Que 1: Square S is inscribed in circle T. If the perimeter of S is 24, what is the circumference of T?

A. 6π

B. 12π

C. 3√2 π

D. 6√2 π

E. 12√2 π

My strategy to solve this ques is :

We need to find out circumference,which is C=2pi r.so,I need radius of circle.Perimeter is known P=24.so square one side is 4a=24,then a =6.

therefore,radius is r= 3 root of 2

now,C=2pi r

so C= 6root of 2 pi

my answer is D.

but in question paper Answer is "C". Can some one help me where I'm going wrong?

Ques 2:The operation ⊗ is defined for all nonzero numbers a and b by a ⊗ b = a/b – b/a. If x and y are nonzero numbers, which of the following statements must be true?

I. x ⊗ xy = x(1 ⊗ y)

II. x ⊗ y = -(y ⊗ x)

III. 1/x ⊗ 1/y = y ⊗ x

A. I only

B. II only

C. III only

D. I and II

E. II and III

My answer is E.

please explain me how answer can be only "C".

Ques 3: What was the price at which a merchant sold a certain appliance?

(1) The merchant’s gross profit on the appliance was 20 percent of the price at which the merchant sold the appliance.

(2) The price at which the merchant sold the appliance was $50 more than the merchant’s cost of the appliance.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

below is my solution:

taken 1: profit (P)=120/100 SP let say selling price is SP. not sufficient because don't know the value of SP. so A option is gone.

taken 2: SP=50+CP(cost price) ,not sufficient coz CP is unknown.so option B is also gone.

Taken 1 & 2 together

P=SP-CP,which is 50

put this value in equation 1 I'm able to find out SP. so,I opt option is "C".

why answer is "E"?

Please tell me where I'm going wrong?

Thank you very much in Advance!!!!

Sonia saini