equilateral triangle h=(√3/2)e
for square d=s√2

on solving we get e=(4/3)s ...............sufficient

So each statement alone is sufficient, answer D

OOps I did a mistake again in haste...though I corrected my sol. I missed out correcting the option..yeah the ans should be D..Thanks Mom4MBA